Algebra 2 Flashcards, test questions and answers
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We've found 24 Algebra 2 tests
Algebra 1
Algebra 2
Annual Interest Rate
Five Years Ago
Growth
The New York Times
Years
Writing Exponential Functions Given Initial Amount and Percent of Change – Flashcards 12 terms

Kolby Cobb
12 terms
Preview
Writing Exponential Functions Given Initial Amount and Percent of Change – Flashcards
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Write an exponential function for Initial amount: 62 19% increase
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Write an exponential function for Initial amount: 75 25% decrease
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Write an exponential function for Initial amount: 90 3.2% increase
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Write an exponential function for Initial amount: 16 2.5% decrease
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Write an exponential function for Initial amount: 25 30% decrease
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Write an exponential function for Initial amount: 51 150% increase
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Write an exponential function for Initial amount: 32 10% decrease
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Write an exponential function for Initial amount: 45 0.5% increase
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Write an exponential function for Initial amount: 6500 20% increase
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Write an exponential function for Initial amount: 30 15% decrease
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Write an exponential function for Initial amount: 15 3% decrease
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Write an exponential function for Initial amount: 450 2% increase
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Algebra
Algebra 1
Algebra 2
Algebra 8 Chapter 10 Vocabulary – Flashcards 35 terms

Tara Rose
35 terms
Preview
Algebra 8 Chapter 10 Vocabulary – Flashcards
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An expression which is the sum of terms of the form ax^k, where k is a nonnegative integer
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polynomial
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The form of a polynomial ax^n + bx^(n-1) + ... + qx + r
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standard form
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The name for the exponent of the variable in a term of a polynomial
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degree
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The largest degree of any of the terms of a polynomial.
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degree of a polynomial
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When a polynomial is written in standard form, the coefficient of the first term is the ____.
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leading coefficient
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A polynomial with only one term is called a ____.
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monomial
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A polynomial with two terms is called a ____.
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binomial
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A polynomial with three terms is called a ____.
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trinomial
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The growth of a polynomial is ____ in a monomial of degree zero.
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constant
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The growth of a polynomial is ____ in a monomial of degree one.
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linear
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The growth of a polynomial is ____ in a polynomial of degree two.
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quadratic
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The growth of a polynomial is ____ in a polynomial of degree three.
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cubic
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The growth of a polynomial is ____ in a polynomial of degree four.
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quartic
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Which is the constant term in 2x^3 + 5x^2 - 4^x + 7 ???
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7
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Which is the leading coefficient in 2x^3 + 5x^2 - 4^x + 7 ???
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2
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What is the degree of the polynomial in 2x^3 + 5x^2 - 4^x + 7 ???
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3
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What is the degree of the 2nd monomial in 2x^3 + 5x^2 - 4^x + 7 ???
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2
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What is the degree of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???
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1
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What is the coefficient of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???
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4
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What is the coefficient of the fourth monomial in 2x^3 + 5x^2 - 4^x + 7 ???
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7
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What does FOIL stand for?
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First Outer Inner Last
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What is the sum and difference pattern?
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(a+b)(a-b) = a^2 - b^2
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What pattern? (a+b)(a-b) = a^2 - b^2
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sum and difference
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What pattern? (a+b)^2 = a^2 + 2ab + b^2
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square of a binomial
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What pattern? (a-b)^2 = a^2 - 2ab + b^2
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square of a binomial
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A polynomial is in ____ if it is written as the product of two or more linear factors.
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factored form
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Zero Product Property: Let 'a' and 'b' be real numbers. If ____, then 'a' = 0 or 'b' = 0
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ab=0
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What property? LPr
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zero property
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What pattern? a^2 - b^2 = (a+b)(a-b)
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difference of two squares
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What is the difference of two squares pattern?
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a^2 - b^2 = (a+b)(a-b)
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What pattern? a^2 + 2ab + b^2 = (a+b)^2
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perfect square trinomial
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What pattern? a^2 - 2ab + b^2 = (a-b)^2
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perfect square trinomial
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A polynomial is ___ if it is not the product of polynomials having integer coefficients
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prime
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To factor a monomial completely, write it as the product of 1.) ____ and 2.) prime factors with at least two terms
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monomial factors
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To factor a monomial completely, write it as the product of 1.) monomial factors and 2.) ____
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prime factors with at least two terms
Algebra 1
Algebra 2
Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards 12 terms

Maddison Bailey
12 terms
Preview
Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards
question
Suppose that w and t vary inversely and that t=1/5 when w=4. Write a function that models the inverse variation, and find t when w=9.
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t=4/5w; 4/45
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Suppose that y varies directly with x and inversely with z, and y=18 when x=15 and z=5. Write the equation that models the relationship. Then find y when x=21 and z=7.
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y=6x/z; 18
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Graph the function y=13/6x
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Graph C
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Sketch the asymptotes, and graph the function y= 5/(x-2) +3
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Graph C
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This graph of a function is translation of y=4/x. what is an equation for the function?
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4/x+6 +2
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Find any points of discontinuity for the rational function y=(x+6)(x+2)(x+8)/(x+9)(x+7)
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x=-9, x=-7
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Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1)
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asymptote: x=-1 and hole: x=-4
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Find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10
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There is no horizontal asymptote
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What is the graph of the rational function? y=-3x+5/-5x+2
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Graph A
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The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. How many barrels of oil are used when the ship travels 26 miles at 54 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.
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15.2 barrels.
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The yearbook committee is distributing yearbooks to students by class. Each class has approximately the same number of students. The table shows the number of volunteers who helped to distribute the yearbooks to each of the four classes and the time needed to distribute the yearbooks. What function models the data?
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nt=440
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You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y=100(0.05)+x(0.2)/100+x gives the concentration y of the blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated?
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87.5 mL
Algebra 1
Algebra 2
Algebra I: Write Linear Equations – Flashcards 25 terms

Noah Thomson
25 terms
Preview
Algebra I: Write Linear Equations – Flashcards
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slope intercept form
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where m is the slope and (x1, y1) is a point on the line This is another format for straight line equations. Use when you know a point and the slope; it helps find the y-intercept
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point slope form
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the y-coordinate of the point where the line crosses the y-axis
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y - intercept
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1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17) 2 - Calculate the slope using the formula 3 - The y-intercept is 5 because the line crosses at (0,5) Write in slope intercept form: y = mx + b
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How to Write a Linear Function Ex: Write an equation for the linear function ƒ with the values ƒ(0) = 5 and ƒ(4) = 17.
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1 - Identify the slope m. You can use the slope formula if you know two points on the line. 2 - Find the y-intercept. You can substitute the slope and the coordinates (x, y) of a point on the line in y = mx + b. Then solve for b. 3 - Write an equation using y = mx + b
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How to Write an Equation of a Line in Slope-Intercept Form
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can be used to find the x- and y-intercepts. Ax + By = C A, B, C are integers (no fractions or decimals) A should be positive
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Standard Form
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Slope Formula
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the slope and the y-intercept
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What do you need to graph a line?
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plug the slope and a point into y = mx + b solve for b Write the equation
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Write the equation of a line that passes through the point with the given slope
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use the formula to find the slope plug the slope and a point into y = mx + b solve for b Write the equation
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Write the equation of a line in slope intercept form that passes through two points
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the statement formed by exchanging the hypothesis and conclusion of a conditional statement (the opposite)
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converse
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If two nonvertical lines in the same plane have the same slope, then they are parallel. If two nonvertical lines in the same plane are parallel, then they have the same slope.
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Parallel Lines
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1 - Identify the slope (in this case = 3) 2 - Use the slope and the point to solve for b in y = mx + b 3 - Write the equation using y = mx + b
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To Write an Equation of a Parallel Line: Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1
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If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.
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Perpendicular Lines
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write all equations in slope-intercept form ( y = mx + b) compare their m value: if the same, then parallel; if negative reciprocals, then perpendicular
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To determine whether lines are parallel or perpendicular
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is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.
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Scatter Plot
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y tends to increase, as x increases
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Positive Correlation
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y tends to decrease, as x increases
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Negative Correlation
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x and y have no apparent relationship
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Relatively No Correlation
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The line that most closely follows a trend in data is called the best-fitting line.
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Line of Best Fit
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the process of finding the best-fitting line to model a set of data; you can use technology to do this
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Linear Regression
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using a line or its equation to approximate a value between two known values
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Linear Interpolation
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1 - Make a scatter plot of the data 2 - Graph the best fitting line
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Interpolate Using an Equation
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using a line or its equation to approximate a value outside the range of known values
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Linear Extrapolation
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for the function ƒ, any number x such that ƒ(x) = 0
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Zeros of a Function
Algebra 2
Measure Of Central Tendency
AQR Unit 4 – Flashcards 70 terms

Ewan Tanner
70 terms
Preview
AQR Unit 4 – Flashcards
question
1. A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?
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72
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2. In how many different orders can you line up 8 cards on a table?
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40,320
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3. There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?
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90 ways
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4. Evaluate 60C3/15C3
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6,844/91
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5. There are 6 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0, 1, 2, 3, or 4 judges. In how many different ways can a person vote?
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57
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1. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P (red or blue).
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5/8
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2. A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day. Carry out a simulation of 20 trials using the random number table below to find the probability that the osprey will actually catch a fish on all of the next three days. Explain your method. 945 025 354 793 236 106 746 981 105 012 832 180 250 871 835 793 726 864 496 947
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Using the digits 0-6 to represent a caught fish, the probability of catching a fish on each of the next three days is 35%.
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3. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3 and 4?
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3/8
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4. What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52- card deck?
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94/54145
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5. If a dart hits the target at random, what is the probability that it will land in the shaded region?
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1/16
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1. Which are dependent events?
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Taking two marbles from a box without replacing the first marble
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2. Suppose Q and R are independent events. Find P(Q and R). P(Q) = 0.41, P(R) = 0.44
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0.1804
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3. You roll a six-sided number cube. Which events are mutually exclusive?
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Rolling an even number and an odd number
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4. Suppose S and T are mutually exclusive events. Find P(S or T). P(S) = 20%, P(T) = 22%
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42%
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5. A jar contains 7 blue cubes, 4 blue spheres, 5 green cubes, and 6 green spheres. If you select an object at random, what is the probability that the object is green or a cube?
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9/11
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1. Suppose Ruth Ann has 3 routes she can travel between the school to the library, and 5 routes from the library to her home. How many routes are there from Ruth Ann's school to her home with a stop at the library?
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15
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2. Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny?
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696
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3. Evaluate 7C6
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7
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4. In how many ways can 3 singers be selected from 5 who came to an audition?
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10
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6. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single spin?
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2/5
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7. On the following dartboard, the radius of the bullseye (area A) is 4 inches. The radius of each concentric circle is 4 inches more than the circle inside it. If a person throws randomly onto the dartboard, what is the probability that the dart will hit in area B?
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3/16
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8. Two urns contain white balls and yellow balls. The first urn contains 9 white balls and 9 yellow balls and the second urn contains 8 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
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4/11
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9. If all possible results are equally likely, what is the probability that a spin of the spinner will land on an upper case letter or a consonant?
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0.9
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10. Joey's sock drawer is unorganized and contains 3 black dress socks, 5 black ankle socks, 7 brown dress socks, and 6 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out a sock that is brown or a dress sock?
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16/21
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11. The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night?
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0.565
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12. The probability that a city bus is ready for service when needed is 84%. The probability that a city bus is ready for service and has a working radio is 67%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.
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79.8%
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13. A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.
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0.241
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1. Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13
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Mean = 9.3 Median = 10 Mode = 13
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2. Find the outlier in the set of data. 17, 13, 16, 18, 38, 14, 21, 24
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38
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3. Over the first five years of owning a car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year. a. Find the mean, median, and mode of this data. b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year.
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Mean = 13,156 Median = 12,700 No mode The median is the best choice because it is not skewed by the high outlier
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4. Make a box-and-whisker plot of the data. 24, 18, 29, 21, 16, 23, 13, 11
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A
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5. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20
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30th percentile = 7 90th percentile = 19
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1. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 92, 97, 53, 90, 95, 98
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Mean = 87.5 Variance = 245.6 Standard deviation = 15.7
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2. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth.
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Mean = 47.6 Variance = 31 Standard deviation = 5.6
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3. Susan keeps track of the number of tickets sold for each play presented at the community theater. Within how many standard deviations of the mean do all the values fall? 135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85
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2
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4. The graph below displays how many pieces of candy Timmy and his five friends each received last Halloween. Within how many standard deviations of the mean do the values fall?
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2
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1. A citizens' group wants to determine peoples' opinions about a new road. The members of the group conduct a survey at the largest mall in the city. Which best describes the sampling method used by the citizens' group?
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Convenience sample
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2. The town council must decide how to allocate next year's budget. They survey a sample of the town population to determine residents' preferences. Which survey question shows the least bias?
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Do you think we should plant gardens in the park or buy new park benches?
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3. You want to determine what percentage of working adults in your neighborhood regularly ride the bus to work. Which sampling method and survey question are best?
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Go to every fifth house and ask the working adults, "How many times per week do you ride the bus to work?"
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4. A researcher tags 20 squirrels in a wood. The next month, she returns to the wood and observes a sample of 12 squirrels, 5 of which are tagged, and a sample of 25 squirrels, 9 of which are tagged. If the two samples are representative of the squirrel population, which is the best estimate of the number of squirrels in the wood?
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50
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1. A survey of high school juniors found that 82% of students plan on attending college. If you pick three students at random, what is the probability that at least two plan on attending college? Round to the nearest percent.
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91%
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2. A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?
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5.1%
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3. Use the Binomial Theorem to find the binomial expansion of the expression. (s - 5v)^5
answer
C
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4. A recent poll found that 45% of eligible voters are planning to vote in favor of a new by-law. Suppose you randomly survey six voters. What is the probability that at least three of the voters plan to vote in favor of the new by-law?
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55.8%
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1. Find the mean, median, and mode of the data set. Round to the nearest tenth. Test scores on a math exam: 88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82, 66, 88, 79, 60, 86, 63, 93, 99, 60, 85
answer
Mean = 75.8 Median = 76.5 Mode = 63
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2. Make a boxandwhisker plot of the data. Average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63
answer
A
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3. Find the values of the 30th and 90th percentiles of the data. 129, 113, 200, 100, 105, 132, 100, 176, 146, 152
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30th percentile = 105 90th percentile = 176
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4. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 11, 11, 3, 1, 11, 11
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Mean = 8 Variance = 18.3 Standard deviation = 4.3
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5. Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone received an A. Within how many standard deviations of the mean do all the quiz grades fall? 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
answer
2
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6. According to one study, 61% of the population swallow at least one spider per year in their sleep. Based on this study, what is the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year.
answer
22%
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7. Use the Binomial Theorem to find the binomial expansion of the expression. (d-5)^6
answer
D
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8. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay from $600 to $749 per month.
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93%
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9. The scores on an exam are normally distributed with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87?
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16%
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10. A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a crop of onions with diameters that are normally distributed with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?
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84%
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1. In how many ways can 12 basketball players be listed in a program?
answer
479,001,600
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2. Evaluate 9P4
answer
3,024
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3. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many possible meal combinations are there?
answer
30
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4. Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn's results?
answer
11/20
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5. Teesha is in the French club. There are 29 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?
answer
27/29
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6. A game uses 26 tiles, lettered from A to Z. To start, you randomly choose a set of 5 tiles. What is the theoretical probability of drawing exactly 2 vowels (A, E, I, O, or U) in your set of 5? Round to the nearest percent.
answer
20%
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7. A dartboard consists of two concentric circles. The probability of hitting the inner circle is 16%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?
answer
4 inches
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8. Eli has 7 black pens and 5 blue pens in his desk drawer. He also has 3 yellow highlighters, 2 green highlighters, and 5 pink highlighters in his pencil case. If he chooses one pen and one highlighter without looking, what is the probability that he will get a black pen and he will not get a green highlighter?
answer
46.7%
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9. Using a sixteen-sided number cube, what is the probability that you will roll an even number or an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
answer
0.813
question
10. Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth.
answer
0.464
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11. The probability that a dessert sold at a certain cafe contains chocolate is 73%. The probability that a dessert containing chocolate also contains nuts is 25%. Find the probability that a dessert chosen at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.
answer
34.2%
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12. An airline has 81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule.
answer
0.85
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13. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20
answer
30th percentile = 7 90th percentile = 19
question
14. Use the Binomial Theorem to find the binomial expansion of the expression. (d + 3)7
answer
A
question
15. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay less than $650 per month.
answer
30%
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16. Betty's Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 4 bags contain fewer than 47 candies. How many bags were probably taken as samples?
answer
25 bags
Algebra 1
Algebra 2
Completing The Square
Greater Than Zero
Algebra 2: Midterm Exam (study guide) – Flashcards 50 terms

Roman Peck
50 terms
Preview
Algebra 2: Midterm Exam (study guide) – Flashcards
question
What is the number of real solutions? - x² + 9x + 7 = 0
answer
use b^2-4ac
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What is the number of real solutions? 8x² - 11x = -3
answer
use b^2-4ac
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What is the number of real solutions? x² = -7x + 7
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use b^2-4ac
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What is the number of real solutions? - 4x² - 4 = 8x
answer
use b^2-4ac
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What is the expression in factored form? 2x² + 16x + 30
answer
2(x+3)(x+5)
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What is the expression in factored form? - 4x² + 8x + 32
answer
__________________
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What is the expression in factored form? 3x² + 26x + 35
answer
__________________
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What is the expression in factored form? 9x² - 18x + 9
answer
__________________
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What is the expression in factored form? x² - 64
answer
__________________
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What are the solutions of the quadratic equation? x² - 9x + 18 = 0
answer
__________________
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What are the solutions of the quadratic equation? 3x² + 25X + 42 = 0
answer
__________________
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What are the solutions of the quadratic equation? 4x² - 18x + 20 = 0
answer
__________________
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Solve by using tables. Give each answer to a most two decimal places. 2x² + 5x - 3 = 0
answer
__________________
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Solve by using tables. Give each answer to a most two decimal places. - 7x² - 2 = -10x
answer
__________________
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What is the solution of each equation? 3x² = 21
answer
__________________
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What is the solution of each equation? 108x² =147
answer
__________________
question
Solve the equation. x² + 18x + 81 = 25
answer
__________________
question
Solve the equation. x² - 8x + 16 = 16
answer
__________________
question
Solve the equation. 0.125r - 0.0625 + 0.25r = 0.25 + r
answer
__________________
question
Solve the equation. - 5y - 9 = - ( y - 1 )
answer
__________________
question
Solve the quadratic equation by completing the square. x² + 10x + 14 = 0
answer
__________________
question
Solve the quadratic equation by completing the square. - 3x² + 7x = - 5
answer
__________________
question
Rewrite the equation in vertex form. Name the vertex and y- intercept. y = 3/5x² + 30x + 382
answer
__________________
question
Use the quadratic formula to solve the equation. - 2x² - 5x + 5 = 0
answer
__________________
question
Use the quadratic formula to solve the equation. 2x² + x - 4 = 0
answer
__________________
question
Use the quadratic formula to solve the equation. - 4 x² + x = - 4
answer
__________________
question
Simplify the number using the imaginary unit i. √(-144)
answer
__________________
question
Simplify the number using the imaginary unit i. √(-360)
answer
__________________
question
Simplify the expression. (-1 + 6i) + ( -4 + 2i)
answer
__________________
question
Simplify the expression. (1 + 2i) - (5 + 3i)
answer
__________________
question
Simplify the expression. (-5i) (6i)
answer
__________________
question
Simplify the expression. (6 - 4i) (-1 + 6i)
answer
__________________
question
Simplify the expression. -1+3i ------------ 4 - i
answer
__________________
question
Simplify the expression. -5 +4i ----------- -6i
answer
__________________
question
What are the solutions? 9x² + 16 = 0
answer
__________________
question
What are the solutions? ½ x² - x + 5 = 0
answer
__________________
question
Which algebraic expression models the given word phrase? 40 fewer than a number t
answer
__________________
question
Which algebraic expression models the given word phrase? You start with $15.00 and save $8.00 each week. What algebraic expression models the total amount you save?
answer
__________________
question
Write an algebraic model for the situation and evaluate it for the given information? You are going shopping for some new sweaters, t-shirts, and pants. Sweater (s) cost $30, t-shirts (t) cost $19, and pants (p) cost $18. What algebraic expression models the total cost of the clothes that you buy? Suppose you bought 26 sweaters, 9 t-shirts, and 23 pairs of pants. How much did you spend?
answer
__________________
question
Is the relation a function? {(15, 11), (5, 1), (4,11) ,(9,9),(5,5)}
answer
__________________
question
What is the slope of the line that passes through the given points? (-12,12) and (2,4)
answer
__________________
question
What is the slope of the line that passes through the given points? (7,-9) and (7,-1)
answer
__________________
question
What is an equation of the line in slope intercept form? m = ½ and the y-intercept is (0,-2)
answer
__________________
question
see graph
answer
__________________
question
Write the equation in slope intercept form. What are the slope and y-intercept? -8x +3x = -10
answer
__________________
question
Write the equation in slope intercept form. What are the slope and y-intercept? ¾x + 4/5y = 4
answer
__________________
question
What is the graph of the equation? 3x - y = 3
answer
__________________
question
What is the graph of the equation? -5x + 5y =4
answer
__________________
question
Write an equation of the line, in point-slope form, that passes through the 2 given points. points: (-9,4) , (13, -7)
answer
__________________
question
What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? point: (9,6) ; slope: 1/3
answer
__________________
Algebra
Algebra 1
Algebra 2
Equations
Algebra 2/Trigonometry Regents Review – Flashcards 56 terms

Alexandra Robertson
56 terms
Preview
Algebra 2/Trigonometry Regents Review – Flashcards
question
When raising a negative number to a power always put the negative number in a parenthesis.
answer
Raising a negative number to a power
question
answer
Factoring ax²+bx+c
question
answer
Factoring by grouping
question
If both terms are opposite signs they can be crossed out and replaced by a negative 1.
answer
Canceling out opposites
question
To factor out a -1, remove the negative and change the signs of the terms
answer
Factoring out a -1
question
answer
Operations with fractions
question
answer
Complex fractions
question
To solve equations with fraction, find a common denominator. Drop the denominators Solve the resulting equation. Check the answer(s) in the denominators for extraneous roots.
answer
Equations with fractions
question
the quadratic formula is x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a.
answer
Quadratic formula (Find the Roots)
question
answer
Completing the square
question
if the discriminant is 0, the roots are real, rational and equal. if the discriminant is negative, the roots are complex or imaginary. if the discriminant is a perfect square, the roots are real, rational, and unequal. if the discriminant is not a perfect square, the roots are real, irrational, and unequal
answer
Discriminant (describe the roots)
question
The sum of the roots is negative b divided by a. The product of the roots is c divided by a. The equation for sum and product of the roots is x squared minus the sum times x plus the product equals 0.
answer
Sum and product of roots
question
To solve absolute value inequalities Isolate the absolute value on one side of the equation. Change the inequality sign and the sign(s) of the terms on the right to the opposite signs. If the original inequality has a greater than or greater than or equal to (≥ or >) sign use or between your solutions. Solution is (≥) solution. If the original inequality has a less than or less than or equal to (≤ or <) write as an interval. Solution <(≤) x <(≤) solution. You have to divide by a negative, do not forget to flip the inequality sign.
answer
Absolute value inequalities
question
To solve an absolute value equation Isolate the absolute value on one side of the equation. Change the sign(s) of the terms on the right to the opposite sign(s). check your answer(s) for extraneous roots.
answer
Absolute value equations
question
The inverse variation formula is x one times x two equals y one times y two. Inverse variation creates a corner hyperbola.
answer
Inverse variation
question
To find the conjugate The first term stays the same. Change the sign of the second term.
answer
Conjugate
question
The domain is the x coordinates. The range is the y coordinates. To find the inverse switch the x and y coordinates.
answer
Domain, range, inverse
question
To be a function It must pass the vertical line test. No x coordinate can repeat. An equation must have a y, but the y cannot be squared.
answer
Function
question
A one to one function must pass the vertical and horizontal line test. No x or y coordinate can repeat.
answer
One to one function
question
answer
Logarithms
question
To convert from degrees to radians multiply the degrees by pi and divide by 180.
answer
Convert degrees to radians
question
To convert from radians to degrees, multiply the radians by 180 and divide by pi.
answer
Convert radians to degrees
question
Once around a circle is 2 pi radians or 360 degrees. ½ of the way around a circle is pi radians or 180 degrees. ¼ of the way around a circle is pi divided by 2 or 90 degrees.
answer
Degrees and radians
question
In a circle the central angle in radians equals the arc length divided by radius.
answer
Arc length - radius formula
question
The circle formula is x minus h squared plus y minus k squared equals the radius squared.
answer
Circle formula
question
Secant equals 1 divided by cosine.
answer
Secant
question
Cosecant equals 1 divided by sine.
answer
Cosecant
question
cotangent equals 1 divided by tangent or cosine divided by sine.
answer
Cotangent
question
Tangent equals sine divided by cosine.
answer
Tangent
question
Cosine squared plus sine squared equals 1.
answer
Trigonometric identity
question
answer
Exact values of trigonometric functions
question
An arithmetic sequence is created by adding or subtracting a common difference.
answer
Arithmetic sequence
question
A geometric sequence is created by multiplying or dividing a common ratio. If the terms alternate between positive and negative, the common ratio is negative.
answer
Geometric sequence
question
a to the n minus 1 - look to the term behind. a to the n plus 1 - loot to the term in front.
answer
Recursive sequences
question
To rationalize a denominator multiply the numerator (top) and denominator (bottom) by the conjugate of the denominator (bottom).
answer
Rationalizing the denominator
question
Survey - ask Observation study - watch Experiment - change
answer
Survey, observational study, experiment
question
All students take classes. Sine and cosecant are positive in quadrants 1 and 2. Cosine and secant are positive in quadrants 1 and 4. Tangent and cotangent are positive in quadrants 1 and 3.
answer
Quadrants
question
answer
Sine, Cosine, Tangent on the unit circle
question
Multiply by 180 and then divide by pi. The part before the decimal is the degrees. Multiply the decimal by 60 to find the minutes.
answer
Converting radians to degrees and minutes
question
Coterminal angles are just different ways of naming the same angle.
answer
Conterminal Angles
question
answer
Arc functions
question
Need side angle side (S.A.S) to find area. The area of a triangle equals ½ times a times b times sine of C.
answer
Area of a triangle (need S.A.S.)
question
A parallelogram is made up of 2 congruent triangles.
answer
Area of a parallelogram
question
The law of sines is a divided by sine of A equals b divided by sine of B equals c divided by sine of C.
answer
Law of Sines
question
The law of cosines is b squared plus c squared minus 2 times b times c times the cosine of A. Take the square root of the answer to find the missing side.
answer
Law of cosines given (S.A.S.)
question
The law of cosines a squared(the side across from the angle) equals b squared plus c squared minus 2 times b times c times the cosine of x (A). Use numerical solve to find the measure of angle A.
answer
Law of cosines given (S.S.S.)
question
To solve vector problems remember that The opposite sides in a parallelogram are congruent. The consecutive angles in a parallelogram are supplemental (add up to 180 degrees). Use law of Cosines to find the resultant and the angle between the 2 forces. Use law of Sines to find the angle between a force and the resultant.
answer
Vector problems
question
answer
Ambiguous Case (0,1,2 triangles?
question
answer
Permutations with repetition
question
answer
Binomial Expansion
question
answer
∑ (Sigma)
question
To solve square root equations Isolate the square root on one side of the equation. Square both sides of the equation Check the answer(s) in the original equation for extraneous roots.
answer
Square root equations
question
To convert from logarithmic form to exponent form the base remains the base and the rest of the stuff crosses. the b and the n can never be negative.
answer
Converting between logarithm and exponent form
question
answer
Common Logarithms
question
answer
Natural Logarithms
question
...
answer
Inverses of exponential and logarithmic equations
Algebra 1
Algebra 2
Algebra II Final – Flashcards 281 terms

Ray Collins
281 terms
Preview
Algebra II Final – Flashcards
question
Hans pays $205 in advance on his account at the athletic club. Each time he uses the club, $10 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 11 visits.
answer
V = 205 - 10x; $95
question
Solve the proportion (x−8)/8 = 4/5
answer
x=14 or 72/5
question
Solve for x. x-7=1
answer
x=8
question
Solve the equation or formula for the variable specified. B = 7a²b, for b.
answer
b = B/(7a²)
question
Which equation best describes the graph below? (Evernote)
answer
y = -2x + 5
question
solve for x. 3x - 3 = x - 9
answer
x = -3
question
Which inequality has the solution shown in the graph? (Evernote)
answer
m + 7 ≥ 9
question
What inequality describes the graph? (Evernote)
answer
x ≤ -5
question
For the data given, find the equation of the line of best fit. (Evernote)
answer
Incorrect: None of the listed answers are correct Correct: y = 0.63x + 1.90
question
Write a proportion that models the statement 10 is to 5 as 16 is to 8.
answer
10/5 = 16/8
question
Write an equation in slope-intercept form for a line that passes through the given pair of points. (4,-7), (-2,-10)
answer
y = 1/2x - 9 Solution Slope Formula: slope(m) = (y2 - y1) / (x2 - x1) Substitute and Solve m = (-10 +7) / (-2 - 4) m = (-3) / (-6) m = 1/2 or 0.5 Slope intercept form: y = mx + b Pick one of the two points (4,-7) or (-2,-10), substitute and solve -7 = 1/2(4) + b -7 = 2 + b -7 - 2 = b -9 = b Final Answer y = 1/2x - 9
question
Write an equation in slope-intercept form for a line that passes through the given pair of points. (-6,5), (-9,0)
answer
y = 5x/3 + 15
question
Write an equation in slope-intercept form of the line that passes through (- 5, 4) and is parallel to the graph of y = -4x + 1.
answer
y = -4x -16
question
When Spheres-R-Us ships bags of golf balls, each bag must be within 5 balls of 370. Identify the inequality which results in an acceptable number of golf balls in each bag.
answer
365 ≥ 375
question
Abbiville is a small town that has been steadily growing since 1960. Use the table below to create a linear equation that estimates Abbiville's population over time. What will the population be in 2014 if the growth remains constant? (Evernote)
answer
364 people
question
Which is the equation of the line with slope -4 and y-intercept 5?
answer
4x + y -5 = 0 y = -4x + 5
question
A server at a restaurant kept track of the number of requests for the daily special, and the time of day the request was made. The data is displayed below. (Evernote)
answer
Incorrect: It is a linear model with a positive correlation.
question
Write the equation of the line, in slope-intercept form, that contains the point (-1, - 5) and is perpendicular to the line -8x - 4y = 3.
answer
y = -2x -7
question
Write the slope-intercept form of an equation of the line that passes through the point (3, - 6) and has the slope m = -4.
answer
y = -4x + 6
question
If x = 78 when y = 130 and x varies directly as y, then find x when y = 190.
answer
x = 114 when y = 190 Formula: y = ky(solving for y) or x = ky(solving for x) Substitute 78 = k(130) Divide by 130 on both sides k = 0.6 x = 0.6(190) x = 114
question
Describe how the graph of the function y = f(x-3) can be obtained from the graph of y = f(x).
answer
move it 3 to the right
question
Evaluate the expression. (2/5)⁵
answer
32/3125
question
Which of the following is an example of the Commutative Property of Addition?
answer
5 + 2 = 2 + 5
question
Evaluate the expression. 64 × 4² - 2 × 2²
answer
1016
question
Ivan Bogdanovich plans to decorate stuffed animals to sell at a crafts fair. The decorations cost $44.00 and the stuffed animals cost $5.25 each. a. Write a function expressing the cost, C(x), of the project in terms of the number of stuffed animals decorated, x. b. Determine the cost of decorating 25 stuffed animals. c. How many stuffed animals can be decorated with a budget of $227.75?
answer
a. C(x) = 5.25x + 44.00 b. $175.25 c. 35
question
For the pair of functions, f and g, find (g o f)(x) and (f o g)(x). f(x) = 6 - x, g(x) = x² - 2
answer
(g o f)(x) = x² - 12x + 34 Solution (6-x)² - 2 36 - 6x - 6x + x² - 2 x² - 6x - 6x + 36 - 2 x² - 12x + 34 (f o g)(x) = -x² + 8 Solution -x(x² - 2) + 6 -(x² - 2) + 6 -x² + 2 + 6 -x² + 8
question
Evaluate the expression. (3/8)⁻²
answer
64/9
question
Describe how the graph of the function y = 15(x + 2) + 4 can be obtained from the graph of y = 3(x + 2).
answer
shift up 4 units, and vertically stretch by a factor of 5
question
Simplify the expression. ((-u)³(-u⁹)⁸)/(u⁵)³
answer
-u⁶⁰ Solution (-u³ × u⁷²)/u¹⁵ -u⁷⁵/u¹⁵ = -u⁶⁰
question
Evaluate the expression. (-3/8)²
answer
9/64
question
The graph of f(x) = x² is stretched vertically by a factor of 3, translated 4 units to the right, and translated 8 units downward. Determine the equation of the transformed function, g(x).
answer
g(x) = 3(x - 4)² - 8
question
A T-shirt company estimates that the average cost per shirt can be approximated by the function A(x) = (3.75x + 200)/x, where x is the number of T-shirts made. Find the average cost per T-shirt when the company makes 10 shirts.
answer
$23.75
question
Find the inverse of the function and determine whether the inverse is a function. y = 7x²
answer
y = ±√(x/7), y is not a function.
question
Find the inverse of the function and determine whether the inverse is a function. f(x) = 19x²
answer
f⁻¹(x) = ±√(x/19), f⁻¹(x) is not a function.
question
Since 1993, Daphne Hamilton has owned a franchise of take-out restaurants called The Burger Barn. The number of customers, C, in thousands, that The Burger Barn has served each year can be modeled by the function C(t) = t² + 38t + 600, where t is the number of years from 1993. Using this model, estimate the number of customers served in 1999.
answer
864,000
question
If f(x) = 9 - x² and g(x) = 3 - x, which is the rule of function (f × g)(x)?
answer
x³ - 3x² - 9x + 27
question
Evaluate the expression. 3 - 14 × 6 ÷ 7 + 3
answer
-6
question
If f(x) = 3x + 4 and g(x) = 2 + x, which is the rule of function 3g(x) - 3f(x)?
answer
-6x - 6
question
Which property is shown by the following statement? (13 + 3)+ 8 = 13 + (3 + 8)
answer
The Associative Property of Addition
question
Given the graph of y = 3(x + 1), what function would be obtained by moving the graph up 4 and moving it 6 to the right?
answer
f(x) = 3(x - 5) + 4
question
Use elimination to solve the system of equations. {7x - 3y = -43 {5x + 6y = -47
answer
(-7, -2)
question
Write the pair of parametric equations as a single equation in x and y. {x = 8t - 4 {y = 6t² - 2
answer
y = 6((x+4)/8)² - 2 Solution x = 8t - 4 Add 4 to both sides x + 4 = 8t Divide by 8 on both sides t = (x + 4)/8 Substitute y = 6((x+4)/8)² - 2
question
Mr. Reaich, the ticket agent for a small commuter airline, has developed a model to forecast the total monthly revenue from the airline's passenger service. Under this model, the total revenue, R, is equal to $368 times the number of first-class, F, plus $324 times the number of coach passengers, C. Their flight schedule and overall aircraft capacity limit the total number of passengers carried during a single month to a maximum of 30,775. The number of coach class passengers is at least seven times the number of first-class passengers, and logically, the number of airline passengers in either class cannot be negative. Express the model in mathematical form.
answer
$368F + $324C = R F + C ≤ 30,775 C ≥ 7F F ≥ 0; C ≥ 0
question
Solve the system of equations by substitution. {3x + 4y = 32 {3x + y = 17
answer
(4, 5)
question
Use a graph to solve the system of equations. {x + y = -1 {y = 3x + 19
answer
(-5, 4)
question
Graph and classify the system of equations as independent, inconsistent, or dependent. If the system is independent, find the solution from the graph. {3x + 3y = 2 {3x - y = 8
answer
Independent (2, -2)
question
Use elimination to solve the system of equations. {2x - 5y = 1 {5x -2y = -4
answer
(-22/21, -13/21)
question
Use elimination to solve the system of equations. {-16x - 6y = 170 {8x + 3y = -85
answer
Incorrect: no solutions Correct: Infinitely Many Solutions
question
Use a graph to solve the system of equations. {x + y = -4 {y = 3x - 8
answer
(1, -5)
question
Which of the given ordered pairs are NOT solutions to the system of inequalities? {2x + 3y 2 (3, 1), (-3, -2), (5, -5), (-2, 4), (-4, 5)
answer
(-4, 5), (3, 1), (-2, 4)
question
Write the system of inequalities whose solution is graphed as the shaded region.
answer
Incorrect: y -2x + 5 Use mathway; Graph the intersection (and)
question
Use the graph of the feasible region for the set of constraints to find the maximum and minimum values of the objective function C = 3x + 5y. Constraints: {x + y ≥ 1 {4x - 2y ≤ 4 {3y ≤ 3x + 3
answer
The maximum value of C is 29 at (3, 4) and the minimum value is 3 at (1, 0) .
question
Determine which ordered pair (x, y) is a solution of 3x - y ≤ 15.
answer
(5, 4) Solution Substitute 3(5) - 4 ≤ 15 11 ≤ 15 True
question
Which inequality has (1, 7) as a solution?
answer
Incorrect: -2x - 5y ≥ -32 Solution Substitute -2(1) - 5(7) ≥ -32 -2 - 35 ≥ -32 -37 ≥ -32 False, not a solution of the inequality
question
Use elimination to solve the system of equations. {4x + 2y = -12 {3x - 2y = 5
answer
(-1, -4)
question
An airplane, flying at an altitude of 3.21 miles above the ground, has a horizontal speed of 350 miles per hour and is descending at a rate of 14 miles per hour. Use parametric equations to find the airplane's altitude above ground after it has traveled 11 miles, as measured along the ground.
answer
2.77 mi Solution x(t)=350t y(t)=3.21-14t Solve either equation for "t" x=350t t=x/350 Substitute y=3.21-14(x/350) Substitute for "x", x=11 y=3.21-14(11/350) y=2.77
question
Use the set of constraints to find the maximum and minimum values of the objective function C = 5x + 11y Constraints: {x + y ≥ 2 {6x - 6y ≤ 12 {8y ≤ 4x + 16
answer
Incorrect: The maximum value of C is 139 at (8, 9) and the minimum value is 10 at (0, 2). Correct: The maximum value of C is 106 at (8,6) and the minimum value is 10 at (2,0).
question
Ms. Kim, an analyst at Multi-Fastener Corp, has developed a model to forecast the company's total production of metal fasteners. Under this model, production, P, is equal to 4500 times the man-hours spent producing machine screws (S) plus 2900 times the man-hours spent producing nuts and bolts (P). Manpower constraints mean that total number of man-hours per year cannot exceed 44,000; logically, the number of man-hours assigned to either task cannot be negative. Express the model in mathematical form.
answer
P = 4500S + 2900B {S + B ≤ 44,000 {S ≥ 0 {B ≥ 0
question
Solve the system of equations by substitution. {4y = 4 {x + 2y + z = 10 {y - 2z = -5
answer
Incorrect: None of the listed answers are correct Correct: x=5 y=1 z=3
question
Write the pair of parametric equations as a single equation in x and y. {x = 8t² -3 [y = 6t - 7
answer
x = 8((y + 7)/6)² - 3
question
Find [1 17 14][11 3] [19 7] [9 5]
answer
[460 192]
question
Which system of equations can be classified as independent?
answer
none of these
question
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {4x + y = -24 {2x + 2y = -18
answer
(-5, -4) You can just solve by using Elimination or Substitution
question
Find the determinant, and tell whether the matrix has an inverse. det [10 -7] [-5 -6 ]
answer
-95; Yes
question
Write the augmented matrix for the system of equations. {x - y = -9 {5x = 0
answer
[1 -1| -9] [5 0| 0] Solution x=1, y=-1 5x=5
question
The band and the cheerleading squad at a local school are ordering supplies. The supplies they need are listed in the table. (Evernote)
answer
[10 13 5] [ 5 ] [10 16 8] [12] [ 2 ] = [216] [258]
question
Perform the indicated operations on the given matrices. [3 -6 -7] [-2 -1 7] [-3 -2 4] + [ 3 5 -7] [-4 -1 7] [4 -9 -3]
answer
[ 1 -7 0 ] [ 0 3 -3 ] [0 -10 4]
question
Write the augmented matrix for the system of equations. {8x + 2y + 6z = -3 {3x - y + 10z = 3 {-9x -2y -4z = -7
answer
[8 2 6| -3 ] [3 -1 10| 3 ] [-9 -2 -4 |-7 ]
question
The Student Government secretary, and two teacher's aides are ordering supplies. The supplies they need are listed in the table. (Evernote)
answer
(Evernote)
question
Kozinski played in 16 basketball games this season, Hussein played in 32 games, and Johnson played in 55 games. Kozinski averaged 6 points and 2 rebounds per game, Hussein averaged 8 points and 11 rebounds, and Johnson averaged 18 points and 16 rebounds. Multiply the following matrices to get the total number of points scored and the total number of rebounds made, by all three players combined. [ 6 2 ] [16 32 55] [ 8 11] [18 16]
answer
1342 points, 1264 rebounds
question
Solve: (Evernote) det[x+3 2] [3 x-2] =0
answer
Incorrect: x =-4 Correct: x = 0 Mathway: Find the Determinant
question
Classify the following system of equations as inconsistent, dependent, or independent: {-3x -7y -2z = -25 {-6x +21y -6z = 57 {-3x +14y -4z = 40
answer
independent, because there is an intersection
question
Find the reduced row-echelon form of the augmented matrix that represents the following system of equations: (Evernote) {-6x + 9y = -5 {-8x - 4y = 0
answer
Incorrect: [1 0| 5/24 ] [0 1|-5/12] Correct: [1 0| -5/24] [0 1| 5/12
question
Perform the indicated operations on the given matrices. (Evernote) [-8 -8] + [-2 3] [-6 4] + [3 -1] (2×2 matrice + 2×2 matrice)
answer
[-10 -5] [-3 3]
question
Find AC - CB (Evernote)
answer
[-13 19] [-12 -44]
question
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {3x + 2y + z = -2 {3x -2y -z = -22 {3x + 2y -z = -10
answer
[3 2 1] [x] [ -2 ] [3 -2 -1] [y] = [-22] [3 2 -1] [z] [-10] ;(-4, 3, 4)
question
Find the inverse of the following matrix (if it exists): [2 -13 -6] [0 5 0] [0 -24 0]
answer
The matrix has no inverse.
question
Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {x + 2y + z = -17 {3x + 7y + 2z = -56 {x - y + 2z = 0
answer
x = -4, y = -6, z = -1
question
In May, Victor bought 24 styrofoam balls and decorated them as toy figurines. In June, he sold 17 figurines. In May, Wanda bought 28 styrofoam balls to decorate and in June, she sold 12 figurines. Which matrix represents all of their May purchases and their June sales?
answer
May June Victor [24 -17] Wanda [28 -12]
question
Which matrix represents the graph of polygon PQRS? (Evernote)
answer
P Q R S [2 -3 -3 2] [6 2 -7 3]
question
Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 4x² = 8
answer
±√2; ±1.41
question
Use factoring and the Zero-Product Property to solve the quadratic equation 2x² + 5x -3 = 0
answer
1/2, -3 Use Quadratic equation: (-b ± √((b² - 4ac))/2a
question
Find a quadratic function that fits the set of data points exactly, in the form y = ax² + bx + c with values of a, b, and c to two decimal places. (1, 4.1), (5, 2.3), (11, 4.9)
answer
y = 0.09x² - 0.98x + 4.99 Mathway: Find the Equation of the Parabola
question
Which function is the correct match with the the given graph and vertex (Evernote)
answer
f(x) = -3(x + 1)²
question
Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = -6x² - 24x - 31
answer
Incorrect: y = 6(x + 2)² - 7 x = -2; (2,-7) Correct: y = -6(x + 2)² - 7 x = -2; (-2, -7) Mathway: Find the Vertex Form Find the Axis of Symmetry Find the Vertex (Coordinates)
question
Use the quadratic formula to solve the equation. 6x² - 24x - 30 = 0
answer
5, -1
question
Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 2(x + 4)² - 48 = 0
answer
Incorrect: 4 ± 2√6; 5.8 or -13.9 Correct: -4 ± 2√6; 0.9 or -8.9
question
Simplify: (2 + 5i)/(5 + 4i)
answer
(30/41) + (17/41)i
question
Solve the quadratic inequality, and graph the solution on a number line. x² - 2x ≥ 24
answer
x ≤ -4 or x ≥ 6
question
Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = x² + 14x + 4
answer
Incorrect: None of the listed answers are correct Correct: y = (x+7)² - 45 x = -7; (-7, -45)
question
Which inequality is best represented by the graph shown: (Evernote)
answer
y ≤ -x² + 5x
question
Use factoring and the Zero-Product Property to find the zeros of the quadratic function. f(x) = x² -7x - 8
answer
8, -1
question
Which of the following is a quadratic function?
answer
f(x) = -1 + 9x² + 7x
question
Find the value of x to the nearest hundredth.
answer
17.2
question
Solve the quadratic inequality, and graph the solution on a number line. (Evernote) x² - 4x + 3 < 0
answer
1 < x < 3
question
Factor the quadratic expression. x² - 11x + 30
answer
(x - 5) (x - 6)
question
Gupta threw a baseball off a cliff into an open field 50 feet below. The chart gives the horizontal distance, x (in feet), the baseball traveled from Gupta and the height, y (in feet), of the baseball above the field. (Evernote) distance, x | 8 | 18 | 33 | 43 | height, y | 65 | 76 | 79 | 71 | Choose the quadratic equation that best fits the baseball's trajectory from Gupta to the open field below.
answer
y = -0.0383x² + 2.143x + 50
question
Show that the function is a quadratic function by writing it in the form f(x) = ax² + bx + c and indentifying a, b and c. f(x) = (5x - 4) (5x + 3)
answer
f(x) = 25x² - 5x - 12 a = 25, b =5, c = -12
question
The turnstiles at the entrance to the State Fair kept track of the number of people entering the fairgrounds, for the first seven hours following the openning of the fair. Find a quadratic equation that models the data shown. (Evernote)
answer
0.083x² - 0.197x + 7.62 Graphing Calculator STAT→Edit Put x values into L1 and y values into L2. 2ND→MODE→STAT→CALC →5:QuadReg
question
Solve the equation by completing the square. Give exact solutions. x² - 2x - 24 = 0
answer
-4, 6
question
Solve the equation for x. Write the exact solution and the approximate solution to the nearest hundredth, when appropriate. In(8x - 6) = 3
answer
x = (3/4) + (e³/8) x ≈ 3.26 Exponential form e³= 8x - 6
question
Solve the equation for x: 10^x = 18
answer
1.26
question
Evaluate 8^log₈ 9
answer
9
question
Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: In 10
answer
2.303
question
Solve log₇ 8 - log₇ (x + 3) = log₇ 3, for x
answer
Incorrect: None of the listed answers are correct Correct: x=-1/3 Solution log(x) - log(y) = log(x/y) log₇ 8 - log₇ (x+3) = log₇ (8/(x+3)) log₇ (8/(x+3)) = log₇ 3 (Mathway can solve once the left terms are combined)
question
If a principal of $1250 is invested at an annual interest rate of 4% compounded annually, what is the account balance at the end of 6 years?
answer
$1581.648
question
Solve the equation 3^4x = 27^x+3
answer
x = 9
question
The magnitude of an earthquake is found by the equation M = 2/3 log E/10^11.8 , where M is the magnitude and E is the energy released. Find the magnitude of an earthquake that released 10^24.4 ergs of energy.
answer
Incorrect: None of the listed answers are correct Correct: M = 8.4 Solution M = 2/3 log₁₀ (10^24.4/10^11.8)
question
The formula for estimating the number, N, of a certain product sold is N = 7400 In(7t + 3), where t is the number of years after the product is introduced. What is the expected number of sales 7 years after the product is introduced? Round to the nearest whole number.
answer
29,239
question
Solve the equation. Round your answers to the nearest hundredth. 5^x-1 = 25
answer
3
question
Find the final amount of the investment: $3000 at 8% interest compounded quarterly for 4 years.
answer
$4118.36
question
Describe the value of b for the function y(x) = 1/3(1/b)^x to represent exponential growth.
answer
Incorrect: None of the listed answers are correct Correct: "b" has to be greater than 0 and less than 1. (0 < b < 1)
question
Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: e^¼
answer
1.284
question
Solve log₃(x+4) - log₃(x-4) = log₃5 for x
answer
6
question
The inflation rate of the U.S. dollar is 3.1 percent. What this means is that every year, prices increase by 3.1 percent. If a pound of meat cost $2.37 nine years ago, what does it cost now?
answer
$3.12 Solution 2.37(1+0.031)⁹
question
Erosion gradually reduces the size of a small Pacific island that has a current area of just 460 acres. If the island's area decreases at an annual rate of 0.05%. Find the multiplier for the rate of exponential decay.
answer
Incorrect: 0.95 Correct: 0.9995 Solution 100 - 0.05 = 99.95 99.95/100 = 0.9995
question
Write the equation in logarithmic form. 6^-4 = 1/1296
answer
log₆ 1/1296 = -4
question
Which function represents exponential decay?
answer
y(x) = 5(0.44)^x
question
Evaluate the logarithmic expression to the nearest thousandth. log₈ 1/2
answer
-0.333
question
If $1500 is invested at an interest rate of 10%, compounded continuously, determine the balance in the account after 2 years. Use the formula A = Pe^rt.
answer
$1832.10
question
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - 9x³ + 10x² + 90x - 200
answer
4, 5, ±3.16
question
Divide x³ + 5x² + 9x + 9 ÷ x + 3
answer
x² + 2x + 3
question
Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - 7x² + 14x - 8 = 0
answer
2, 1, 4
question
Find all the zeros of the polynomial function. f(x) = x² - 10x + 34
answer
Incorrect: 5 ± 6i Correct: 5 ± 3i
question
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998. (Evernote)
answer
T(x) = 0.2x³ + 0.3x² + 0.2x + 0.1; 304.8 thousand
question
Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - x² - 14x + 24 = 0
answer
-4, 2, 3
question
Find all the zeros of the polynomial function. f(x) = x³ + 4x² + 6x + 9
answer
-3, (-1 ±i√11)/2
question
Write the product as a polynomial in standard form. (5x² - 2x + 5)(x² - 8x - 2)
answer
5x⁴ - 42x³ + 11x² - 36x - 10
question
Write a polynomial equation in standard form by using the given information. P is of degree 3; P(0) = 24; zeros: 3, -4, 2
answer
P(x) = x³ - x² - 14x + 24
question
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x³ - 4x² + 7x - 12
answer
None of the listed answers are correct
question
Simplify 3x² - 4x - 5 + 4x² + 8x - 7
answer
7x² + 4x - 12
question
Classify the polynomial by degree and number of terms. Describe the shape of its graph. 3x³
answer
cubic monomial; 'S' shaped with 2 turns
question
Evaluate 2x² + 3x + 4 when x=2
answer
18
question
For the function, use synthetic division and substitution to determine whether the given value is a zero of the function. P(x) = 3x⁴ - 10x³ - 41x² + 68x + 60
answer
Zeroes are 5, 2, -2/3, -3
question
Evaluate x⁴ - 10x² + 24 when x=3
answer
15
question
Write the product as a polynomial in standard form. (x - 6)(x + 5)(x - 4)
answer
x³ - 5x² - 26x + 120
question
Use substitution to determine which of the given linear expressions is a not a factor of 3x⁴ - 16x³ - 15x² + 88x + 60
answer
x + 5 Mathway (Algebra) Factor
question
Determine the end behavior of the graph of the function f(x) = 3x⁴ - 2x³ + 2x + 2
answer
rises to the left; rises to the right
question
Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - x³ - 16x² + 10x + 60
answer
3, -2, ±3.16
question
Classify the polynomial by degree and number of terms. Describe the shape of its graph. 7x² + 7x + 7
answer
quadratic trinomial; parabola
question
Determine whether the function is a rational function. If so, find the domain and identify the horizontal and vertical asymptotes, and any holes in the graph. If the function is not rational, state why not. f(x) = (x - 1)/((x - 7)(x + 3))
answer
Incorrect: rational; x≠1, 7 or -3; asymptotes at y=0, x=1, x=7 and x=-3 Correct: rational; x≠-3,7 asymptotes at y=0, x=-3, and x=7
question
Simplify the rational expression. (Evernote) ( 3/(x² + 7x + 12) + 1/(x² + 11x + 28) ) ÷ ( 2/(x² + 10x + 21) + 1/x² + 13x + 36) )
answer
( 4(x + 9)(x + 6) ) / ( 3(x² + 12x + 31) )
question
Simplify. ( (x - 2)/(2x²) ) - ( (2x + 1)/(9x) ) + ( (7x)/(12) )
answer
( 21x³ - 8x² + 14x - 36 ) / 36x²
question
Solve the radical inequality. ³√(3x-6) + 6 ≥ 7
answer
x ≥ 7/3
question
Simplify the rational expression. ( (x² + 14x + 49)/8x ) ÷ ( (x+7)/4x )
answer
(x+7)/2
question
Evaluate the radical expression: (-1/7)(³√-64)⁴
answer
-256/7
question
Rationalize the denominator. 2 ÷ √5
answer
(2√5)/5
question
Rationalize the denominator. (√11) ÷ (9 + √5)
answer
( 9√11 - √55) / 76
question
Simplify. (-3x + 8)/(x² - 49) - (-2x + 1)/(x² - 49)
answer
-1/(x+7)
question
Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and the inverse of z. y=-99.4 when x=-11 and z=4. Find y when x=2 and z=-8.
answer
y = 9x/z; -9/4
question
Simplify the sum, difference, product, or quotient. Assume that the value of any variable is positive ³√(-27x) - 4 ³√(x⁴) + 9 ³√(x) + 9x ³√(x)
answer
6 ³√(x) + 5x ³√(x)
question
Evaluate the radical expression: 8(⁴√(81)²
answer
72
question
Solve the equation or inequality. 4/(x-3) - 2/(x+4) = 0
answer
x=-11
question
Find the domain of the radical function. f(x) - √(9-x)
answer
x ≤ 9 Solution f(x) - √(9-x) = 0 Add √(9-x) to both sides f(x) = √(9-x) Mathway: Find the Domain
question
Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and z. y=98/3 when x=2 and z=7. Find y when x=8 and z=3
answer
y = 7/3(x)(z); 56
question
Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 8400 dolls when $84,000 was spent on advertising and the price of a doll was set at $70. Determine the number of dolls sold when the amount spent on advertising is increased to $98,000.
answer
9800
question
Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?
answer
x/3 + x/9 = 1; 2.25 hr
question
The wattage rating of an appliance is given as "W", in watts, and varies jointly as the resistance, "R", in ohms, and as the square of the current, "I", in amperes. If the wattage is 2 watts when the resistance is 200 ohms and the current is 0.1 amperes, find the wattage when the resistance is 150 ohms and the current is 0.4 amperes.
answer
Incorrect: None of the listed answers are correct Correct: W (wattage) = 24
question
Solve the equation or inequality. (2x-2)/(x²-36) ≥ 1/(x+6)
answer
-6 ≤ x ≤ -4 or x ≥ 6
question
Solve the radical inequality. √(x + 14) ≤ x - 16
answer
x ≥ 22
question
Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (-2, 0) asymptote: y=1/2x
answer
x²/4 - y² = 1 Put in each answer using Mathway: Find the Vertex Form, till the verices and asymptote matches up
question
Which equation describes a parabola?
answer
6y² + 11x - 13y = -1
question
Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, C(-1, -4), D(5, 4)
answer
center: (2, 0) radius: 5
question
Find the standard equation for the ellipse, using the given characteristics taken from the graph. (Evernote)
answer
(x+4)²/16 + (y+3)²/9 = 1
question
Write the equation in standard form and classify the conic section it defines. 2x² + 2y² - 28x + 24y + 162 = 0
answer
(x-7)² + (y+6)² = 4; circle
question
Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, with endpoints C(- 1, 5), D(5, 9)
answer
center: (2, 7) radius: √13; 3.61 Mathway: Find the Midpoint
question
Find the standard equation of a circle with the given radius and center. radius: 7 center: (1, 1)
answer
(x - 1)² + (y - 1)² = 49
question
Solve the nonlinear system of equations. {x² + y² = 144 {x² - 4y² = 64
answer
four solutions: (±8√2, ±4)
question
Which set of characteristics matches the given standard equation and parabola graph? (Evernote) x = 1/24 y²
answer
vertex: (0, 0) directrix: x=-6
question
Solve the nonlinear system of equations. {x² + y² = 256 {x + y = 16
answer
two solutions: (0, 16) and (16, 0)
question
Which set of characteristics matches the given parabola graph and standard equation? (Evernote) x = -1/4 y²
answer
axis of symmetry: y=0 focus: (-1, 0) vertex: (0, 0) Mathway: Graph
question
Find the standard equation for the hyperbola with the given characteristics. center: (5, 4) one focus: (-25, 4) one vertex: (23, 4)
answer
(x-5)²/324 - (y-4)²/576 = 1
question
The two hyperbolas in the graph are conjugates, meaning they share the same asymptotes. Given the following equation of the hyperbola represented by the thin curve, find the equation of its conjugate, which is represented by the thick curve. (Evernote) x²/9 - y²/25 = 1
answer
y²/25 - x²/9 = 1
question
Identify the conic section produced by the following diagram. (Evernote)
answer
hyperbola
question
Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (−2, 0) asymptote: y = 3x
answer
x²/4 - y²/36 = 1
question
Which set of characteristics matches the given standard equation and parabola graph? (Evernote)
answer
focus: (-1, -4) vertex: (-1, 2)
question
Identify the conic section produced by the intersection of the plane and the cones in the following diagram.
answer
circle
question
Find the standard equation of a circle with the given radius and center. radius: 4 center: (3, - 5)
answer
(x - 3)² + (y + 5)² = 16 Mathway: Find the Equation (put coordinate points comma r=4)
question
Find the distance between points B(5, 7) and F(1, 2), and the coordinates of the midpoint of BF.
answer
distance = √41; 6.4 midpoint = (3, 9/2) Mathway
question
Find the standard equation for the ellipse, using the given characteristics. vertices: (0, ±8) foci: (0, ±√55)
answer
x²/9 + y²/64 = 1
question
Find: ₇P₄
answer
840
question
A hat contains 22 names, 10 of which are female. If five names are randomly drawn from the hat, what is the probability that at least four female names are drawn?
answer
0.105 ((₁₀C₄ × ₁₂C₁)+(₁₀C₅ × ₁₂C₀))÷(₂₂C₅) ((210 × 12)+(252 × 1))÷(26334) 2772÷26334 = 0.105
question
Teesha is in the bowling club. There are 33 students in the club. Five of them will be picked at random to attend an awards banquet. What is the probability that Teesha will not be randomly chosen to attend the banquet?
answer
28/33 Solution Probability of getting chosen is 5/33, so the the probability of not getting chosen is 33 - 5 = 28
question
How many different arrangements can be made using all of the letters in the word GAME?
answer
24 Solution ₄P₄
question
A spinner is evenly divided into 8 equal areas and numbered from 1 through 8. What is the probability of spinning a number less than 4 in a single spin?
answer
3/8
question
A lunch menu consists of 4 different kinds of sandwiches, 2 different kinds of soup, and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
answer
40 4 × 2 × 5 = 40
question
Two cards are randomly drawn in succession from a deck of 52 playing cards. Find the probability that the king of spades and any ace are drawn, in that order, without replacement.
answer
1/663 or 0.0015082 Solution 1/52 × 4/51 = 0.0015082
question
Evaluate: (₁₂C₇ × ₁₄C₁₀)/₁₃C₅
answer
616 Solution ₁₂C₇ = 792 ₁₄C₁₀ = 1001 ₁₃C₅ = 1287 (792 × 1001)/1287 = 616
question
If 2 blocks are randomly taken from a bag containing 10 blue blocks, 10 red blocks, and 7 yellow blocks, what is the probability of drawing a blue block and a red block?
answer
50/351 or 0.1424501 Solution 10/27 × 10/26 = 0.1424501
question
Determine the probability that you will roll a number greater than 1 on a number cube.
answer
5/6
question
Evaluate: ₇C₄
answer
35
question
A circular, rotating, serving tray has 5 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the circular tray?
answer
24 Solution (n-1)! (5-1)! 4! = 4 × 3 × 2 × 1 = 24
question
How many different ways can 6 people be seated around a circular table?
answer
120 Solution (n-1)! (6-1)! 5! = 5 × 4 × 3 × 2 × 1 = 120
question
Three cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of three cards are possible?
answer
22,100 Solution 52 choose 3 ₅₂C₃ = 22,100
question
How many distinct committees of 14 people can be formed if the people are drawn from a pool of 23 people? Use factorials to express the answer.
answer
₂₃C₁₄ = 23!/(9! 14!) Solution nCr = n!/(r!(n-r)!) 23!/(14!(23-14)!) 23!/(14!(9)!) 23!/ (9! 14!)
question
Jamila spins a spinner with 3 sections of equal area, like the one below, 25 times. It lands on the 1eight times. What is the experimental probability of spinning a 1?
answer
8/25
question
In a bag there are 3 green jelly beans, 2 black jelly beans, and 8 yellow jelly beans. Once a jelly bean is drawn, it is not replaced. Find the probability of randomly drawing a green jelly bean and then a black jelly bean in two consecutive draws.
answer
1/26
question
Suppose you mix-up the cards below and choose one without looking. What is the probability of selecting neither "E" nor "G"? H E H E G W I
answer
4/7 Solution Probability of selecting "E" or "G" is 3/7. 7/7 - 3/7 = 4/7
question
Two cards are randomly selected from a standard 52-card deck. What is the probability of getting 2 diamonds or 2 face cards?
answer
Incorrect: 0.108 Correct: 0.106 or 47/442 Solution (13/52 × 12/51) + (12/52 × 11/51) - (3/52 × 2/51)
question
A box contains 2 green, 6 yellow, and 3 purple balls. Find the probability of obtaining a purple ball in a single random draw.
answer
3/11
question
Find the four arithmetic means between -3 and 102.
answer
18, 39, 60, 81 Solution t(n) = t(1) + (n - 1)d 102 = -3 + (6 -1)d 102 = -3 + 5d 105 = 5d d = 21 Substitute t(2) = -3 + (2 - 1)21 -3 + (1)21 -3 + 21 18 t(3) = -3 + (3 - 1)21 -3 + (2)21 -3 + 42 39 And so on
question
Use Pascal's Triangle to determine the probability that you will get three green lights in a row of five lights. Assume red and green are equally likely occurrences.
answer
Incorrect: 7/32 Correct: 5/16 (10/32) Solution (n C k)(p∧k)(1 - p)∧(n-k) (₅C₃)(½)³(1 - ½)⁵⁻³ (₅C₃)(½)³(1 - ½)² 10 × 1/8 × 1/4 = 5/16
question
Write the first five terms of the sequence defined by the given recursive or explicit formula. (Evernote)
answer
4, -3, 31, -167, 959
question
Expand the binomial raised to a power. (3a - b)⁵
answer
243a⁵ - 405a⁴b + 270a³b² - 90a²b³ + 15ab⁴ - b⁵ Mathway: Expand Using the Binomial Theorem
question
Express 0.7312 as a geometric series, and write its sum as the ratio of two integers.
answer
(Evernote)
question
Evaluate the sum. (Evernote)
answer
-3003
question
Find the sum of the geometric series 0.2 + 0.02 + 0.002 + . . . given the formula S=a/(1 - r), where "a" is the first term, "r" is the common ratio, and "S" is the sum.
answer
2/9 Solution S = 0.2/(1 - 0.1) S = 0.222... or 2/9
question
Find the 6th and 8th entries in the row 12 of Pascal's triangle.
answer
792;792 Solution Use nCk-₁ to love for nth entry ₁₂C₆-₁ = ₁₂C₅ = 792 ₁₂C₈-₁ = ₁₂C₇ = 792
question
Use Pascal's triangle to find the number of ways to choose 3 boxes from 7 boxes.
answer
Incorrect: 21 Correct: 35 Solution ₇C₃ = 35
question
Find the three positive geometric means between 6 and 1875/8.
answer
15, 75/2, 375/4 Solution t₁=6 and t₅=1875/8 t(n) = t₁r^(n-1) t₅ = 6r⁴ 1875/8 = 6r⁴ r = 2.5 t₂ = 6(2.5)¹ 15 t₃ = 6(2.5)² 37.5 or 75/2 t₄ = 6(2.5)³ 9375 or 375/4
question
A 50-row theater has 30 seats in the front row. The second row has 31 seats. If each row has one more than the row in front of it, how many seats are there in the theater?
answer
2725 Solution t₁ = 30 and d = 1 t(n) = t₁ + (n-1)d t₅₀ = 30 + (49)1 t₅₀ = 79 S = n/2[2t₁ + (n - 1)d] S = 50/2[2(30) + 49] S = 25(60 + 49) S = 25(109) S = 2725
question
Find the sum of the infinite geometric series, if it exists. 3 - 9/5 + 27/25 - 81/125 + 243/625 - ...
answer
15/8 Solution (9/5) ÷ 3 = 0.6 r = 0.6 (common ration) t₁ = 3 S = t₁ ÷ (1 - r) S = 3 ÷ (1 - 0.6) S = 3 ÷ 0.4 S = 7.5 or 15/8
question
Use the given formula to find the first four terms of the arithmetic sequence. t(n) = 12 - 3n
answer
9, 6, 3, 0 Solution t(1) = 12 - 3(1) 9 t(2) = 12 - 3(2) 6 ...
question
There are 8 cars in a parking lot on a very cold day. Suppose the probability of any one of them not starting is 0.14. What is the probability that exactly 3 of the cars will not start?
answer
Incorrect: ≈ 0.003 Correct: ≈ 0.072 Solution (nCk) × (p)^n × (1 - p)^(n - k) (₈C₃) × (0.14)³ × (1 - 0.14)⁵ = 0.072
question
Write an explicit formula for the nth term of the geometric sequence. 7/4, 49/24, 343/144, 2401/864, ...
answer
(Evernote) Solution explicit formula for nth term in a geometric sequence is t(n) = t₁r^(n-1) t₁ = 7/4 and r = 7/6 t(n) = 7/4(7/6)^(n-1)
question
Find the sum of the infinite geometric series, if it exists. (Evernote) ∑3(-½)^(k-1)
answer
2 Solution ∑3(-½)^(k-1) t₁ = 3(-½)⁰ 3 t₂ = 3(-½)¹ -1.5 r = t₂/t₁ r = -1.5 ÷ 3 r = -½ S = t₁/(1 - r) S = 3/(1 - (-½)) S = 3/1.5 S = 2
question
Find the sum of the first 7 terms of the geometric series 8 + 8/3 + 8/9 + 8/27 + ...
answer
11.99 Solution r ≠ 1 r = 8/3 ÷ 8 r = 1/3 & t₁ = 8 S(n) = t₁[(1 - r^n) ÷ (1 - r)] S₇ = 8[(1 - (1/3)⁷) ÷ (1 - 1/3)] S₇ = 11.99
question
Use Pascal's triangle to solve for the value of n: 2(n C 3) = n+4 C ₇ (Evernote)
answer
Incorrect: 2 Correct: 4
question
Make a conjecture about the pattern of the given data. Find the sum of the 7th row. 3 3 + 6 + 3 3 + 6 + 9 + 6 + 3 3 + 6 + . . . + ( 3n − 3) + ( 3n ) + ( 3n − 3) + . . . + 3
answer
Incorrect: The sums of the rows are 3, 12, 27, . . . . The sum of the nth row is n(2n +3). The sum of the 7th row is 119. Correct: The sum of the rows are 3, 12, 27, . . . . The sum of the nth row is 3(n²). The sum of the 7th row is 147.
question
Find the two geometric means between 7 and 3584.
answer
Incorrect: 63, 567 Correct: 56, 448 Solution t₁=7 and t₄=3584 Formula t(n) = t₁r^(n - 1) Substitute t(4) = 7r⁴⁻¹ 3584 = 7r³ divide both sides by 7 r³ = 512 Take cube root of both sides r = 8 t(2)=7 × 8 56 t(3)=7 × 8² 448 7, 56, 448, 3584
question
Find the mean, the median, and mode of the data set: 14, 6, 21, 16, 16, 7, 20, 19, 7
answer
Mean: 14 Median: 16 Mode: 7, 16
question
Using the given information, which data set is the correct choice? (Evernote)
answer
20, 12, 27, 14, 16, 13, 12, 13, 26, 27, 21, 28, 20, 22, 20
question
Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 29, 14, 40, 12, 16, 46, 22, 23, 19, 31, 7, 9
answer
Minimum = 7 Maximum = 46 Q₁=13; Q₂=20.5; Q₃=30 Range = 39 IQR = 17 Q₂ = mean
question
Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 205 cm and a standard deviation of 13 cm. What is the probability that a randomly selected high jumper has a personal best between 218 and 244 cm? (Evernote)
answer
0.1574 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(→Enter→75, 90, 85, 7) Between, mean, then standard deviation
question
The bowling scores of all of the bowlers in 12 bowling leagues are normally distributed. Their mean score is 201 points, with a standard deviation of 33 points. If one league has 120 bowlers, how many of them are likely to score more than 168 points?
answer
101 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(168, 10⁹⁹, 201, 33)→Enter = 0.84 .84 or 84% 84% of 120 is 100.8 rounded to the nearest whole number equals 101
question
Find the variance and the standard deviation for the following data. 7, 20, 7, 15, 21, 4, 22, 17, 13
answer
variance ≈ 39.78; standard deviation ≈ 6.31 https://www.easycalculation.com/statistics/standard-deviation.php Take the Variance (Population Standard deviation) and Population Standard deviation
question
Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 27, 8, 9, 48, 19, 10, 29, 42, 2, 50, 44
answer
Minimum = 2 Maximum = 50 Q₁=9; Q₂=27; Q₃=44 Range = 48 IQR = 35 Mathway Find the Five Number Summary, range, and Find the Interquartile Range (H-Spread)
question
Using the given stem and leaf plot and and it's median and mode, select the data set on which it was created. (Evernote)
answer
7, 6.9, 8.2, 7.6, 6, 7.2, 8.4, 7.6, 7.3, 7.8, 6.2, 9.5, 8.9, 6.5, 9
question
An English class was taken by 28 students. Their final scores were: three As, five Bs, nine Cs, six Ds, and five Fs. Using the given frequency table, find the mean grade point score, using A = 4, for the entire group of 28 students. Give the answer to the nearest hundredth, if necessary. (Evernote)
answer
Incorrect: [none] Correct: 1.82 (Close to a "C")
question
NCUse the frequency table below, with the a total of 18 catalog items sold at four different prices, to find the average price per item. (Evernote)
answer
$16.50
question
The relative frequency histogram below represents the age in years of the first 100 children to have their portraits taken at the "See What Develops" photography studio. What is the probability that the next child to have portraits taken will be between 1 and 2 years old?
answer
Incorrect: None of the listed answers are correct Correct: 31/100 or 31% (maybe 0.315 or 32%) Solution .11 + .20 + .31 + 30 + .15 + 24 = 1 (or 100%) Age 1= .20 Age 2= .11 .20 + .11 = .31 (or 31%) 31/100 or 31% Probability
question
A number cube is tossed 10 times with the following results. 5, 6, 1, 5, 5, 2, 6, 1, 2, 2 Find the range and the mean deviation of the data.
answer
None of the listed answers are correct To find mean deviation minus the mean from each data value, add everything up, then divide by the number of data values. Example: 54, 49, 47, 48, 52 mean of data = 50 54 - 50 = | 4 | = 4 49 - 50 = |-1| = 1 47 - 50 = |-3| = 3 48 - 50 = |-2| = 2 52 - 50 = | 2 | = 2 4 + 1 + 3 + 2 + 2 = 12 12 ÷ 5 = 2.4 Mean deviation = 2.4
question
A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of the purchases are returned. What is the probability that no more than 1 of the next 6 purchases will be returned?
answer
0.954 Solution ((₆C₁)(0.06)¹(1 - 0.06)⁵) + ((₆C₀)(0.06)⁰(1 - 0.06)⁶) = 0.954
question
In Sean's school there are 96 families which have 4 children. The circle graph shows the probability of each combination of girls and boys in a family with four children. Use the circle graph to predict the probability that one of these 96 families, chosen at random, will only have children of the same sex. (Evernote)
answer
12.5%
question
A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?
answer
0.21617 Solution (₆C₃)(0.67)³(1-0.67)³ = 0.21617
question
The depth of snow at seven different mountain lodges is 13 in., 15 in., 21 in., 17 in., 90 in., 13 in., and 19 in. Find the mean, median, and mode. Tell which measure is the most useful for predicting how deep the snow will be at an eighth lodge.
answer
Mean = 26.9 in Median = 17 in Mode = 13 The median is the most useful.
question
The personal savings of the Young Saver Club were normally distributed with a mean of $525 and a standard deviation of $64. What is the probability that a randomly selected saver has an account total between $525 and $589?
answer
0.3413 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(525, 589, 525, 64)→Enter = 0.3413
question
A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of all purchases are returned. What is the probability that no more than 1 of the next 7 purchases will be returned?
answer
≈ 0.938 ((₇C₁)(0.06)¹(1 - 0.06)⁶) + ((₇C₀)(0.06)⁰(1 - 0.06)⁷) ≈ 0.938
question
The class average on a math test was 77.5 and the standard deviation was 5.8. Find the z-score for a test score of 83, and the percentage of the class who scored below 83.
answer
≈ 0.95; 82.89% Solution z-score z = (x - x̅) ÷ σ z = (83 - 77.5) ÷ 5.8 = 0.948 → 0.95 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 83, 77.5, 5.8)→Enter = 0.83 or 83%
question
In a certain normal distribution of scores, the mean is 30 and the standard deviation is 5.5. Find the z-score corresponding to a score of 37 and find the percentage of the scores that are below 37.
answer
1.27; 89.80% Solution z-score z = (x - x̅) ÷ σ z = (37 - 30) ÷ 5.5 = 1.27 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 37, 30, 5.5)→Enter = 0.8984 or 89.80%
question
Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. Find tan x (Evernote)
answer
3/4 or 0.75 Solution tan x = opp./adj. 24/32 = 0.75
question
Evaluate the trigonometric expression. Sin⁻¹(-½)
answer
-30° Solution π = 180° -π/6 -180°/6 = 30° Mathway Evaluate (Do not use Find the Exact Value)
question
Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. (Evernote)
answer
8/17 or 0.4706 sinθ = opp./hyp.
question
Use the following information to find the unknown sides and angles. m∠B = 28°; c=18
answer
b = 8.5; a = 15.9; m∠A = 62°; m∠C = 90° Solution We have two angles m∠A + m∠B + m∠C = 180 m∠A + 28° + 90° = 180° m∠A = 62° Use Law of Sines to solve for side "a" or "b' a/sin A = c/sin C a/sin(62°) = 18/sin(90°) a = 18sin(62°)/sin(90°) a = 15.89 → 15.9 b/sin B = a/sin A b/sin(28°) = 15.9/sin(62°) b = 15.9sin(28°)/sin(62°) b = 8.45 → 8.5
question
What is the reference angle for 516° ?
answer
24° Mathway (Trigonometry) Find the Reference Angle
question
Find tan 421°.
answer
1.804 Mathway (Trigonometry) Find the Exact Value
question
For ∆ ABC, find the measure of ∠A to the nearest degree. (Evernote)
answer
19° Solution Use Law of Cosines for "c" c = √(a² + b² - 2ab cos C) c = 37 a = 12, b = 35, and c = 37 Use Law of Sines sin A/a = sin C/c sin A/12 = sin(90°)/37 sin A = 12sin(90°)/37 sin A ≈ 12/37 Convert from radians to degrees ∠A = 18.58° → 19°
question
Evaluate the trigonometric expression. cos(Cot⁻¹1)
answer
√2/2 Mathway (Trigonometry) Find the Exact Value
question
Given the quadrant of θ in standard position and a trigonometric function value of θ, find exact values for the remaining functions. Quadrant II, sinθ = 2/7
answer
cosθ = -3√5/7 tanθ = -2√5/15 cotθ = -3√5/2 secθ = -7√5/15 cscθ = 7/2 Mathway (Trigonometry) Find the Other Trig Values in Quadrant II
question
Find tan 382°.
answer
0.404 Mathway (Trigonometry) Find the Exact Value
question
Convert 279° to radians.
answer
(31/20)π Mathway (Trigonometry) Convert from Degrees to Radians
question
Find the reference angle for 525°.
answer
15° Mathway (Trigonometry) Find the Reference Angle
question
Point P is located at the intersection of a circle with a radius of r and the terminal side of an angle θ. Find the coordinates of P to the nearest hundredth. θ = 120° , r = 13
answer
P(- 6.5, 11.26) Solution 120° is in Quadrant II Coordinates: (cos θ = x/r, sin θ = y/r) θ = 120° and r = 13 cos(120°) = x/13 -½ = x/13 x = -13/2 or -6.5 sin(120°) = y/13 √3/2 = y/13 y = 13√3/2 or 11.26 P(-6.5, 11.26)
question
The function d = - 6 cos 3t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the frequency?
answer
Incorrect: 3π/2 cycles/seconds Correct: 3/2π Solution d = A cos wt d = -6 cos 3t w = 3 f (frequency) = w/2π f = 3/2π
question
For a circle of radius 4 feet, find the arc length "s" subtended by a central angle of π/30 radians. Round to the nearest hundredth.
answer
None of the listed answers are correct Solution r = 4 and θ = π/30 s = rθ s = 4(π/30) s = 2π/15
question
The function d = 9 cos 2t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the maximum displacement of the object from its resting position?
answer
9 m Solution A = displacement d = A cos wt d = 9 cos 2t A = 9 or 9m
question
Find cot (-290°).
answer
0.364 Mathway (Trigonometry) Find the Exact Value
question
For a circle of radius 8 feet, find the arc length of a central angle of 30°.
answer
(4/3)π feet Solution r = 8 and θ = π/6 (change 30° to radians) s = rθ s = 8(π/6) s = (4/3)π or 4π/3
question
Find the amplitude, the period, and the frequency of the graph. Then write an equation for the sine function for the graph.
answer
3/4, 180°, 2, y = 3/4 sin 2x Graph all multiple choices and pick the one that fits
question
Find the exact value of the sine, cosine, and tangent of -210°.
answer
sin = 1/2 cos = -√3/2 tan = -√3/3 Mathway (Trigonometry) Find the Exact Value
question
Suppose the depth of the tide in a certain harbor can be modeled by y = 25 - 4 cos(π/6t), where "y" is the water depth in feet and "t" is the time in hours. Consider a day in which t = 0 represents 12:00 midnight. For that day, when are high tide and low tide and what is the depth of each?
answer
Incorrect: high tide at 12:00 noon and 12:00 midnight, depth 29 ft low tide at 6:00 a.m. and 6:00 p.m., depth 21 ft Correct: high tide at 12:00 noon and 12:00 midnight, depth 21 ft low tide at 6:00 a.m. and 6:00 p.m., depth 29 ft
question
Use either the Law of Sines or the Law of Cosines to solve for "a" to the nearest tenth. (Evernote)
answer
28.8 Solution ∠A + 61° + 76° = 180° ∠A = 43° Use Law of Sines a/sin(43°) = 41/sin(76°) a = 41sin(43°)/sin(76°) a = 28.8
question
Find cos((1/2)A) and sin((1/2)A) if sin(A)=4/5 and Ais a first-quadrant angle. (Evernote)
answer
Incorrect: cos(A/2) = √3/5 sin(A/2) = 2/5 Correct: cos(A/2) = (2√5)/5 sin(A/2) = √5/5 Solution Pathagorean Identities sin A = 4/5 cos²A = 1 - sin²A cos A = 1 - (4/5)² cos A = 3/5 Use Half-Angle Identities sin(A/2) = √((1 - cos A)/2) sin(A/2) = √((1 - 3/5)/2) sin(A/2) = √5/5 cos(A/2) = √((1 + cos A)/2) cos(A/2) = √((1 + 3/5)/2) cos(A/2) = (2√5)/5 A = θ and the cos((1/2)A) is the same as cos(A/2)
question
Find all solutions of cos(x) - √(1 - 3cos²(x)) = 0
answer
Incorrect: None of the listed answers are correct Correct: No Solution
question
Use the Law of Sines to solve for m∠A to the nearest tenth. (Evernote)
answer
29.8 Solution sin B/b = sin C/c sin B/43 = sin(80°)/45 sin B = 43sin(80°)/45 sin B = 0.94103 sin⁻¹(sin B) = ∠B sin⁻¹((43sin¹(80°)/45)) sin⁻¹(0.94103) = 70.2° (rounded to the nearest tenth) ∠B = 70.2° ∠A + 70.2° + 80° = 180° ∠A = 29.8° Use graphing calculator on degree mode or use Mathway and change answer to degrees.
question
Write the expression csc(2x) + cot(2x) in terms of tan x or cot x.
answer
Incorrect: None of the listed answers are correct Correct: cot(x)
question
Use the Law of Cosines to solve for "A" to the nearest tenth of a degree. (Evernote)
answer
35.3° Law of Cosines cos A = (b² + c² - a²)/(2bc) cos A = (43² + 50² - 29²)/(2 × 43 × 50) cos A = 0.8158 cos⁻¹(0.8158) = 35.3° Just do this ↓ ∠A = cos⁻¹((b² + c² - a²)/(2 × 43 × 50)) ∠A = 35.3°
question
Find the exact value of sin(- 450° + 300°).
answer
-1/2 Solution Use Sum and Diffrence Identities: sin(A + B) = sinAcosB + cosAsinB sin(450°)cos(300°) + cos(450°)sin(300°) = -1/2 Mathway (Trigonometry) Find the Exact Value
question
Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°.
answer
Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°
question
Find the image of (5, -6) after a counterclockwise rotation of 270° about the origin. (Evernote)
answer
(-6, -5)
question
Wilfred is checking his bicycle's wheel. The wheel has a radius of 25 cm, and its center is 54 cm above the ground. Wilfred is rotating the wheel at a constant speed of 230° /s. The height of a point on the tire as a function of time is given by h = 54 + 25 sin(230t), where h is the height in centimeters and t is the time in seconds. Find h when t = 5.5 s. Round your answer to the nearest tenth of a centimeter.
answer
Incorrect: None of the listed answers are correct Correct: 51.8 Solution h = 54 + 25 sin(230t) h = 54 + 25 sin(230 × 5.5) h = 51.8
question
Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°
answer
Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°
question
Given that F = 32°, G = 55°, and f = 10, solve the triangle. If no such triangles exist, write none. Round to the nearest tenth. (Evernote)
answer
E = 93° , g = 15.5, e = 18.8 Solution F = 32°, G = 55° , E = ?° f = 10, g = ?, e = ? 32° + 55° + ∠E = 180° ∠E = 93° Use Law of Sines 10/sin(32) = g/sin(55) g = 10sin(55)/sin(32) g = 15.5 10/sin(32) = e/sin(93) e = 10sin(93)/sin(32) e = 18.8
question
Given sinθ = 5/9, where π/2 < θ < π, find the exact values of sin 2θ and cos 2θ.
answer
Incorrect: -31/81, (20√14)/81 Correct: 10/9, -(4√14)/9
question
Which of the following is equal to sin²(x)/(1 - cos(x))
answer
Incorrect: None of the listed answers are correct Correct: 1 + cos(x) or 1 + cosθ Mathway Rationalize the Denominator Mathway Verify the Identity+
question
Find the exact value of cos(345°).
answer
(√6 + √2)/4 Mathway (Trigonometry) Find the Exact Value
question
Whitney starts the engine on her small private airplane. The engine drives a propeller with a radius of 7.5 feet and its centerline 12.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 850 revolutions per minute. The height of one propeller tip as a function of time is given by h = 12.5 + 7.5 sin(850t), where h is the height in feet and t is the time in minutes. Find h when t = 2.5
answer
8.2 ft Solution h = 12.5 + 7.5 sin(850t) h = 12.5 + 7.5 sin(850 × 2.5) h = 8.2
question
Solve triangle ABC given that a = 11, b = 13, and c = 15.
answer
A = 45.6° , B = 57.6° , C = 76.9° Solution Use Law of Cosines cos A = (b² + c² - a²)/2bc cos A = (13² + 15² - 11²)/(2 × 13 ×15) cos A = 7/10 cos⁻¹(7/10) = 45.6° cos B = (c² + a² - b²)/2ca cos B = (15² + 11² - 13²)/(2 × 15 × 11) cos B = 59/110 cos⁻¹(59/110) = 57.6° cos C = (a² + b² - c²)/2ab cos C = (11² + 13² - 15²)/(2 × 11 × 13) cos C = 5/22 cos⁻¹(5/22) = 76.9°
question
csc(2x) + cot(2x) forms an identity with which of the following?
answer
cot x Use Mathway to "Verify the Identity" csc(2x) + cot(2x) = cot(x)
question
Which of the following is an identity?
answer
(cos(x))/(1 + sin(x)) = (1 - sin(x))/(cos(x)) Mathway Verify the Identity
question
√((6x + 2)² - 4(9)(x²+1))/(2(9)) I got √(12x - 16)/9 → √(4(3x - 4))/9 But the book has √(6x - 8)/9 → √(2(3x -4))/9
answer
Algebra 2
Data
Measure Of Central Tendency
Statistics
Validity and Reliability Assessments-Epidemiology – Flashcards 35 terms

Henry Smith
35 terms
Preview
Validity and Reliability Assessments-Epidemiology – Flashcards
question
What are the three indices of central tendency?
answer
1. mode 2. median 3. mean
question
the most frequently occurring observation
answer
mode
question
the measurement level below which half the observations fall, the 50th percentile
answer
median
question
the sum of the observed measurements divided by the number of observations
answer
mean
question
ability to distinguish between who has a disease and who does not
answer
validity
question
What are two ways to measures validity?
answer
1. specificity 2. sensitivity
question
ability of the test to determine correctly those who have the disease
answer
sensitivity
question
ability of the test to determine correctly those who do not have the disease
answer
specificity
question
true positive/true positive + false negative
answer
sensitivity
question
true negative/true negative + false positive
answer
specificity
question
the degree to which the study accurately answers the question it is intended to answer
answer
internal validity (study)
question
What are threats to internal validity?
answer
1. selection bias 2. information bias 3. uncontrolled confounding 4. small study sample
question
the extent to which we can generalize the results of a study to a broader population beyond the study population
answer
external validity (generalizability)
question
What is the threats to external validity?
answer
1. small study sample 2. improper selection of sample
question
the degree to which a test actually measures what it is designed to measure
answer
measurement validity (variable)
question
What are the threats to measurement validity?
answer
1. observer bias 2. instrument bias
question
restrict the study population to individuals who are comparable in other respects for the outcome under study
answer
increasing validity
question
restrict the study population to individuals whom complete and accurate information can be obtained
answer
increasing validity
question
provides information about the proportion of people who have the disease and those who do not have the disease
answer
predictive value
question
found by dividing the number of true positives by the total number who tested positive (true positives + false positives)
answer
positive predictive value
question
found by dividing the number of true negatives by the total number who tested negative (true negatives + false negatives)
answer
negative predictive value
question
What are the factors that affect the predictive value?
answer
1. prevalence of disease 2. specificity of the test
question
the degree to which a measurement procedure can be reproduced
answer
reliability
question
What are the threats to reliability?
answer
1. differences in observations 2. differences in instruments of measurements 3. instability of the attribute being measured
question
What affects reliability?
answer
1. intrasubject variation 2. intraobserver variation 3. interobserver variation
question
variation within individual subjects
answer
intrasubject variation
question
intrinsic biologic variability in the study subjects due to such things as fluctuations in mood or circadian rhythms
answer
intrasubject variation
question
variation in the reading of test results by the same reader
answer
intraobserver variation
question
variability in measurement that is due to the observer and includes such things as choice of words in an interview.
answer
intraobserver variation
question
variation between those reading the test results
answer
interobserver variation
question
variation between observers
answer
interobserver variation
question
What is used to evaluate interobserver variation?
answer
1. Percent agreement 2. Kappa Statistic
question
total agreed observations/total observations x 100
answer
percent agreement
question
quantifies the agreement that exceeds that which would be expected by chance alone
answer
kappa statistic
question
What are ways to increase reliability?
answer
1. standardizing the study procedures 2. standardizing the measurement methods 3. using the most up to date equipment 4. using similar testing conditions 5. repeat testing of samples
Algebra
Algebra 2
Greater Than Zero
Multiplication
6th Grade Math – 100 things to know – Flashcards 100 terms

Kevin Stewart
100 terms
Preview
6th Grade Math – 100 things to know – Flashcards
question
1. Addition, subtraction, multiplication and division are called the
answer
operations.
question
2. A pneumonic device to help you remember the order of operations is
answer
PEMDAS.
question
3. If an equation contains both addition and subtraction with neither in parenthesis, you do the first one
answer
first.
question
4. If an equation contains both multiplication and division with neither in parenthesis, you do the first one
answer
first.
question
5. The answer to an addition problem is a
answer
sum.
question
6. The answer to a subtraction problem is the
answer
difference.
question
7. The answer to a division problem is a
answer
quotient.
question
8. The answer to a multiplication problem is a
answer
product.
question
9. A lower case letter that stands for an unknown number is a
answer
variable.
question
10. A complete number sentence with an equal sign is called an
answer
equation.
question
11. A combination of numbers and algebraic terms which does not include an equal sign is an
answer
expression.
question
12. An expression does not contain an
answer
equal sign.
question
13. To multiply by 10, move the decimal one place to the
answer
right.
question
14. To multiply by 100, move the decimal two places to the
answer
right.
question
15. To divide by 10, move the decimal one place to the
answer
left.
question
16. To divide by 100, move the decimal two places to the
answer
left.
question
17. Fractions and decimals can be multiplied and divided, but percents
answer
cannot.
question
18. By dividing the numerator by the denominator, a fraction is changed to a
answer
decimal.
question
19. Moving the decimal two places to the right changes a decimal number to a
answer
percent.
question
20. A percent can be changed to a fraction by putting the number over 100 and
answer
reducing to lowest terms.
question
21. When dividing a fraction to change it to a decimal, the top number goes in the
answer
"house".
question
22. To change a percent to a decimal, remove the percent sign and
answer
move the decimal two places to the left.
question
23. To add or subtract fractions, you must first find a common denominator and
answer
change both fractions.
question
24. To add or subtract decimals, you must first
answer
align the decimals.
question
25. To multiply decimals, you multiply the problem first and then put the decimal in the answer,
answer
counting the same number of decimal places from the right as found in the problem.
question
26. To divide by a decimal, change the divisor to a whole number and move the decimal in the dividend
answer
the same number of places to the right.
question
27. To multiply fractions, multiply the numerators and denominators
answer
straight across and simplify.
question
28. To divide fractions,
answer
flip the second fraction and multiply.
question
29. A triangle with all sides congruent is
answer
equilateral.
question
30. A triangle with two congruent sides is
answer
isosceles.
question
31. A triangle with no congruent sides is
answer
scalene.
question
32. Every triangle can be classified by its
answer
sides or angles.
question
33. A triangle with two congruent angles and two congruent sides is
answer
isosceles.
question
34. A triangle with 2 acute angles and one obtuse angle is
answer
obtuse.
question
35. A triangle with 3 angles which measure less than 90° is
answer
acute.
question
36. A triangle with one angle which measures exactly 90° is
answer
right.
question
37. Two values that are the same are
answer
equal.
question
38. Two shapes that are exactly the same are
answer
congruent.
question
39. Two shapes that are the same shape but different sizes are
answer
similar.
question
40. A number can be divided evenly by 2 if it is
answer
even.
question
41. A number can be divided evenly by 5 if it ends
answer
in 5 or 0.
question
42. A number can be divided evenly by 3 if the sum of its digits can be divided evenly by
answer
3
question
43. A number can be divided evenly by 9 if the sum of its digits can be divided evenly by .
answer
9
question
44. A number can be divided evenly by 6 if it is even and can be divided by
answer
3
question
45. A closed figure made of straight lines is a
answer
polygon.
question
46. A polygon with 5 sides is a
answer
pentagon.
question
47. A polygon with 6 sides is a
answer
hexagon.
question
48. A polygon with 7 sides is a
answer
heptagon.
question
49. A polygon with 8 sides is an
answer
octagon.
question
50. A polygon with 10 sides is a
answer
decagon.
question
51. A polygon with 4 sides is a
answer
quadrilateral.
question
52. The symbol for "is less than" is
answer
<.
question
53. When placing numbers on a number line, negative numbers always go the
answer
left of zero.
question
54. When comparing two numbers, the largest is always the one to the
answer
right on a number line.
question
55. When comparing two fractions with different denominators, use the
answer
bottoms-up method.
question
56. When comparing 3 or more fractions with different denominators, you must find a
answer
common denominator.
question
57. When comparing decimals, write the decimals in a list,
answer
align the decimals, annex zeros, and compare.
question
58. An angle measuring exactly 90°is a
answer
right angle.
question
59. An angle measuring less that 90°is called
answer
acute.
question
60. An angle measuring more than 90°is called
answer
obtuse.
question
61. An angle measuring exactly 180°is called a
answer
straight angle.
question
62. Two angles which are next to each other and share a leg are said to be
answer
adjacent.
question
63. Two angles whose measurement totals 90°are
answer
complementary.
question
64. Two angles whose measurement totals 180° are
answer
supplementary.
question
65. When two lines cross, the two angles directly across from each other look like kissing foxes and are classified as
answer
vertical angles.
question
66. Lines that cross are
answer
intersecting lines.
question
67. Lines that cross at a 90° angle are
answer
perpendicular lines.
question
68. Two lines that are in the same plane and stay the same distance apart are
answer
parallel lines.
question
69. Two lines that are not in the same plane and never touch are
answer
skew lines.
question
70. Numbers that only have themselves and one as factors are
answer
prime numbers.
question
71. Numbers that are not prime are
answer
composite.
question
72. Little numbers that are multiplied to make a product are called
answer
factors.
question
73. Two numbers equal distance from zero are called
answer
opposites.
question
74. The distance a number is from zero is called its
answer
absolute value.
question
75. The smallest number in a set of data is called the
answer
minimum.
question
76. The highest number in a set of data is called the
answer
maximum.
question
77. The middle number in a set of data is called the
answer
median.
question
78. The average is also called the
answer
mean.
question
79. To solve for the variable in a one-step equation, you must do the
answer
inverse operation.
question
80. On a coordinate plane, the horizontal number line is called the
answer
x-axis.
question
81. On a coordinate plane, the vertical number line is called the
answer
y-axis.
question
82. The place where the x- and y-axis cross is called the
answer
origin.
question
83. The points on a coordinate plane are designated by two numbers in parenthesis called the
answer
ordered pair.
question
84. In an ordered pair, the first number tells you to go left or right from the
answer
origin.
question
85. In an ordered pair, the second number tells you to go up or down from the
answer
x-axis.
question
86. Compound probability can be displayed by making a
answer
list or drawing trees.
question
87. The list of all possible outcomes when figuring probability is known as a
answer
sample space.
question
88. The result of an experiment or even is an
answer
outcome
question
89. An outcome is always shown as a
answer
whole number.
question
90. Probability is shown as a
answer
decimal or a fraction.
question
91. Sliding a point or one dimensional figure on a coordinate plane is called
answer
translation.
question
92. Flipping a point over an axis on a coordinate plane is called
answer
reflection.
question
93. Turning a figure around a point on a coordinate plane is called
answer
rotation.
question
94. To convert a metric measurement to a smaller unit, move the decimal to the
answer
right.
question
95. To convert a metric measurement to a larger unit, move the decimal to the
answer
left.
question
96. The formula for perimeter of a polygon is
answer
add all sides.
question
97. The formula for area of a square is
answer
side squared. (length x width)
question
98. The formula for area of a rectangle is length times
answer
width.
question
99. The formula for area of a triangle is base times height divided by
answer
two.
question
100. The area of a polygon is always labeled in
answer
square units.
Algebra
Algebra 2
Completing The Square
Quadratic Functions – Vocabulary – Flashcards 20 terms

Martha Hill
20 terms
Preview
Quadratic Functions – Vocabulary – Flashcards
question
Quadratic Function
answer
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
question
Parabola

answer
a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
question
Parent Function

answer
the most basic function of a family of functions, or the original function before a transformation is applied
question
Vertex

answer
the point of intersection of lines or the point opposite the base of a figure
question
Axis Of Symmetry

answer
A line that divides a figure in half so that each half is the mirror image of the other
question
Minimum Value
answer
The lowest point of a parabola (when a>0)
question
Maximum Value

answer
The highest point of a parabola ( when a<0)
question
Intercept Form
answer
y=a(x-p)(x-q)
question
Quadratic Equation

answer
ax² + bx + c = 0
question
x-intercept
answer
x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero
question
Square Root

answer
√(xy) = √x · √y, a number that when multiplied by itself equals a given number
question
Zero Of a Function

answer
a value of x that makes the function's value zero
question
Roots

answer
the solutions to a quadratic equation
question
Perfect Square

answer
a square of a whole number
question
Linear Function

answer
a function in which the graph of the solutions forms a line
question
Exponential Function

answer
a function in which an independent variable appears as an exponent
question
Discriminant

answer
b²-4ac
question
Perfect Square Trinomial
answer
a trinomial in the form a²+2ab+b² or a²+2ab+b²
question
Axis of symmetry (mathematically)
answer
X = - b/2a
question
vertex has a x-coordinate of
answer
X = - b/2a, (X,Y)
Algebra
Algebra 1
Algebra 2
AP Macroeconomics
Macroeconomics
Principles Of Economics: Macroeconomics
Ap Macroeconomics Unit 2 Test Test Questions – Flashcards 87 terms

Henry Lowe
87 terms
Preview
Ap Macroeconomics Unit 2 Test Test Questions – Flashcards
question
A) Rate of Change [IR]
answer
Current Year-Base Year/Base Year [CPI,rGDP]
question
B) Inflation Rate [IR]
answer
Rate of Change x 100 [CPI,rGDP]
question
A) Rate of Change [PI]
answer
Current Year/Base Year
question
B) Price Index [PI]
answer
Rate of Change x 100
question
Real Wage
answer
Wage Rate/Price Level
question
Real Income
answer
Income/Price Level
question
A) Causes of Inflation-Demand Pull
answer
1) Increase in D for g/s 2) Over employment and wage inflation because of economic growth
question
B) Causes of Inflation-Cost & Push
answer
1) Increase in natural disasters, political disasters 2) Decrease in S because increase in input costs
question
C) Causes of Inflation-Political
answer
Government printing of money to cover debts
question
Fixed Rates
answer
1) Payment form loan and savings 2) Doesn't change based on interest rate from inflation
question
Adjusted Rates
answer
Payment could change based on interest rate from inflation
question
A) Frictional Unemployment
answer
Between jobs
question
B) Seasonal Unemployment
answer
Waiting for the right reason in which to work
question
C) Cyclical Unemployment
answer
Victims of the business cycle
question
D) Structural Unemployment
answer
Skills don't match available jobs
question
Labor Force Participation Rate [LFPR]
answer
Labor Force/Population x 100
question
Unemployment Rate [UR]
answer
Number of Unemployed/Labor Force x 100
question
A) GDP 4 Components
answer
C+Ig+G+Xn
question
B) Consumer Spending [C]
answer
Purchases of finished g/s excluding houses
question
C) Gross Private Business Investment Spending [Ig]
answer
1) Factory equipment maitnance-unsold innovatory bolt within a year, but not sold that year 2) New equipment 3) Construction of housing
question
D) Government Spending [G]
answer
Spending on purchases of g/s
question
E) Exports-Imports [Ex]
answer
1) Exports-cash inflow (credits) 2) Inports-cash outflow (debts)
question
Items NOT counted in GDP
answer
1) Intermediate g/s 2) Used Goods 3) Stocks & Bonds 4) Gifts & Transfers 5) Unreported Business Activity 6) Illegal Activity 7) Non-Market Activities
question
Business Cycle Aggregates
answer
1) Price Levels 2) Outputs 3) Unemployment Rates 4) Current Economy
question
Secular Trend [BC]
answer
Private assumption of long term growth
question
Expansion [BC]
answer
Growth for 6 months minimum
question
Peak [BC]
answer
Time expansion ends
question
Contraction Recession [BC]
answer
Decline for 6 months minimum of rGDP
question
Trough [BC]
answer
Time contractions end
question
Six Months [BC]
answer
Minimum time GDP data is relevant
question
Trough to Trough [BC]
answer
"Length" of a cycle
question
Six Years [BC]
answer
Average length of cycle in the US from 1776-2011
question
Fourteen Months [BC]
answer
Average length of recession in the US from 1900-2011
question
Stagflation [BC]
answer
Both expansion & recession at the same time
question
Misery Index [BC]
answer
Unemployment Rate and Inflation Rate together
question
Recession-Chart [BC]
answer
Increase in unemployment rate and inflation
question
Expansion-Chart [BC]
answer
Decrease in unemployment rate and deflation
question
Aggregate Output
answer
Total quantity of final goods and services produced within and economy
question
rGDP
answer
Total value of all final goods and services produced in the economy during a given year, calculated with base years
question
Nominal GDP
answer
Total value of all final goods and services produced in the economy during a given year, calculated with the prices current in the year in which the output is produced
question
Chain-Linking
answer
Method of calculating changes in real GDP using the average between the growth rate calculated using an early base year and the growth rate calculated using a late base year
question
GDP Per Capita
answer
GDP/total population of a country
question
Employed
answer
Currently holding a job in the economy, either full time or part time
question
Unemployed
answer
Not working and looking for work
question
Labor Force
answer
Employed+Unemployed
question
Discouraged Workers
answer
Individuals who would like to work but have given up looking for a job
question
Marginally Attached Workers
answer
A person who currently is neither working nor looking for work but has indicated that he or she wants and is available for a job
question
Underemployed
answer
People who have part- time jobs but want full- time work or whose jobs are below their experience and education level
question
Job Search
answer
Workers who spend time looking for employment
question
Efficiency Wages
answer
Above-equilibrium wages paid by firms to increase worker productivity
question
Natural Rate of Unemployment
answer
Frictional Unemployment + Structural Unemployment
question
Shoe Leather Costs
answer
The increased costs of transactions caused by inflation
question
Menu Costs
answer
The costs of changing prices
question
Unit-of-Account Costs
answer
Arise from the way inflation makes money a less reliable unit of measurement
question
Nominal Interest Rate
answer
Rate actually paid for a loan
question
Real Interest Rate
answer
Nominal Interest Rate - Inflation Rate
question
Disinflation
answer
A reduction in the rate of inflation
question
Aggregate Price Level
answer
A measure of the overall level of prices in the economy
question
Market Basket
answer
A representative collection of goods and services
question
Price Index
answer
1) A measure of price of a specified collection of goods and services in a given year 2) Equal to 100 in base year
question
Consumer Price Index [CPI]
answer
Measures the cost of the market basket of a typical urban American family
question
Producer Price Index [PPI]
answer
Measures changes in the prices of goods and services purchased by producers
question
GDP Deflator
answer
Nominal GDP/Real GDP x 100
question
National Accounts
answer
Keep track of the flows of money between different sectors of the economy
question
Household
answer
Person or group who share income
question
Firm
answer
Organization that produces g/s for sale
question
Product Markets
answer
Where g/s are bought and sold
question
Factor Markets
answer
Where resources, capital and labor, are bought and sold
question
Consumer Spending
answer
Household spending on g/s
question
Stock
answer
A share of ownership in a corporation held by a shareholder
question
Bond
answer
Loan in the form of an IOU that pays interest
question
Government Transfers
answer
Payments by the government to individuals for which no good or service is provided in return
question
Disposable Income
answer
Income remaining for a person to spend or save after all taxes have been paid
question
Private Savings
answer
1) Disposable Income - Consumer Spending 2) Disposable income that is not spent on consumption
question
Financial Markets
answer
Banking, stock, and bond markets, which channel private savings and foreign lending into investment spending, government and foreign borrowing
question
Government Borrowing
answer
The amount of funds borrowed by the government in the financial markets
question
Government Purchases of Goods and Services
answer
Spending by federal, state, and local governments on goods and services
question
Exports
answer
Goods and Services sold to other countries
question
Imports
answer
Goods and services bought from other countries
question
Inventories
answer
Stocks of goods and raw materials held to facilitate business operations
question
Investment Spending
answer
Spending on productive physical capital, such as machinery and construction of structures, and on changes to inventories
question
Final Goods and Services
answer
Goods and services produced for final use
question
Intermediate Goods and Services
answer
Goods and services purchased by firms for further reprocessing and resale for final use
question
GDP
answer
The total market value of all final goods and services produced annually in an economy
question
Aggregate Spending
answer
Consumer Spending + Investment Spending + Government Purchases of goods & services + (exports - imports)
question
Value Added
answer
Value of Sales-Value of Purchases of Inputs
question
Net Exports
answer
Exports - Imports
Algebra 2
Fish
Standard Deviation Of The Mean
Physics GRE 5. Quantum Mechanics and Atomic Physics – Flashcards 59 terms

Viola Marenco
59 terms
Preview
Physics GRE 5. Quantum Mechanics and Atomic Physics – Flashcards
question
5.1 Average Value of Operator, "A", on state psi

answer
question
5.2 Position-Probability Normalization of state psi
answer
question
5.3 Property of Hermitian Operator "Q" acting on states f and g

answer
question
5.4 Position and Momentum Operators
answer
question
5.5 Probability of Obtaining nth eigenvalue
answer
question
5.6 Expectation (Average) Value
answer
question
5.7 Inner product of and a and b (Bracket Notation)
answer
question
5.8 Bracket Notation Inner product commutative property
answer
question
5.9 Hermitian Conjugate Condition for inner product

answer
question
5.10 f(x), inner product relation for continuum states
answer
question
5.11 inner product relation for states f,g with continuous position locations x

answer
question
5.12 Schrodinger Equation
answer
question
5.13 Hamiltonian Operator

answer
question
5.14 Schrodinger, Eigenvalue Equation
answer
question
5.15 Position, Momentum commutation relation
answer
question
5.16 Uncertainty relation of operators A and B based off of their commutator
answer
question
5.17 Statistical variance/ Uncertainty
answer
question
5.18 Uncertainty Product for position and momentum
answer
question
5.19 Order of Magnitude estimate of position and momentum uncertainty

answer
question
5.20 Energy and Time order of magnitude momentum and position uncertainty
answer
question
5.21 One Dimensional Harmonic Oscillator Hamiltonian
answer
question
5.22 One dimensional Harmonic Oscillator Hamiltonian using raising and lowering operators
answer
question
5.23 Commutation relation of lowering and raising operators
answer
question
5.24 One Dimensional Harmonic Oscillator Energy Eigenvalues
answer
question
5.25 Virial's Theorem for Harmonic Oscillator
answer
question
5.26 Three Dimensional Harmonic Oscillator Energy Eigenvalues

answer
question
5.27 Eigenfunctions and Energy Eigenvalues of a free particle
answer
question
5.28 De Broglie Formula

answer
question
5.29 Einstein's relation (energy of a free particle)
answer
question
5.30 General Hamiltonian in Three Dimensions
answer
question
5.31 3 Dimensional, position-momentum commutation along same direction

answer
question
5.32 3 Dimensional, position-momentum commutation along different directions
answer
question
5.33 Radial Wave function Normalization conditions
answer
question
5.34 x component of orbital angular momentum
answer
question
5.35 y component of orbital angular momentum

answer
question
5.36 z component of orbital angular momentum
answer
question
5.37 Commutator relation of orthogonal components of orbital angular momentum
answer
question
5.38 Total orbital angular momentum
answer
question
5.39 Z component of angular momentum acting on a spherical harmonic state
answer
question
5.40 Total orbital angular momentum acting on a spherical harmonic state
answer
question
5.41 Allowed values of m (magnetic moment) in terms of l (orbital angular momentum)

answer
question
5.42 Orthonormaility of Spherical Harmonics

answer
question
5.43 Hamiltonian of Hydrogen Atom
answer
question
5.44 Bohr Radius
answer
question
5.45 Un-normalized Ground state of Hydrogen Atom
answer
question
5.46 Hydrogen Ground State Energy
answer
question
5.47 nth Energy Eigenvalues of Hydrogen considering quantum number n only
answer
question
5.48 fine structure constant

answer
question
5.49 spin up and down along x in the z basis
answer
question
5.50 spin up and down along y in z basis
answer
question
5.51 Raising and Lowering Operators for spin 1/2 in terms of spin along x and y
answer
question
5.54 Adding spins s and s'
answer
question
5.55 Adding z component of spin quantum number m

answer
question
5.56 Singlet State a system of 2 spin 1/2 particles
answer
question
5.57 Perturbation Theory, 1st order energy Shift
answer
question
5.58 Perturbation Theory, 2nd order energy shift

answer
question
5.59 Eigenvalues of Spin-Orbit Operator, fine structure perturbation
answer
question
5.60 Change in Hamiltonian from Stark Effect
answer
question
5.61 Change in Hamiltonian for Zeeman Effect
answer
Algebra 1
Algebra 2
The Hunger Games Vocabulary Chapter 22-27 20 terms

Alice Rees
20 terms
Preview
The Hunger Games Vocabulary Chapter 22-27
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
question
How would you go about doing x times 5%?
answer
1.05x
Algebra 1
Algebra 2
Fractions
Multiplication
Math study guide 29 terms

Marta Browning
29 terms
Preview
Math study guide
question
Write two equivalent fractions: 1/6
answer
2/12, 4/24
question
Write two equivalent fractions: 3/5
answer
6/10, 12/20
question
Write two equivalent fractions: 6/10
answer
12/20, 24/40
question
Add the sign (><= ) 1/3___1/5
answer
>
question
Add the sign (><= ) 13/14___3/14
answer
>
question
Add the sign (><= ) 3/7___6/14
answer
=
question
Add the sign (><= ) 5/16___3/5
answer
<
question
Write the set of fractions in order from small to big: 4/10, 3/10, 9/10, 7/10, 5/10
answer
3/10, 4/10, 5/10, 7/10, 9/10
question
Write the set of fractions in order from small to big: 1/3, 1/14, 1/2, 1/7, 1/8
answer
1/14, 1/8, 1/7, 1/3, 1/2
question
If the pattern block trapezoid is the whole, what fraction of the whole is the pattern block triangle.
answer
1/3
question
________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction of the given rectangle are 2 squares?
answer
1/2
question
________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction is 1 rectangle?
answer
1/2
question
________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction of the rectangle do 2 squares and 1 rectangle cover?
answer
1
question
If the cube represents 1/10, what represents the unit whole?
answer
1/10
question
Sara had 8 quarters. She spent 1/4 of them on video games. a. How many quarters did she spend?
answer
2
question
Sara had 8 quarters. She spent 1/4 of them on video games. b. How many quarters does she have left?
answer
6
question
Sara had 8 quarters. She spent 1/4 of them on video games. c. How much money does she have left?
answer
$1.50
question
Multiply. Use a paper and pencil algorithm of your choice. 40*65 = ______
answer
2,600
question
Multiply. Use a paper and pencil algorithm of your choice. _____=54*61
answer
3,294
question
Divide. Use a paper and pencil algorithm of your choice. 65/2=____
answer
32 r 1
question
Multiply. Use a paper and pencil algorithm of your choice. 7/495=___
answer
70r5
question
Which fraction is larger: 5/16 or 3/5? Explain how you know.
answer
...
question
Add or subtract. Use pattern blocks. ___/___=6/9 +3/9
answer
9/9
question
___/___=2/4+2/4
answer
4/4
question
3/4-1/4= ___/___
answer
2/4
question
6/9-1/9=___/___
answer
5/9
question
Solve using pattern blocks. Explain your strategy. 1/6+1/3=____
answer
1/6+2/6=3/6
question
It took Denise1/3 of an hour to drive from Zion to Platt and 2/6 of an hour to drive from Platt to Rome. To figure out her total driving time, Densie wrote the following number model: 1/3+2/6=3/9.
answer
2/6+2/6=4/6
question
Do you agree that it took her about 3/9 of an hour? Explain your answer.
answer
NO!!!! Because you don't add the top AND the bottom!!!!!
Algebra
Algebra 1
Algebra 2
College Algebra Final Exam 30 terms

Kevin Stewart
30 terms
Preview
College Algebra Final Exam
question
Remainder Theorem
answer
If polynomial p(x) of degree n>1 is divided by (x-a) where a is a constant, then the remainder is p(a)
question
Find minima or maxima
answer
find -b/2a and than plug back in to equation
question
What strategies can you use to find all the zeros of a polynomial?
answer
synthetic division, graphing, factoring
question
Percent Profit Formula
answer
Percentage Profit = ((selling price-cost price)/(cost price))*100
question
Polynomials
answer
Monomial- 5x2 Binomial- 2x2+5x Trinomial- 5x2+3x+6
question
The Rational Roots Test p/q
answer
This relationship is always true: If a polynomial has rational roots, then those roots will be fractions of the form (plus-or-minus) (factor of the constant term) / (factor of the leading coefficient). However, not all fractions of this form are necessarily zeroes of the polynomial. Indeed, it may happen that none of the fractions so formed is actually a zero of the polynomial. Find all possible rational x-intercepts of x4 + 2x3 - 7x2 - 8x + 12. The constant term is 12, with factors of 1, 2, 3, 4, 6, and 12. The leading coefficient in this case is just 1, which makes my work a lot simpler. The Rational Roots Test says that the possible zeroes are at: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved ± 1, 2, 3, 4, 6, 12 = -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12
question
Graphs of Polynomials: Predicting End Behavior of a Function
answer
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function.
question
Graphs of Polynomials: Predicting End Behavior of a Function (2)
answer
Polynomial End Behavior: 1. If the degree n of a polynomial is even, then the arms of the graph are either both up or both down. 2. If the degree n is odd, then one arm of the graph is up and one is down. 3. If the leading coefficient an is positive, the right arm of the graph is up. 4. If the leading coefficient an is negative, the right arm of the graph is down.
question
Graphs of Polynomials: Predicting End Behavior of a Function (3)
answer
To predict the end-behavior of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
question
Graphs of Polynomials: Turning Points
answer
Turning Points A Turning Point is an x-value where a local maximum or local minimum happens:
question
How many turning points does a polynomial have?
answer
Never more than the Degree minus 1
question
How do you determine the degree of a polynomial?
answer
The Degree of a Polynomial with one variable is the largest exponent of that variable.
question
How do the graphs of polynomials behave?
answer
Graphs will be continuous and smooth Even exponents behave the same: above (or equal to) 0; go through (0,0), (1,1) and (-1,1); larger values of n flatten out near 0, and rise more sharply. Odd exponents behave the same: go from negative x and y to positive x and y; go through (0,0), (1,1) and (-1,-1); larger values of n flatten out near 0, and fall/rise more sharply Factors: Larger values squash the curve (inwards to y-axis) Smaller values expand it (away from y-axis) And negative values flip it upside down Turning points: there will be \"Degree-1\" or less. End Behavior: use the term with the largest exponent
question
Hooke's Law
answer
The formula for Hooke's Law is \"F = kd\", where \"F\" is the force and \"d\" is the distance. (Note that, in physics, \"weight\" is a force. These Hooke's Law problems are often stated in terms of weight, and the weight is the force.)
question
Variation Equations
answer
\"F varies as x\" means F = kx \"F varies jointly as x and y\" means F = kxy \"F varies as x + y\" means F = k(x + y) \"F varies inversely as x\" means F = k/x
question
Graphing Rational Functions
answer
To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph.
question
Rational Functions: find the vertical asymptotes
answer
set the denominator equal to zero to find any forbidden points
question
Rational Functions: find the horizontal or slant asymptote
answer
If the numerator and denominator have the same degree (they're both linear), the asymptote will be horizontal, not slant, and the horizontal asymptote will be the result of dividing the leading coefficients
question
Vertical Asymptotes
answer
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as logarithms, but you'll almost certainly first encounter asymptotes in the context of rationals.)
question
Suggested Attack to Finding Zeros of a Polynomial
answer
1. Identify the total number of real or complex zeros (corollary to Fundamental Theorem of Algebra). 2. Identify the possible number of positive, negative, and complex zeros (Descartes' Rule of Signs). 3. List the possible rational zeros (Rational Root Theorem) 4. Try possible rational zeros until you find one that works. 5. After each division by a positive value, check for possible upper bounds. 6. After each division by a negative value, check for possible lower bounds (Upper and Lower Bound Theorems) 7. After you find a possible rational root that actually works, take the quotient and continue to try to factor it until it is down to a quadratic or less. Once it is a quadratic or less, there are other ways to solve it. 8. Write the linear and or linear / irreducible quadratic factorization (next section)
question
Rational Root Test
answer
If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient. Make sure the polynomial has integer coefficients. Multiply to get rid of fractions or decimals if need be (be sure to later divide). This only addresses the rational zeros. There may be real, but non-rational roots. There may be complex roots involving i. This says that rational zeros will have this form. It does not say that everything that has this form is a rational zero. What it does give you is a list of possible rational zeros Example: f(x) = 4x^5 - x^2 + 12 Possible rational zeros will be of the form (factor of 12) over (factor of 4). A division table can help you find all these values
question
Descartes' Rule of Signs
answer
The maximum number of positive real roots can be found by counting the number of sign changes in f(x). The actual number of positive real roots may be the maximum, or the maximum decreased by a multiple of two. The maximum number of negative real roots can be found by counting the number of sign changes in f(-x). The actual number of negative real roots may be the maximum, or the maximum decreased by a multiple of two. Complex roots always come in pairs. That's why the number of positive or number of negative roots must decrease by two. Consider: f(x) = 3x^6 + x^5 - x^4 + 3x^3 + 2x^2 - x + 1. The signs in f(x) are + + - + + - +. There are 4 sign changes (+ to -) or (- to +). Now, f(-x) = 3x^6 - x^5 - x^4 - 3x^3 + 2x^2 + x + 1. The signs in f(-x) are + - - - + + +. There are 2 sign changes (+ to -) or (- to +).
question
Complex Roots
answer
Complex solutions come in pairs. If (a+bi) is a solution, then its complex conjugate (a-bi) is also a solution.
question
Corollary to the Fundamental Theorem of Algebra
answer
Every polynomial in one variable of degree n, n > 0, has exactly n real or complex zeros.
question
Fundamental Theorem of Algebra
answer
Every polynomial in one variable of degree n, n > 0, has at least one real or complex zero.
question
Synthetic Division
answer
Synthetic Division To divide a polynomial synthetically by x-k, perform the following steps. Setup Write k down, leave some space after it. On the same line, right the coefficients of the polynomial function. Make sure you write the coefficients in order of decreasing power. Be sure to put a zero down if a power is missing. Place holders are very important For now, leave a blank line. Draw the left and bottom portions of a box. The left portion goes between the k and the coefficients. The bottom portion goes under the blank line you left. Synthetic Division Once you have things set up, you can actually start to perform the synthetic division. Bring the first coefficient down to the bottom row (below the line) Multiply the number in the bottom row by the constant k, and write the product in the next column of the second row (above the line). Add the numbers in the next column and write the total below the line. Repeat steps 2 and 3 until all the columns are filled. Interpreting the Results The very last value is the remainder. If the remainder is zero, you have found a zero of the function. The rest of the values are the coefficients of the quotient. Each term will be raised to the one less power than the original dividend. (If it was a fourth degree polynomial to start with, the quotient will be a third degree polynomial).
question
Remainder Theorem
answer
When a polynomial function f is divided by x-k, the remainder r is f(k). Okay, now in English. If you divide a polynomial by a linear factor, x-k, the remainder is the value you would get if you plugged x=k into the function and evaluated. Now, tie that into what we just said above. If the remainder is zero, then you have successfully factored the polynomial. If the remainder when dividing by (x-k) is zero, then the function evaluated at x=k is zero and you have found a zero or root of the polynomial. Plus, you now have a factored polynomial (the quotient) which is one less degree than the original polynomial. If the quotient is down to a quadratic or linear factor, then you can solve and find the other solutions.
question
What are the real zeroes of a polynomial?
answer
The real (that is, the non-complex) zeroes of a polynomial correspond to the x-intercepts of the graph of that polynomial. So you can find information about the number of real zeroes of a polynomial by looking at the graph, and conversely you can tell how many times the graph is going to touch or cross the x-axis by looking at the zeroes of the polynomial (or at the factored form of the polynomial).
question
Guidelines for Graphing Polynomial Functions
answer
1. Zeros 2. Test Points 3. End Behavior 4. Graph
question
How do you determine Local Extrema
answer
The amount of local extrema is determined by n - 1, where as N is the highest exponent in the graph. A graph of x4 will have 3 local extrema.
Algebra
Algebra 1
Algebra 2
College Algebra Final Review 48 terms

Margaret Bruce
48 terms
Preview
College Algebra Final Review
question
What is the special factorization of A^3-B^3?
answer
(A-B)(A^2+AB+B^2)
question
What is the special factorization of A^3+B^3?
answer
A+B)(A^2-AB+B^2)
question
When is a relation a function?
answer
If each member of the domain corresponds to exactly one member of the range
question
How can you test whether a graph is demonstrating a function?
answer
Use the vertical line test
question
A horizontal line is represented by
answer
y=#
question
A vertical line is represented by
answer
x=#
question
What is the equation for slope?
answer
(Y2-Y1/X2-X1)
question
What is the point slope form equation?
answer
Y-Y0=m(X-X0)
question
How do you test for an odd function?
answer
Replace x with -x and see if the resulting equation is completely opposite of the original.
question
Odd functions are symmetric with respect to the
answer
x-axis
question
How do you test for an even function?
answer
Replace x with -x and see if the resulting equation is identical to the original
question
What does the basic graph y=x look like?
answer
diagonal line going up towards right corner
question
What does the basic graph y-x^2 look like?
answer
U
question
What does the basic graph y=sqrt(x) look like?
answer
half parabola on right half of graph moving up towards right
question
What does the basic graph y=x^3 look like?
answer
two parabola halves, left bottom is left half of arch, right upper is right half of a u, more vertical
question
What does the basic graph y=cube root of x look like?
answer
two parabola halves, one on left and one on right, more horizontal
question
What does the basic graph y=1/x look like?
answer
Two flipped curves approaching horizontal and vertical asymptotes
question
What does the basic graph abs value (x) look like?
answer
V
question
A vertical reflection flips the graph over which axis?
answer
The x axis
question
A horizontal reflection reflects the graph over which axis?
answer
The y axis
question
What is the equation for a vertical reflection?
answer
-f(x)
question
What is the equation for a horizontal reflection?
answer
f(-x)
question
In the function af(x), the graph will stretch ____ by a factor of __ if ___
answer
vertically, a, abs value (a)>1
question
In the function af(x), the graph will shrink __by a factor of ___if ____
answer
vertically, a, 0<abs value (a)<1
question
In the function f(cx), the graph will stretch ___ by a factor of ___ if ___
answer
horizontally, 1/c, if 0<abs value (c)<1
question
In the function f(cx), the graph will shrink ___ by a factor of ___if ___
answer
horizontally, 1/c, abs value(c)>1
question
How would you find the axis from a quadratic equation?
answer
x: -b/2a, then plug into quadratic for y
question
What will the end behavior of a positive coefficient to the even degree leading an equation look like?
answer
Up on both ends
question
What will the end behavior of a negative coefficient to the even degree leading an equation look like?
answer
Down on both ends
question
What will the end behavior of a positive coefficient to an odd degree look like?
answer
Down on left up on right
question
What will the end behavior of a negative coefficient to an even degree look like?
answer
Up on left, down on right
question
How does one find horizontal asymptote?
answer
Divide leading coefficients of top and bottom
question
How does one find vertical asymptotes?
answer
Set bottom equal to zero
question
How does one find zeros?
answer
numerator equal to zero
question
When will an x-intercept be a bounce?
answer
if it's to an even degree
question
When will an x-intercept be a cross?
answer
if it's to an odd degree
question
How do you find a y-intercept of a rational function?
answer
replace x values with zero
question
What does it mean to be one to one?
answer
Each x corresponds with only one y and each y corresponds with only one x
question
How can we test for one-to-one functions?
answer
Horizontal and vertical line test
question
In exponential graphs, exponential growth occurs when in the function a^x ____
answer
A>1
question
In exponential graphs, exponential decay (lowercase L shape) occurs when in the function a^x___
answer
0<a<1
question
In the exponential graph y=a^x, the points (__,__) and (__,___) are always present
answer
(0,1) (1,a)
question
In exponenetial functions, the horizontal asymptote is always y=0 unless
answer
vertical shift occurs
question
To find the y intercept in an exponeniial function, replace x with
answer
zero
question
In logarithmic graphs, growth occurs (in the shape of the left half of an arch) when in the equation logbasea(x), __
answer
a>1
question
In logarithmic graphs, decay occurs (in the shale of a lowercase L) when in the function logbasea(x)__
answer
0<a<1
question
in logarithmic graphs logbasea(x), what two sets of points are always present?
answer
(1,0) (a,1)
question
What does the change of base formula look like for the equation logbasea(x)?
answer
lnx/lna
Algebra 2
Equations
college mathematics one finals 34 terms

Misty Porter
34 terms
Preview
college mathematics one finals
question
1) -42x + 36 < - 6 (6x-8)
answer
.
question
2) X12/X9
answer
.
question
3) 12X / 3X
answer
.
question
4) (X-5) (X + 5X)
answer
.
question
5) X - 13X + 36
answer
...
question
6) 5X-5 . 6X X 9X-9
answer
...
question
7) Identify which graphs corresponds to the point ( 5, -3 )
answer
...
question
8) Identify the intercepts on the ff graph: x-intercept is -1, y-intercept is 4
answer
...
question
9) When 5 is added to 4X a no. the number increases by 35, Find the no.
answer
...
question
10) (6+9i) - (-5+i)
answer
...
question
11) Find the value of X : 3X - 2 = 2
answer
...
question
12) Find the value of X: IxI = 8
answer
...
question
13) This relation is a function: {(-6,-7), (-1,4),(3,4),(3,-7)} True/False
answer
...
question
14) The ff graph represents a function True or False
answer
...
question
15) Which of the ff equations corresponds to the given graph? y = -2x - 3
answer
...
question
16) Given f(x)= 8x-2 and g(x)= 2x-3 find f-g
answer
...
question
17) Solid line=f(x), In which one of the 4 graphs does the dotted line represent g(x) = f(x-2) ?
answer
...
question
18) Find the midpoint of the line bet. two points (-5,2) and (2,7)
answer
...
question
19) Solve the system: 2y = x+16 5x + 10y = 0
answer
...
question
20) Solve the system x-6y=11, 4x-7y=10
answer
...
question
21)Solve the system: x+3y+4z=-14 4y+2z= -22, z = -1
answer
...
question
23) Solve the system of equations: -5x-y-8z= -49, -4x-6z= -36, 6y+z= 20
answer
...
question
24) Using Cramer's Rule solve the ff system 6x = -4y-10, 5x = -y-13
answer
...
question
25) Express the solution set of -27 < -4x + 1< -7 in interval notation
answer
...
question
26) Express the solution set of Ix+3I -9 < -3 in interval notation
answer
...
question
27) Determine the domain of the ff function [ 1, oo )
answer
...
question
28) Find the inverse of the ff function : f(x) = x + 5 if x > 0
answer
...
question
29) Which graph represents the solution to the following inequalities? x -3
answer
...
question
31) Write the equation of a line in slope-intercept form passing through (5,2) and parallel to y= -1/2x +2
answer
...
question
32) If f(x)= 4x + 4x + 8 and g(x)=4x-4 find ( g o f ) (x)
answer
...
question
33) Write the standard form of the equation of a circle with center (3, -1) and a radius of 6
answer
...
question
36) Solve (2x+9) +2 = 3(x+8)
answer
...
question
38) Solve 2x = -6x -2
answer
...
question
40) Use the rational zero theorem to list all the possible rational zeros for f(x)= x -5x +3x +2
answer
...
Algebra 2
College Prep Algebra I Midterm Vocabulary 60 terms

Ken Ericksen
60 terms
Preview
College Prep Algebra I Midterm Vocabulary
question
algebraic expression
answer
a collection of numbers, variables, and operations
question
base
answer
the number being multiplied in a power
question
domain
answer
the list of inputs in a function (x)
question
equation
answer
formed when an equal sign (=) is placed between two expressions creating a left and right side
question
evaluate
answer
replacing each variable in an expression by a number
question
exponent
answer
value that shows how many times the base is being multiplied by itself
question
function
answer
a rule that establishes a relationship between two quantities (input/output)
question
inequality
answer
formed when a symbol such as (<) is placed between two expressions
question
input
answer
(x) in a function
question
order of operations
answer
to evaluate an expression with more than one operation
question
ordered pair
answer
A pair of numbers that can be used to locate a point on a coordinate plane (x,y)
question
output
answer
(y) in a function
question
power
answer
an expression that contains a base and exponent
question
range
answer
the list of outputs in a function (y)
question
simplify
answer
to write an expression in a simpler form; also used to indicate "evaluation"
question
solution
answer
the value in place of the variable that makes the equation or inequality true
question
variable
answer
a letter that is used to represent one or more numbers
question
absolute value
answer
The distance a number is from zero on a number line
question
coefficient
answer
A number multiplied by a variable in an algebraic expression
question
constant
answer
a term that does not contain a variable in an expression or equation
question
coordinate
answer
a number that identifies a position relative to an axis
question
Distributive Property
answer
a(b + c) = ab + ac; a number outside the parentheses can be multiplied to each term within the parentheses
question
integer
answer
numbers on a number line that can be positive, negative or zero
question
like terms
answer
terms that have identical variables and exponents; when simplifying an expression, you can combine these
question
matrix
answer
a rectangular array of numbers into horizontal rows and vertical columns
question
opposites
answer
two numbers that are the same distance from zero on a number line, but are in opposing directions. (-2 and 2)
question
real number
answer
all rational or irrational numbers; these numbers can be represented on the number line
question
reciprocal
answer
The inverse of a fraction; when multiplied by the original fraction, it results in a product that equals one
question
speed
answer
a rate at which something happens
question
terms
answer
values in an equation or expression that are separated by operations such as multiplying, adding, subtracting, or dividing
question
velocity
answer
speed in a given direction
question
Division Property of Equality
answer
if you divide the same number to each side of an equation, the two sides remain equal
question
Addition Property of Equality
answer
if you add the same number to each side of an equation, the two sides remain equal
question
formula
answer
an expression or equation that is set to solve real-life fundamental principles
question
inverse operations
answer
operations that undo each other, such as addition and subtraction
question
linear equation
answer
an equation whose graph is a line
question
Multiplication Property of Equality
answer
if you multiply the same number to each side of an equation, the two sides remain equal
question
ratio
answer
a comparison of two quantities by division
question
simplest form
answer
an algebraic expression in this form has no like terms and no parentheses; also a fraction that cannot be reduced
question
Subtraction Property of Equality
answer
if you subtract the same number to each side of an equation, the two sides remain equal
question
unit rate
answer
a rate per one given unit, such as 60 miles per one gallon
question
constant of variation
answer
the slope, or rate of change, in the equation y=kx, represented by k
question
coordinate plane
answer
formed by a horizontal number line called the x-axis and a vertical number line called the y-axis
question
direct variation
answer
an equation of the form y=kx, where k does not equal 0
question
function notation
answer
an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x
question
origin
answer
the point of intersection of coordinate axes (0,0)
question
slope
answer
the steepness of a line on a graph, equal to its vertical change divided by its horizontal change (rise over run)
question
slope intercept form
answer
y=mx+b, where m is the slope and b is the y-intercept of the line.
question
standard form
answer
Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
question
x-axis
answer
the horizontal axis on a coordinate plane
question
x-coordinate
answer
The value on the x-axis used to locate a point on the coordinate graph. It is the first value in an ordered pair.
question
x-intercept
answer
the x-coordinate of a point where a graph crosses the x-axis
question
y-axis
answer
the vertical axis on a coordinate plane
question
y-coordinate
answer
The value on the y-axis used to locate a point on the coordinate graph. It is the second value in an ordered pair.
question
y-intercept
answer
the y-coordinate of the point where the line crosses the y-axis
question
Communitive Property
answer
when adding or multiplying, you can switch the numbers
question
Associative Property
answer
states you can change the groupings of additions or multiplications ex. (4+5)+8=4+(5+8)
question
Property of Zero
answer
any number multiplied by 0 will equal 0
question
Identity Property of Multiplication
answer
the product of any number and 1 is equal to the original number (a x 1 = a)
question
Identity Property of Addition
answer
The property that states: the sum of any number & zero is that number; n + 0 = n
Algebra 2
Expressions
Geometry
Geometry for College Students 29 terms

Bernice Cooper
29 terms
Preview
Geometry for College Students
question
Let P,Q, and R be the points of tangency of the incircle of ∆ABC with sides BC, CA, and AB, respectively. Then lines AP, BQ, and CR:
answer
are concurrent.
question
Gergonne point
answer
Point of congruency of lines AP, BQ, and CR, where P,Q, and R are the points of tangency of the incircle of ∆ABC.
question
Ceva's Theorem: Let AP, BQ, and CR be three lines joining the vertices of ∆ABC to pints P, Q, and R on the opposite sides. Then these three lines are concurrent if and only if:
answer
(AR/RB)(BP/PC)(CQ/QA) = 1
question
Given distinct points A and B and a positive number µ, there is exactly ______ point X such that _________________. Also there is at most _________ other point on the line ____ for which this equation holds.
answer
one AX/XB = µ one AB
question
Let AP, BQ, and CR be Cevians in ∆ABC, where P, Q, and R lie on sides BC, CA, and AB respectively. If these Cevians are concurrent at point T, then:
answer
AT/AP = [(AR·CQ) + (QA·RB)] / [AR·CQ) + (QA·RB) + (RB·CQ)]
question
Let T be the Gergonne point of ∆ABC. If coincides with the incenter or the circumcenter or the orthocenter or the centroid of ∆ABC, then:
answer
The triangle must be an equilateral.
question
Let U and V be points on sides of AB and AC, respectively, of ∆ABC and suppose UV is parallel to BC. Then the intersection of UC and VB:
answer
lies on the median of AM.
question
The lines joining the vertices of a triangle to the points of tangency of the opposite exscribed circles are:
answer
concurrent.
question
Given three concurrent Cevians in a triangle, the the lines obtained by joining the midpoints of the Cevians to the midpoints of the coorresponding sides are:
answer
concurrent.
question
Suppose Cevians AP, BQ, and CR are concurrent at point T so that ∆ABC is decomposed into six small triangles. If areas of ∆ART, ∆BPT, and ∆CQT are equal, then:
answer
All six small triangles have equal areas.
question
General Form of Ceva's Theorem: Let AP, BQ, and CR be Cevians of ∆ABC, where points P, Q, and R lie on lines BC, CA, and AB, respectively. Then these Cevians are either concurrent OR parallel if and only if:
answer
an ODD number of them are interior and (AR/RB)(BP/PC)(CQ/QA) = 1
question
In figure 4.5 on p 135, BQ/QC = ___ and XP/PY = ______. And if XP/PY =BQ/QC, then:
answer
st/ru; [s(t+u)]/[u(r+s)] then both ratios are equal to 1 and in that case XY is parallel to BC.
question
If Cevians AP, BQ, and CR are parallel, then:
answer
the Cevian product is trivial.
question
Angular Cevian Product: Suppose that AP, BQ, and CR are Ceviansin ∆ABC. Then the corresponding Cevian product is equal to:
answer
[sin(∠ACR)sin(∠BAP)sin(∠CBQ)]/[sin(∠RCB)sin(∠PAC)sin(∠QBA)] In particular, the three Cevians are concurrent or parallel if and only if an odd number of them are interior and this angular Cevian product is equal to 1.
question
Given an arbitrary ∆ABC, build three outward-pointing triangles BCU, CAB, and ABW, each sharing a sides with the original triangle. Assume that ∠BAW = ∠CAV, ∠CBU = ∠ABW, and ∠ACV = ∠BCU. And assume that AU, BV, and CW cut across the interior of ∆ABC. Then:
answer
lines AU, BV, and CW are concurrent.
question
The pedal triangle of acute ∆ABC is ∆DEF, and perpendicular AU, BV, and CW are dropped from the vertices of the original triangle to the sides of the pedal triangle. Then lines AU, BV, and CW are:
answer
concurrent and the point of concurrence is at the circumcenter.
question
If Cevians AP, BQ, and CR of ∆ABC are concurrent or parallel, then:
answer
their isogonal Cevians are also concurrent or parallel.
question
Isogonal line:
answer
The line reflected across an angle bisector.
question
Symmedians:
answer
The isogonals of the medians.
question
Lemoine point:
answer
The point of concurrence of the symmedians.
question
Isogonal conjugate:
answer
The point of concurrence of the isogonal lines.
question
Let X be a point other than A, B, or C on the circumcircle of ∆ABC. Then:
answer
the isogonal Cevians of AX, BX, and CX are parallel.
question
Let X be any point in the interior of ∆ABC and let Y be the circumcenter of the triangle whose vertices are the reflections of X in the sides of ∆ABC. Then:
answer
Y is the isogonal conjugate of X with respect to ∆ABC.
question
Let ABCDEF be a hexagon inscribed in a circle. Then the diagonals AD, BE, and CF are concurrent if and only if:
answer
(AB/BC)(CD/DE)(EF/FA)=1
question
Given and acute angled ∆ABC, show that the lines joining A, B, and C to the midpoints of the nearer sides of the pedal triangle are:
answer
concurrent
question
The only point in the interior of ∆ABC that is its own isogonal conjugate is:
answer
the incenter.
question
If ∆ABC is not a right triangle then the circumcenter and orthocenter are:
answer
isogonal conjugates.
question
If ∠C = 90 in ∆ABC, then the Lemoine point of the triangle lies on:
answer
the altitude from vertex C.
question
If the Lemoine point of ∆ABC lies on the altitude from vertex C, then:
answer
either AC = BC or ∠C = 90.
Algebra
Algebra 1
Algebra 2
Form
Algebra 2 – Flashcards 602 terms

Brandon Ruffin
602 terms
Preview
Algebra 2 – Flashcards
question
What is an equation for a direct variation whose graph passes through the point (-5, 3)?
answer
y=-3/5x
question
Which line, having the given slope and passing through the given point, represents a direct variation?
answer
m= 2/3 ; (9, 6)
question
The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.
answer
True Test: “Study Guide Algebra”
question
A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour?
answer
525
question
The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?
answer
y = x + 6
question
A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.
answer
False
question
What is the vertex of the graph of y = |x| - 6?
answer
(0, -6)
question
Which is the graph of the equation y = |x - 1|?
answer
Graph C
question
The graph of an absolute value function will always be an upward-pointing V shape.
answer
False
question
Which is the graph of 0.4x + 0.1y ≥ 1?
answer
Graph B
question
What is the graph of
answer
Graph D
question
This is the graph of y < |x - 3|.
answer
True
question
Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.
answer
no solution
question
What is true about the system
answer
The system is consistent and independent.
question
A dependent system of equations will have infinitely many answers.
answer
True
question
Jim's wages vary directly with the numbers of hours he works. For 7 hours, he makes $38.85. How much will he make in 37 hours?
answer
$205.35
question
Which line, having the given slope and passing through the given point, represents a direct variation?
answer
C.
question
The graph below models the burning of a candle. At time t = 0, the candle was 8 inches tall. If the candle burns at a rate of 2 inches per hour, what equation models the height h of the candle after burning for t hours?
answer
h = -2t + 8
question
The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?
answer
y = 4x + 10
question
What is the equation of the graph?
answer
y = |x + 5|
question
What is an inequality for this graph?
answer
y - 3x ≥ -5
question
Which is the graph of
answer
Graph C
question
Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.
answer
no solution
question
Which ordered pair is the solution to the given system of equations?
answer
(-3, -4)
question
Two parallel lines form an inconsistent system of equations that has no solution.
answer
True
question
Solve the system of equations. 2x - 4y = 3 -3x + 5y = 1
answer
B.
question
Use substitution to solve the system of equations given below.
answer
(-10, -12)
question
Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).
answer
True
question
Use elimination to solve the system given below. 5x - 2y = 25 5x + 3y = 5
answer
A.
question
Use elimination to solve the system of equations given by 10x - 40y = 60 and 15x + 40y = -10.
answer
(2, -1)
question
Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.
answer
True
question
Which point is in the solution set of this system of inequalities?
answer
(0, 4)
question
Identify the graph that shows the solution to the system of inequalities.
answer
A.
question
A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.
answer
False
question
What is the maximum for the objective function for this graph?
answer
560
question
A factory can produce two products, x and y, with a profit P approximated by P = 12x + 15y. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1000. What production levels yield maximum profit?
answer
x = 1000; y = 0
question
When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.
answer
True
question
Which point lies in the plane represented by the equation 2x + 7y + 3z = 25?
answer
(6, 4, -5)
question
A point (x, y, z) can be used to represent the location of a geographical point in space, where x represents the latitude in degrees, y represents the longitude in degrees, and z represents the elevation in feet above or below sea level. Jerimoth Hill is the highest point of elevation in Rhode Island. It is 812 feet above sea level and lies at about 42° north latitude and 72° west longitude. What ordered triple represents the location of Jerimoth Hill?
answer
(42°, -72°, 812)
question
An equation using three variables is graphed in coordinate space.
answer
True
question
A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?
answer
Bus: d1 = 45t + 90; Car: d2 = 60t
question
An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?
answer
Graph C
question
Classify the system.
answer
independent
question
If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations.Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.
answer
Method II
question
A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them. If x represents the number of type A printers sold, and y represents the number of type B printers sold, what are the constraints for a linear program that models this problem?
answer
A.
question
A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?
answer
question
In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?
answer
C.
question
Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?
answer
Brenda ran 9 miles; Anne ran 6 miles
question
Solve the system of equations. x = 3y + 2z 2x + 3y + 2z = 3 -x + y - z = 6
answer
(1, 3, -4)
question
Solve the system of equations. 2x + y - z = 3 x + y + z = 5 x - 2y + z = 2
answer
(2, 1, 2)
question
Solve the system of three equations by elimination: 5x + 2y - 3z = 10 2x - 2y + 4z = 6 x - y + 2z = 3
answer
infinitely many solutions
question
The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?
answer
72
question
The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?
answer
48
question
What steps would you use to plot (-3, -4, 0) in a three-dimensional coordinate system?
answer
From the origin, move back 3 units and left 4 units.
question
Which statement about 5y = 2x is true?
answer
A.
question
Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?
answer
From the origin, move forward 7 units, left 6 units, and down 5 units.
question
The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?
answer
Graph A
question
The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?
answer
y = 1.25x + 1; y = 21
question
You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?
answer
$162.50
question
Which system of equations is graphed below?
answer
C.
question
Solve the system of equations by using substitution. -2x + 3y = 7 4x - 6y = 8
answer
no solution
question
Solve the system of equations by using substitution. y = 2x + 1 3x - y = 4
answer
(5, 11)
question
Use substitution to solve the system of equations given below.
answer
no solution
question
Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.
answer
A.
question
Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6.
answer
(2, -2)
question
Use elimination to solve the system of equations. -x + 2y = 18 x + 8y = -38
answer
(-22, -2)
question
Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0?
answer
inconsistent
question
Graph the system of inequalities.
answer
A.
question
Which system of inequalities has this graph?
answer
A.
question
A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish. The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?
answer
(0, 0), (0, 53), (71.76, 0), (28, 46); t = 28 and s = 46.
question
An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?
answer
B.
question
Find the values of x and y that maximize the objective function for this graph.
answer
(1, 8)
question
The objective function for this graph is P = 5x + y. What values of x and y maximize this function?
answer
(1000, 0): The maximum is 5000.
question
Using substitution, the equations 2x - 3y = -21 and 3x + 3y = -24 give a solution of (-9,-1).
answer
False
question
Which set of numbers best describes the number -4?
answer
integers
question
Which set of numbers best describes the number π (pi)?
answer
irrationals
question
The expression | -2 | - |-7 | simplifies to 5.
answer
false
question
The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds.
answer
191 feet
question
The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 2.5 seconds.
answer
100 feet
question
The expression 2y - 7x + 3y + 3x evaluated for x = 2 and y = 4 is 12.
answer
True
question
Solve 3(x - 5) - 15 = 48.
answer
x = 26
question
Solve w + 12 = -6 - 2w.
answer
w = -6
question
In the expression 2(x+4) - 12 = 44, x = 24.
answer
True
question
Solve and graph -2x + 7 ≥ 2(3 - x).
answer
Graph A
question
A car salesman receives $50 for each car sale plus 2% of the purchase price. How much must a car sell for in order for the salesperson to earn at least $500?
answer
The car must sell for at least $22,500.
question
The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.
answer
False
question
Solve |5x - 3| ≤ 3.
answer
b
question
Solve |8 - m| + 4 = 21.
answer
m = -9, m = 25
question
The expression | 2 + 4n | - 4 = 14 produces the answers n = 4 and n = 5.
answer
False
question
Simplify the expression |-3| - |-5|.
answer
-2
question
Evaluate 2a - 5b - 3a for a = -2 and b = 5.
answer
-23
question
Find the perimeter of the figure shown below. Simplify the answer. 8a + 2b 10a + 4b 10a + 2b 10a - 2b
answer
10a + 2b
question
One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.
answer
9 1/3, 13 1/3, 15 1/3
question
A certain box of cereal should have a net weight that is within 1.5 grams of 510. After the first phase of production, the weight of the cereal is 308 grams. By how much should the weight of the cereal increase to remain within the specified weight?
answer
between 200.5 and 203.5 grams
question
Graph the solution of -7x + 4 ≥ 11 and 10 - 3x > 1.
answer
Graph D
question
Solve and graph 13 - 3y < -5.
answer
Graph A
question
Solve |5x - 7| = 3.
answer
2, 4/5
question
In the expression 3(x - 6) - 12 = 33, x = 21.
answer
True
question
Suppose that 80% of people surveyed answered 'Yes' to a certain question. Let the digits 0-7 to represent 'Yes' and let 8 and 9 represent 'No.' Use the random numbers shown below to determine how many people out of 20 answered 'No.'
answer
5
question
Suppose you take a true/false quiz that contains five true/false questions. Let an even digit represent a correct answer and an odd digit represent an incorrect answer. In the five trials shown, how often did you get at least 3 questions correct? (Note: Assume there is a 0 before the number 4908 in the first trial.)
answer
3
question
A jar contains 7 red marbles, 4 blue marble, and 6 green marbles. You draw one marble from the jar. The probability of drawing a blue or red marble is 11/17.
answer
True
question
Find f(-5) if f(x) = -8x - 1.
answer
39
question
Find the slope of the line that passes through (5, -5) and (9, -5).
answer
question
The slope of the line that passes through (-2, 6) and (1, 15) is 3.
answer
True
question
Find the equation of the line that passes through the point (-7, 2) and has a slope m = -5 in point-slope form.
answer
y - 2 = -5(x + 7)
question
Find the equation of the line that passes through the points (-6, 3), (5, -2) in point-slope form.
answer
y-3=-5/11(x+6)
question
The point-slope formula of a line that passes through the point (8,5) and has a slope of ¼ is y = 1/4x + 3.
answer
false
question
Which equation represents the line whose slope is 1 and whose y-intercept is (0, 0).
answer
y = x
question
Determine the coordinates of the y-intercept of 2x + 4y = 8.
answer
(0, 2)
question
The line y = 7x - 2 has a slope of 7 and a y-intercept of (-2 ,0).
answer
False
question
A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wishes to have the length be three times the width. If the side of the barn accounts for the length of the fence, find the dimensions of the fence.
answer
144 feet by 48 feet
question
Solve |x + 4| ≥ 1.
answer
x ≤ -5 or x ≥ -3
question
A group of students rolled two number cubes 100 times and recorded a sum of six 14 times. Find the experimental probability of rolling a sum of six.
answer
14%
question
A line passes through the point (-6, 1) and has slope m = -4. Find the equation in point-slope form.
answer
y - 1 = -4(x + 6)
question
Find the slope and the y-intercept of the line. y = 5x - 7
answer
slope: 5 y-intercept: (0, -7)
question
Determine the coordinates of the x-intercept of 3x - 4y = 24.
answer
(8, 0)
question
The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.
answer
False
question
Point M is at the coordinates (-5, 5).
answer
False
question
Find the opposite and reciprocal of -1.8.
answer
1.8, -5/9
question
Name the property of real numbers illustrated by the equation 3(2x - 14) = 6x - 42.
answer
Distributive Property
question
Evaluate -1x + 7y + 4x + 1y for x = 4 and y = -2.
answer
-4
question
Evaluate 3(2m - 3n) - 2(m + 2n) for m = -9 and n = -7.
answer
55
question
Solve 11c - 2(2c + 1) = 3(c - 6).
answer
-4
question
Solve and graph 5x - 2 ≤ 8.
answer
Graph B
question
Solve |x + 8| ≤ 5.
answer
-13 ≤ x ≤ -3
question
Solve |x + 9| = 8.
answer
x = -17, x = -1
question
Write the specification 14.35 ≤ d ≤ 15.15 as an absolute value inequality.
answer
|d - 14.75| ≤ 0.4
question
A jar contains 12 blue marbles, 8 red marbles, and 20 green marbles. You pick one marble from the jar. Find the theoretical probability, P(blue or green).
answer
4/5
question
There are 135 girls in the junior class at West High School. Of these 135 girls, 16 are on the volleyball team (V), 22 are on the softball team (S), and 8 are on both the volleyball and softball team. One student is selected at random. Find the probability that the student plays on the softball team but not the volleyball team.
answer
about 10%
question
You roll a twelve-sided die with the numbers 1 through 12 on the faces of the die. You roll the die once. Find the theoretical probability P(factor of 12).
answer
1/2
question
Find g(-2) if g(x) = 4x + 3.
answer
-5
question
What is the domain and range of this function? Domain: all real numbers; Range: y ≥ -4 Domain: -2 ≤ x ≤ 2; Range: y ≥ -4 Domain: x ≥ -4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0
answer
Domain: all real numbers; Range: y ≥ -4
question
What is the domain and range of this function? Domain: x > 0; Range: y > 0 Domain: x ≥ 0; Range: y ≥ 0 Domain: all real numbers; Range: all real numbers Domain: positive integers; Range: positive integers
answer
Domain: x > 0; Range: y > 0
question
What point has coordinates of (-5, 4)?
answer
Point N
question
Graph 2x + 3y = 9.
answer
Graph A
question
Match the given graph with its corresponding equation.
answer
x + 4y = -4
question
What is the slope of the line through the points P(-5, -6) and Q(-12, 5)?
answer
-11/7
question
Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).
answer
y + 3 = - 2(x - 4)
question
The expression 2y - 5x + 3y + 2x evaluated for x = 3 and y = 2 is -11.
answer
False
question
Solve the question below.
answer
C. h= 3v/piR^2
question
Is y = (2x)2 + 5x - 7 + 1 linear or quadratic? Identify the quadratic, linear, and constant terms.
answer
quadratic function quadratic term: 4x2 linear term: 5x constant term: -6
question
Find a quadratic model for the values in the table.
answer
f(x) = 3x2 + 7x - 9
question
The vertex of a parabola will never be on the axis of symmetry.
answer
False
question
Find the quadratic function
answer
A.
question
Graph
answer
C.
question
The minimum value of a parabola that opens upward will be its vertex.
answer
True
question
Write y = -4x2 - 64x - 265 in vertex form.
answer
y = -4(x + 8)2 - 9
question
Graph y = - (x - 1)2 + 4.
answer
C.
question
The vertex of f(x) = 3(x+2)2 - 4 is (-2,-4).
answer
True
question
Factor x2 - 81.
answer
(x + 9)(x - 9)
question
Use the GCF to factor 15x2 + 6x.
answer
3x(5x + 2)
question
4y is the greatest common factor of 4y2 + 6y.
answer
False
question
Factor x2 - 6x + 8.
answer
(x - 4)(x - 2)
question
Factor 5r2 + 13r - 6.
answer
(5r - 2)(r + 3)
question
3x2 -5x - 2 factors to (3x+1)(x-2).
answer
True
question
A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8.
answer
P(x)= 41x2 - 162x + 433; 1761 waterfowl
question
Identify the vertex and the axis of symmetry of the parabola.
answer
vertex: (1, -6); axis of symmetry: x = 1
question
Graph
answer
D. vertex (-3,-1) x= -3
question
Graph y = (x - 3)2 + 1.
answer
D.
question
Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)2 + 7.
answer
(-3, 7), y-intercept -29
question
Write y = -3x2 + 12x - 21 in vertex form.
answer
y = -3(x - 2)2 - 9
question
Factor x2 - 16.
answer
(x + 4)(x - 4)
question
Factor 4x2 - 49.
answer
(2x + 7)(2x - 7)
question
What is the GCF of 3n3 + 5np2 + n2p2?
answer
n
question
Factor t2 - 10t + 25.
answer
(t - 5)2
question
Factor 4y2 - 3y - 1.
answer
(4y + 1)(y - 1)
question
The vertex of f(x) = 2(x-2)2 +10 is (-2, 10).
answer
False
question
Factor 8ac + 12ad + 10bc + 15bd.
answer
(2c + 3d)(4a + 5b)
question
Factor 3xy - 2by + 3ax - 2ab.
answer
(y + a)(3x - 2b)
question
4n3 + 5n2 + 6n + 15 factors to (3n2 + 2) (3n + 5).
answer
False
question
Solve 6x2 = 48. If necessary, round your answer to the nearest hundredth.
answer
A.
question
Solve x2 - 6x = 0 by graphing or by factoring.
answer
x = 0, x = 6
question
A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.
answer
False
question
Simplify C. -500i
answer
B.
question
The square root of a negative number is an imaginary number.
answer
True
question
Solve 9x2 + 6x + 1 = 64.
answer
D.
question
Rewrite y = x2 + 4x + 5 in vertex form. Then find the vertex.
answer
y = (x + 2)2 + 1; (-2, 1)
question
When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.
answer
False
question
Solve 3x2 - 9x - 12 = 0 using the Quadratic Formula.
answer
x = 4, x = -1
question
Without graphing, tell how many x-intercepts y= 2x2 + 4x + 2 has.
answer
1 intercept
question
Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.
answer
True
question
A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.
answer
P(x)= 42x2 - 186x + 762; 1962 geese
question
Factor 18ab + 9ax -4b - 2x.
answer
(9a - 2)(2b + x)
question
A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.
answer
C. 7.87 sec
question
Evaluate the discriminant of 25x2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.
answer
two real solutions
question
An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.
answer
(x + 3)(y - 2)
question
Complete the square: x2 + 2x + ____ .
answer
1
question
Identify the vertex and the axis of symmetry of the parabola.
answer
A.
question
Solve -11x + 9 + 5x2 = 0 using the Quadratic Formula.
answer
C.
question
Solve -9x + 6 + 5x2 = 0 using the Quadratic Formula.
answer
B.
question
Graph y = -x2 - 1.
answer
A.
question
Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.
answer
a. 1000 units; b. $400
question
Write the equation of the parabola in vertex form.
answer
y = (x + 1)2 - 3
question
Factor 8a4b - 3ab2c.
answer
ab(8a3 - 3bc)
question
Find the GCF of 14a2b4c and 56ab2c2.
answer
14ab2c
question
Factor 4x2 + 5x - 21.
answer
(4x - 7)(x + 3)
question
Factor m3 - 4m2 + 6m - 24.
answer
(m - 4)(m2 + 6)
question
Factor xy - 6 + 2y - 3x.
answer
(x + 2)(y - 3)
question
Solve x2 - 4x - 5 = 0 by factoring.
answer
x = -1, x = 5
question
Find the additive inverse of 6 - 3i.
answer
-6 + 3i
question
Simplify (3 + 3i) - (7 + 6i).
answer
-4 - 3i
question
Simplify 2i(5 - i).
answer
2 + 10i
question
Write A. 1 - 4i B. 1 + 4i C. 3i D. -3i
answer
1 - 4i
question
Complete the square: x2 + 6x + ____ .
answer
9
question
Rewrite y = x2 - 10x + 3 in vertex form. Then find the vertex.
answer
y = (x - 5)2 - 22; (5, -22)
question
Solve 7x2 + 28x = 49 by completing the square.
answer
C.
question
Solve 8x2 - 80x = -24 by completing the square.
answer
C.
question
15x3 - 10x2 + 3x -2 factors to (5x2 + 1) (3x - 2).
answer
True
question
Classify 2x3 - 2x by degree and by number of terms.
answer
cubic binomial
question
The table shows the number of oak trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of oaks planted in 1998.
answer
T(x) = 0.2x3 + 0.7x2 + 0.2x + 0.1; 353.2 thousand trees
question
4x3y4 is a 4th degree monomial.
answer
False
question
The roots of a certain polynomial are -2/5, -6 and 4/3. What might the linear factors of the polynomial be?
answer
(5x + 2)(x + 6)(3x - 4)
question
Write 2r3 + 8r2 - 10r in factored form.
answer
2r(r - 1)(r + 5)
question
The polynomial 3x2 - 7 + 4x3 + x6 is written in standard form.
answer
False
question
Find the zeros of y = (x - 2)(x + 1)(x + 3).
answer
x = 2, x = -1, x = -3
question
Find the zeros of y = (x - 2)(x + 9).
answer
x = 2, x = -9
question
A multiple zero has a multiplicity equal to the number of times the zero occurs.
answer
True
question
Divide (5x3 - 6 - 5x) ÷ (10 + 5x) using synthetic division.
answer
x2 - 2x + 3, R -36
question
Use synthetic division and the Remainder Theorem to find P(-3) if P(x) = x4 + 19x3 + 108x2 + 236x + 176.
answer
8
question
When dividing polynomials, every term of the numerator must be divided by the entire denominator.
answer
True
question
Solve x2 - 12x + 41 = 0
answer
D.
question
Factor 3q3 - 81.
answer
3(q - 3)(q2 + 3q + 9)
question
4x2 - 36 = 0 has a solution of x = +/- 3.
answer
True
question
Classify -4x3 - 2x2 - 2x by degree and by number of terms.
answer
cubic trinomial
question
Classify 2 by degree and by number of terms.
answer
constant monomial
question
Find a polynomial function to model the data.
answer
f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32
question
Find the zeros of y = (x - 1)(x + 2).
answer
x = 1, x = -2
question
Find the zeros of y = x(x + 5)(x - 8).
answer
x = 0, x = -5, x = 8
question
Divide (3x3 + 4x2 - 5x - 2) ÷ (x + 2) using long division.
answer
3x2 - 2x - 1
question
Factor x4 - 8x2 + 15.
answer
C.
question
Solve x - x3 = 2x4 + 3x2 - 5.
answer
x = ±1
question
Solve x2 - 10x + 29 = 0.
answer
No Solution
question
Solve 8x3 + 27 = 0.
answer
B.
question
The polynomial x4- 2x2 + x4 - x is written in standard form.
answer
False
question
Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.
answer
0 = x3 + 4x2 - 2x - 20
question
Use the Rational Root Theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do NOT find the actual roots.
answer
B.
question
The possible rational roots of x3 + 3x2 - 4x + 2 are +/- 3 and +/- 2.
answer
False
question
For 3x9 -7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
answer
D.
question
For 8 - 4x3 + 4x6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
answer
D.
question
The equation f(x) = 4x4 + 4x2 + 9x - 2 can have at most four distinct real roots.
answer
True
question
Evaluate. 9!/6!
answer
504
question
There are 17 students participating in a spelling bee. How many ways can the students who go first and second be chosen?
answer
272 ways
question
7! Is another way of writing 7 * 6 * 5.
answer
False
question
Determine whether the following situation would require calculating a permutation or a combination. Assigning students to their seats on the first day of school.
answer
permutation
question
Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?
answer
176 ways
question
Order does not matter when examining combinations, but order does matter in permutations.
answer
true
question
What is the probability of getting two heads when tossing a coin four times?
answer
3/8
question
Use Pascal's Triangle to expand (s - v)5.
answer
s5 - 5s4v + 10s3v2 - 10s2v3 + 5sv4 - v5
question
If flipping a coin is equally likely to result in heads or tails, the odds of flipping a coin six times and getting only one head are 3 out of 16.
answer
False
question
A fifth-degree polynomial equation with rational coefficients has the roots 2, -7i, and -7 + i. Find the remaining roots.
answer
7i, -7 - i
question
Divide (x4 - 11x3 - 49x2 + 899x - 2506) ÷ (x - 8).
answer
x3 - 3x2 - 73x + 315, R 14
question
Assume red and green are equally likely occurrences. What is probability that you will get one green light in a row of five lights?
answer
5/32
question
A school bought a special type of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. How many different pass codes are possible?
answer
5,040
question
A summer reading list has 20 books on it. In how many ways can you choose four books to read?
answer
4,845 ways
question
Use Pascal's Triangle to expand (3a - b)4.
answer
81a4 - 108a3b + 54a2b2 - 12ab3 + b4
question
Write in standard form. Then classify by degree and by number of terms.
answer
D.
question
Write (x - 2)(x + 9) as a polynomial in standard form.
answer
x2 + 7x - 18
question
Find the zeros of the function. State the multiplicity of multiple zeros. y = (x - 4)2
answer
x = 4 multiplicity 2
question
Divide (2x3 + 4x2 + 3x + 4) ÷ (x + 1) using long division.
answer
2x2 + 2x + 1, R 3
question
Which polynomial is NOT a factor of 3x4 - 10x3 - 29x2 + 16x + 20?
answer
x - 2
question
Which polynomial is NOT a factor of 3x4 - 16x3 - 3x2 + 36x + 20?
answer
x - 1
question
Factor 3q3 - 81.
answer
3(q - 3)(q2 + 3q + 9)
question
Solve x3 + 4x2 - x - 4 = 0.
answer
x = -4, x = -1, x = 1
question
Solve x3 + 5x2 - 9x - 45 = 0.
answer
x = -5, x = -3, x = 3
question
Find only the rational roots of x4 - 9x3 + 16x2 + 18x - 36 = 0.
answer
x = 6, x = 3
question
Find the roots of x3 - x2 + 2 = 0.
answer
x = 1 + i, x = 1 - i, x = -1
question
For x7 - 2x6 + 3x2 - 2x + 5 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
answer
7 complex roots; 1, 3, 5, or 7 real roots possible rational roots: ±1, ±5
question
For 3x3 -2x + 6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
answer
C.
question
Which polynomial function has the highest degree?
answer
the quotient of f(x) and g(x), where f(x) = x9 - 3x and g(x) = 3x2 - 4
question
Seven skiers enter a downhill race. First, second, and third places will be given to the three fastest skiers. How many arrangements of first, second, and third places are possible with seven skiers?
answer
210
question
Evalute 9!
answer
362,880
question
Find 8P3.
answer
336
question
How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?
answer
42 ways
question
In how many ways can the three letters A, B, and C be arranged?
answer
6
question
Determine whether the following situation would require calculating a permutation or a combination. Selecting four teachers to attend a math seminar.
answer
combination
question
Four cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of four cards are possible?
answer
270,725
question
How many combinations of four can you make from the set? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
answer
210 combinations
question
The polynomial 5x3 - 2x2 + x - 13 is written in standard form.
answer
True
question
What is the vertex of the graph of y = |x| - 6?
answer
(0, -6)
question
Which statement describes the relationship between the graph of the equation
answer
C.
question
Graph y = x2 - 6.
answer
C.
question
Write the equation of the parabola in vertex form.T
answer
y = (x - 1)2 - 3
question
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998.
answer
T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees
question
Use Pascal's Triangle to expand (s - v)6.
answer
v6 - 6v5s + 15v4s2 - 20v3s3 + 15v2s4 - 6vs5 + s6
question
Evaluate 8C3.
answer
56
question
Solve 5x - 4 = |2x + 1|. Check for extraneous solutions.
answer
...
question
Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?
answer
1/32
question
Write an explicit formula for the sequence
answer
n+1/n^2+3
question
Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.
answer
an = 2an - 1 - 4 where a1 = 15; 356
question
The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.
answer
True
question
A grocery clerk sets up a display of 12-pack cartons of cola. There are 40 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?
answer
820 cartons
question
Is the sequence -9.9, -13, -16, -19.2, ... arithmetic? If so, identify the common difference.
answer
no
question
The missing term of the arithmetic sequence 13, __, 27 is 21.
answer
False
question
Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)
answer
192, 76.8, 30.72
question
Is the sequence
answer
A. yes .5
question
The sequence 3, 6, 9, 12 is geometric.
answer
False
question
For the sum
answer
6 terms, 25, 0; 75
question
Write the related series for the finite sequence 7.6, 6.3, 5, ... , -1.5. Then evaluate the series.
answer
7.6 + 6.3 + 5 + ... + (-1.5) = 24.4
question
5, 7, 11, 15, 21 is an infinite series.
answer
False
question
Which series will converge?
answer
A.
question
Evaluate the infinite geometric series 2.1 + 0.21 + 0.021 + ... .
answer
7/3
question
The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.
answer
False
question
Describe the pattern
answer
Add 1 to the numerator and 2 to the denominator of the previous number.
question
Describe the pattern 16, -8, 4, -2, 1, ....
answer
Divide the previous number by -2.
question
Which formula does NOT describe the sequence 8, 6, 3, -1, -6, ... ?
answer
an = -0.5n2 - n + 9
question
Find the arithmetic mean an of the terms
answer
19/40
question
Find the missing term of the arithmetic sequence 25, ___, 49, ....
answer
37
question
Determine whether the series -1024 + 256 -64 + 16 - ... is arithmetic or geometric. Then evaluate the series to the ninth term.
answer
geometric; -819.203125
question
Evaluate the infinite geometric series
answer
-12
question
Evaluate the series 3 - 12 + 48 - 192 + ... to the seventh term. Round your answer to the nearest hundredth, if necessary.
answer
9831
question
The sequence 2, 6, 18, 54, ... is a geometric sequence.
answer
True
question
Evaluate the area under g(x) = -x2 - 3x + 7 for -4 ≤ x ≤ 1.
answer
C. 35.83
question
Use inscribed rectangles to approximate the area under g(x) = -0.5x2 + 7 for -3 ≤ x ≤ 0 and rectangle width 0.5.
answer
15.3 units2
question
The area approximated by circumscribed rectangles is greater than the area under the curve.
answer
True
question
Use the frequency table to find P(more than 3 children).
answer
20%
question
Use the frequency table to find P(0 - 2 children).
answer
68%
question
A situation may not be described by more than one sample space.
answer
False
question
The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.
answer
75.3%
question
Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.
answer
1/3 .33333333
question
If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.
answer
True
question
Find the mean, the median, and mode of the set of values. 5, 20, 6, 5, 15, 18, 12, 13, 14
answer
mean: 12, median: 13, mode: 5
question
The cost of ten different portable MP3 players is shown in the table. What is the mean cost?
answer
$90
question
The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.
answer
True
question
The scores of 36 students on a recent geography test are in the table. If Lupe got a 69 on the test, what percentile would that score represent?
answer
44%
question
The box-and-whisker plot represents the test scores of 25 students. What percent of the scores were between 88.5 and 65?
answer
50%
question
If x is at the 63rd percentile, then 37% of the data are less than or equal to x.
answer
False
question
A rubber ball dropped on a hard surface takes a sequence of bounces,
answer
C. 54 24/125
question
Evaluate the infinite geometric series 1.9 + 0.19 + 0.019 + ....
answer
19/9
question
Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.
answer
explicit; 0, -8, -24, -48, -80
question
A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?
answer
2 5 1
question
Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.
answer
D. 1/6
question
A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.
answer
True
question
How do the medians of the two sets of exam scores compare?
answer
The median of Exam A is greater than the median of Exam B.
question
Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2
answer
B.
question
Make a box-and-whisker plot for the set of values. 7.2, 3.2, 5.2, 3.2, 4.2, 7.2, 5.2, 3.2, 6.2, 4.2, 6.2, 3.2, 6.2, 2.2, 4.2
answer
2.2 7.2
question
Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.
answer
yes, 5.4
question
For the geometric sequence 2, -10, 50, -250, ..., find the seventh term.
answer
31, 250
question
Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.
answer
D. an = 120 • 0.3n - 1; 120, 36, 10.8, 3.24, 0.972
question
Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.
answer
128
question
Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.
answer
sequence, finite
question
The sequence -12, -6, 0, 6, ... , 48 has 11 terms. Evaluate the related series.
answer
198
question
Use summation notation to write the arithmetic series -3.9 + (-1.9) + 0.1 + ... for six terms.
answer
6 x=1 -5.9 +2n
question
Evaluate the series
answer
C. 5461/ 16,384
question
A class of 30 students has 11 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.
answer
C. 10/19
question
The table gives data about municipal waste collected and recycled by type. Find P(recycled | glass).
answer
about 6.7%
question
The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).
answer
13/22
question
Find the arithmetic mean an of the terms
answer
91/60
question
You cannot use a table or graph to show a probability distribution.
answer
False
question
A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.
answer
True
question
A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 20, 60, 100, 140, .... Find the distance that the projectile traveled in the 9th second.
answer
340 ft
question
What does the dot at 47 represent?
answer
lower quartile
question
The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.
answer
162
question
Inscribed rectangles are completely under the curve.
answer
True
question
Evaluate the infinite series
answer
It does not have a sum.
question
Which number is an outlier in the data shown in the table?
answer
19
question
The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).
answer
31.7%
question
Evaluate the series
answer
-5.81
question
Write and evaluate a sum to approximate the area under y = (x - 4)2 - 1 for the domain 0 ≤ x ≤ 2. a. Use inscribed rectangles 0.5 units wide. b. Use circumscribed rectangles 0.5 units wide.
answer
a. 13.75 units2; b. 19.75 units2
question
Write an explicit and a recursive formula for the sequence -7, -5.6, -4.2, -2.8, -1.4, ....
answer
explicit: an = -8.4 + 1.4n; recursive: an = an - 1 + 1.4, where a1 = -7
question
Probability over a continuous range of events is cumulative probability.
answer
True
question
Use inscribed rectangles to approximate the area under f(x) = -x2 + 6 for -1.5 ≤ x ≤ 0 and rectangle width 0.5.
answer
7.25 units2
question
Given the set of axes y-axis: a car's velocity, x-axis: time, what does the area under the curve represent?
answer
the total distance traveled by the car
question
Identify the outlier in the temperature data shown.
answer
71°
question
The number of patients treated at Dr. Oster's dentist office each day was recorded for nine days. Using the data 7, 4, 18, 14, 14, 11, 13, 21, and 6, find the mean, median, and mode.
answer
mean: 12, median: 13, mode: 14
question
The number of patients treated at Dr. Holman's dentist office each day was recorded for seven days. Using the data 3, 10, 18, 9, 22, 20, and 2, find the mean, median, and mode.
answer
mean: 12, median: 10, no mode
question
A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.
answer
True
question
Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.
answer
5/23
question
Use the frequency table to find P(2 or 3 children).
answer
42%
question
Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15
answer
mean: 15, standard deviation: 5.66
question
The range of the set 12, 18, 19, 22, 25 is 19.
answer
False
question
Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12
answer
range: 32, interquartile range: 16.5
question
Which sample size will produce a margin of error of ±4.1%?
answer
595
question
Which sample size will produce a margin of error of ±3.5%?
answer
816
question
From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.
answer
True
question
If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.
answer
True
question
The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?
answer
260 fish
question
The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?
answer
2.5%
question
Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15
answer
mean: 15, standard deviation: 5.66
question
The range of the set 12, 18, 19, 22, 25 is 19.
answer
False
question
Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12
answer
range: 32, interquartile range: 16.5
question
Which sample size will produce a margin of error of ±4.1%?
answer
595
question
Which sample size will produce a margin of error of ±3.5%?
answer
816
question
From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.
answer
True
question
If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.
answer
True
question
The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?
answer
260 fish
question
The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?
answer
2.5%
question
Find 49° in radians.
answer
0.86 radians
question
An angle in standard position with a positive measurement will extend below the x-axis.
answer
False
question
pi/3 radians in degrees
answer
60°
question
The amplitude of y = 3 sin(2x) is 3.
answer
True
question
Use the graph to find the value of y = sin θ for θ = 270°.
answer
-1
question
Find the amplitude and period of y = -5 sin (5x).
answer
amplitude=5,period=2/5
question
For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°.
answer
3/10
question
In which quadrant does the terminal side of a 117° angle lie?
answer
second quadrant
question
Find 311° in radians.
answer
5.43 radians
question
When 2251 voters were polled, 52% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.
answer
±2.1%; between 49.9% and 54.1%
question
Write an equation of the cosine function with amplitude 2 and period 8π.
answer
2 cos 1/4 x
question
The range of the set 2, 5, 8, 19, 33, 45 is 43.
answer
True
question
Graph y= 2.5 tan 4x/5
answer
/ closer together
question
Graph y = 5 cos x.
answer
far apart 5 -5
question
Evaluate sec 3.
answer
-1.0101
question
Reciprocal functions cannot be evaluated in radians.
answer
False
question
Evaluate sec 131°.
answer
-1.52
question
Simplify cos θ sec θ.
answer
1
question
Simplify cot/cos
answer
csc θ
question
The tangent of an angle is equal to the ratio of its sine divided by its cosine.
answer
True
question
The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.
answer
False
question
Solve 2 cos θ + 4 = 3 for 0 ≤ θ < 2π.
answer
2pi/3 4pi/3
question
The diagram shows one solution to the equation 3 - sin θ = 5 sin θ. Find the complete solution of the equation.
answer
30° + n • 360°, 150° + n • 360°
question
The length of side RP is approximately 42 cm.
answer
False
question
Find the area of the triangle. Round your answer to the nearest tenth, if necessary.
answer
67.3 in.2
question
Solve the problem below.
answer
3.1 m2
question
The law of cosines is used to find the measures of a triangle when only the three sides are known, because the law of sines requires at least one angle measure.
answer
True
question
Find the angles in the triangle when a = 19, b = 20, and c = 10. Round your answers to the nearest tenth.
answer
69 80 29
question
Solve the problem below.
answer
80.3°
question
Determine the number of standard deviations which include all data values listed for the situation.The mean time employees take of a company to commute to work is 40.75 minutes; the standard deviation is 12.9 minutes.42 min, 45 min, 53 min, 34 min, 12 min, 48 min, 52 min, 24 min, 56 min, 47 min, 28 min, 48 min
answer
3 standard deviations
question
Simplify cot θ tanθ.
answer
1
question
A set of data that is normally distributed has a mean of 35.6 and standard deviation of 2.5. Which number is between 1 and 2 standard deviations of the mean?
answer
38.3
question
In one survey, the shoe sizes of women are distributed normally about the mean. The mean of the data is 7.17, and the standard deviation is 1.44. About what percent of the women are within two standard deviations of the mean in shoe size?
answer
96%
question
Find the angles in the triangle when a = 13, b = 12, and c = 11. Round your answers to the nearest tenth.
answer
68 59 52
question
Solve cot θ sin θ = 1/5 for 0 ≤ θ < 2π.
answer
pi/3 5pi/3
question
Find the range and the interquartile range of the set of values.37, 21, 44, 19, 22, 47, 26, 32, 25, 43, 11, 15
answer
range: 36, interquartile range: 20
question
Which expression completes the equation to make it an identity? cos+ sin + cos / 1+ sin
answer
cos θ
question
In a survey of 368 people, 81 drink milk straight from the milk carton. For the sample, find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.
answer
a. 22%; b. ±5%; c. 17% to 27%
question
Use the Law of Sines to solve for c to the nearest tenth.
answer
51.4
question
Which expression completes the equation to make it an identity?
answer
1+csc2 0 / 1-sin 0
question
What is the period of y = 3 tan 4x + 5?
answer
pi/4
question
Write 11pi/18 radians in degrees
answer
110°
question
Find the value of csc 165°. Round your answer to the nearest hundredth.
answer
3.86
question
In ΔABC, b = 4, c = 1, and ma =118
answer
4.56
question
In ΔABC, b = 1, c = 3 ma= 138
answer
3.8
question
Use the Law of Sines to solve for a to the nearest tenth.
answer
38.1
question
The class average on a math test was 84.5 and the standard deviation was 4.4. Find the z-score for a test score of 94.
answer
≈ 2.16
question
Find the degree measures of the angles whose tangent is sqr 3
answer
60° + n • 180°
question
Find the mean and standard deviation for the set of values. 25, 19, 5, 21, 18, 22, 17, 10, 7
answer
mean: 16, standard deviation: 6.62
question
Solve the problem below.
answer
80.3°
question
Graph Y=-pi/4 cot ( x-pi/4)
answer
about 112 women
question
Solve 3 cos 0 = cos 0 - sqr2 for 0 < 0 < 2pi
answer
3pi/4 5pi/4
question
Which sample size will produce a margin of error of ±6.3%?
answer
252
question
Use the graph to find the value of y = sin θ for θ = 150°.
answer
0.5
question
Simplify sin θ sec θ.
answer
tan θ
question
Find the radian measures of the angles whose sine is -0.8. Round to the nearest hundredth.
answer
-0.93 + 2πn and 4.07 + 2πn
question
When 876 voters were polled, 67% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.
answer
±3.4%; between 63.6% and 70.4%
question
Use the Law of Sines to solve for a to the nearest tenth.
answer
21.2
question
On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 265 feet at an angle of 35° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
answer
218.2 ft
question
A matrix with 4 columns and 3 rows is a matrix of dimensions 4x3.
answer
False
question
Identify a31 in the matrix.
answer
10
question
What are the dimensions of the matrix?
answer
5 × 4
question
Find
answer
-3 5 9 0
question
Two matrices can be subtracted if they have an equal number of rows, regardless of how many columns they have.
answer
False
question
Solve for each variable
answer
-6 -1/4
question
Find AB,
answer
[-25 25] TALL
question
Two matrices with dimensions 2x2 and 2x2 will result in a product matrix with dimensions 2x2 when multiplied.
answer
-32 28
question
Graph the figure and its image after the given rotation.
answer
4
question
Transforming a figure 3 units to the right and 2 units up can be accomplished by adding 3 to each x-coordinate of the vertices and subtracting 2 from the y-coordinates.
answer
False
question
What are the coordinates of the image after a rotation of 90°?
answer
0 1 -4 0 -3 1
question
Find the inverse of -2 2 -1
answer
-1/2 1 -1/10
question
The determinant of this matrix is 7.
answer
False
question
Which matrix has determinant -7?
answer
-14 -1 7 1
question
Find
answer
[21 -63]
question
Find
answer
-70 44 70 -24 71 -73 -71 -71 -35
question
Use matrices A, B, and C. Find B-C if possible.
answer
-2 -7 14 -4 7 0
question
Write the coordinates of the image after a dilation three times the original size.
answer
-21 -12
question
Find
answer
13 -9 -12 -1 -6 18 1 -1 2
question
Find
answer
-3 9 1 -3 -6 9 -14 0 6
question
Solve
answer
13/3 2/3
question
Determine whether
answer
1/10 -3/10 -1/5 -2/5
question
Find
answer
[6 -34]
question
Simplify
answer
3|x5|y4
question
-25 has no real 4th root.
answer
True
question
Find all the real cube roots of
answer
-8/9
question
The fifth root of 12 is equal to the fifth root of 7 times the fifth root of 5.
answer
False
question
Simplify
answer
4a^2b sqr 3a
question
Divide and simplify sqr 24/ sqr 2
answer
2 sqr 3
question
Rationalize the denominator of
answer
-5 -2 sqr 6
question
Multiply
answer
22 + 8 sqr 6
question
These are two like radicals.
answer
False
question
17 1/3 is the same as the cube root of 17.
answer
True
question
Simplify
answer
x -1/2 y 3/4
question
Simplify
answer
1/ 4 sqr x^7
question
The solution to this equation is x = 11.
answer
False
question
Refer to the question below.
answer
x = 60
question
Solve
answer
3/2
question
Find AB,
answer
-22 74
question
Solve
answer
x = 3
question
Multiply and simplify
answer
m^2 sqr 12 m^2
question
Multiply and simplify
answer
6x^2 sqr3^ x
question
Find the coordinates of the image after the reflection in the given line.
answer
-5 6 -1 -3 -9
question
Find
answer
-14 -1 3 7
question
Write
answer
3^13^ sqr x^7
question
The formula for the volume of a sphere is
answer
1.63 in.
question
Two matrices with dimensions 3x1 and 2x4 will produce a product matrix with dimensions 3x4 when multiplied.
answer
False
question
Find all the real square roots of 0.0036.
answer
0.06 and -0.06
question
Solve
answer
-1/3
question
Multiply
answer
5
question
Which matrix is the multiplicative inverse of
answer
0 1 -1 -5 5 -4 1 -1 1
question
Simplify
answer
81
question
What are the dimensions of the matrix?
answer
2 × 1
question
The velocity of sound in air is given by the equation
answer
none of these
question
Find the coordinates of the image of
answer
-14 -3 10 14
question
Solve
answer
f = 0, g = -4, h = 9 or -9
question
Rationalize the denominator of
answer
3 sqr t
question
Determine whether
answer
0 -1/3 -1/2 1/6
question
What are the dimensions of the matrix?
answer
3 × 2
question
What are the dimensions of the matrix?
answer
5 × 4
question
Find the real-number root of
answer
5/7
question
Solve
answer
4/3
question
Write the coordinates of the image after a translation 3 units right and 2 units down.
answer
-1 3 -1 -6 -6 -3
question
In May, Suzanne bought 32 styrofoam balls and decorated them as toy figurines. In June, she sold 12 figurines. In May, Carrie bought 36 styrofoam balls to decorate and in June, she sold 22 figurines. Which matrix represents all of their May purchases and their June sales?
answer
32 -12 36 -22
question
Multiply
answer
180 sqr 10
question
What are the dimensions of the matrix? Identify a12.
answer
3 × 2, -4
question
In May, Marcus bought 48 styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lin bought 44 styrofoam balls to decorate and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?
answer
48 -19 44 -21
question
Write
answer
8x -15/7
question
Let f(x) = 3x + 7 and g(x) = 4x - 2. Find (f composited with g) (-6).
answer
-71
question
Let f(x) = 3x2 + 10x- 8 and g(x) = x + 4.
answer
-9x + 6, all real numbers x ≠ -4
question
If f(x) = 3x + 7 and g(x) = 5x - 2 then (f+g)(x) = 8x + 5.
answer
True
question
The domain of a relation and its inverse are the same.
answer
False
question
Find the inverse of f(x) = 3x2. Is the inverse a function?
answer
x/3 no
question
Identify the graph of y = 2x2 - 5 and its inverse.
answer
up right
question
Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.
answer
f(x) = 260(1.09)x
question
For an annual rate of change of -31%, find the corresponding growth or decay factor.
answer
0.69
question
An annual rate of change is -10%. The corresponding growth or decay factor is 0.10.
answer
False
question
Graph y = 4x - 3 as a translation of its parent function.
answer
backwards L low
question
Evaluate e4.
answer
54.5982
question
y = -4* 2x is a reflection of y = -1/4* 2x.
answer
False
question
Log4 64 = 3
answer
True
question
Given log 15 = B and log 3 = C , find log 5.
answer
B - C
question
Use the properties of logarithms to evaluate log4 256.
answer
4
question
Find the equation of the graph.
answer
y = 1.5x
question
Solve the question below.
answer
-6
question
A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?
answer
$13,616.61
question
Find the inverse of y = 3x2 + 4. Is the inverse a function?
answer
x-4 / 3 no
question
Let f(x) = 4 - x2 and g(x) = 2 - x. Find f(x) • g(x).
answer
x3 - 2x2 - 4x + 8
question
Solve the question below.
answer
505
question
Find the annual percent increase or decrease that y = 0.35(2.3)x models.
answer
+130%
question
Write 5 log x - 4 log (x - 4) as a single logarithm.
answer
log x^5/x-4^4
question
How much money invested at 5% compounded continuously for 2 years will yield $1150?
answer
$1040.56
question
Solve the question below.
answer
29/4
question
Find the inverse of the relation. Graph the given relation and its inverse.
answer
-2 1 5 10
question
Suppose that x and y vary inversely. Write a function rule for the function that x = 4 when y = 7.
answer
28/x
question
If m varies directly as the square root of y, inversely as p2, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?
answer
multiply 10/9
question
If y varies inversely with x and y = 6 when x = 9, then y = 96/x.
answer
False
question
State the excluded values of x in the expression
answer
2 or 3
question
Simplify
answer
2a3/3b
question
This statement simplifies to 16a2.
answer
True
question
Divide
answer
x-4/x-3 3 4
question
The only restriction of the variable in this equation is that x cannot equal positive or negative 5.
answer
False
question
Multiply
answer
xy/2 0 0
question
Solve the question below.
answer
13x-30/x^2-36
question
A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.
answer
True
question
Simplify
answer
x+3/2
question
Solve
answer
1
question
An extraneous solution is a solution of the derived equation, but not of the original equation.
answer
True
question
Solve
answer
-1/16
question
After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?
answer
87
question
Expand
answer
log b (1/2 -
question
State the excluded value(s) of
answer
x cannot equal 5, -5
question
Given log 5 = P and log 2 = Q , find log 10.
answer
P + Q
question
After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?
answer
87
question
Simplify
answer
2y +1 / y+1
question
Simplify
answer
4/3
question
It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.
answer
False
question
Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.
answer
f ( x ) = 300(1.13) x
question
State the excluded values of a and b in the expression
answer
0 0
question
Simplify
answer
21 16 50 54 / 72
question
State the excluded value(s) of
answer
x cannot equal -4
question
Find
answer
x+4 / x+2
question
Which property was used to rewrite log
answer
power property
question
Identify the graph of y = 2 x + 7 and its inverse.
answer
up cross
question
Multiply
answer
x ; x ≠ -7, -4, 0
question
The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.
answer
25,200 coats
question
Graph y = 3 x + 1 as a translation of its parent function.
answer
backwards L high
question
Solve the question below.
answer
4
question
Simplify
answer
5x
question
Simplify
answer
x-7 /2
question
Use the properties of logarithms to evaluate
answer
2/3
question
Let f ( x ) = x 2 + 2 x - 1 and g ( x ) = 2 x - 4. Find 2 f ( x ) - 3 g ( x ).
answer
2 x 2 - 2 x + 10
question
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?
answer
x/3 + x/4 =1, 1.71 h
question
The selling price of x number of a certain stereo can be modeled by the function R ( x ) = 160 x . The total cost of making x stereos is C ( x ) = 71 x - 0.02 x 2. What is the percent markup for 31 stereos?
answer
127%
question
Use the properties of logarithms to evaluate log7343.
answer
3
question
Graph f ( x ) = 2 x + 1 + 3 as a translation of its parent function.
answer
backwards L high
question
For f ( x ) = 5 - 3 x and g ( x ) = x 2 - 1, find f ( g ( x )) and g ( f ( x )).
answer
f ( g ( x )) = -3 x 3 + 8, g ( f ( x )) = 9 x 2 - 30 x + 24
question
For the function f ( x ) = (4 - 2 x )2, find f -1 and the domain and range of f and f -1. Determine whether f -1 is a function.
answer
2 x/2 0
question
Simplify
answer
x-1 / 5(x-3) 1 and 3
question
Find the next three terms in the sequence 1, 2, 4, 8, ....
answer
16, 32, 64
question
Simplify csc θ sin θ.
answer
1
question
Divide
answer
x-5/x-3
question
Find
answer
2
question
Find
answer
4ax^2 /3by
question
Find the 11th term of the sequence 11, 19, 27, 35, ....
answer
91
question
Solve the question below.
answer
7
question
Simplify sin2 θ(1 - csc2 θ).
answer
sin2 θ - 1
question
Divide
answer
x-6 / x-5
question
Find the next two terms in the sequence -5, 8, -13, 20, -29, .... Write a formula for the nth term. Identify the formula as explicit or recursive.
answer
none of these
question
Multiply
answer
x; x ≠ -6, -3, 0
question
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?
answer
2.18
question
Find the exact coordinates of the point at which the terminal side of -135° intersects the unit circle.
answer
- sqr 2 / 2
question
Solve
answer
x = 6
question
Find the values of cos θ and sin θ for -25°. Round your answers to the nearest hundredth.
answer
0.91, -0.42
question
Solve
answer
no solution
question
In which quadrant does the terminal side of a 314° angle lie?
answer
fourth quadrant
question
Is the sequence -5.4, 5.1, 15.6, 26.1, ... arithmetic? If so, identify the common difference.
answer
yes, 10.5
Algebra 1
Algebra 2
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International Business
Study Guide Algebra. Line, numb, fit, model, time. – Flashcards 316 terms

Sarah Adrian
316 terms
Preview
Study Guide Algebra. Line, numb, fit, model, time. – Flashcards
question
Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?
answer
4p - 7 = 13
question
Fiona solved the equation shown. What is the missing step of her solution?
answer
Simplify by combining like terms
question
Which input value produces the same output value for the two functions on the graph? G1
answer
Check Graph #1 in notebook x=1
question
Consider the functions shown on the graph. What is the input value for which the statement f(x) = g(x) is true? G2
answer
Check graph #2 1.5
question
Solve the equation. −10x + 1 + 7x = 37
answer
x = −12
question
Rahul solved the equation 2(x - ) - x = . In which step did he use the addition property of equality?
answer
Step 3
question
The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?
answer
1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
question
Which input value produces the same output value for the two functions on the graph? GRAPH3
answer
x-2 G3
question
What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p
answer
P=1
question
Solve the equation. -3x + 1 + 10x = x + 4
answer
X=1/2
question
The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month.Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
answer
250.5 - 35m = 300 - 45.25m
question
What is the solution to the linear equation? 6k + 10.5 = 3k + 12
answer
k=0.5
question
What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d
answer
d=1
question
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m-1/2=2+1/4m
answer
4
question
What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y - 14
answer
y=10
question
How many solutions exist for the given equation? 3(x - 2) = 22 - x
answer
One
question
Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"?
answer
3 - (n - 1) = 1/2(3n - 4)
question
Which equation has no solution?
answer
5 + 2(3 + 2x) = x + 3(x + 1)
question
How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1
answer
One
question
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
answer
4
question
How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2
answer
infinitely many
question
Solve for n. n + 1 = 4(n - 8)
answer
n=11
question
Karissa begins to solve the equation 1/2(x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below. When she subtracts 4 from both sides, x = -x results. What is the value of ?
answer
question
How many solutions exist for the given equation?
answer
one
question
Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"?
answer
3 - (n - 1) =1/2 (3n - 4)
question
How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1
answer
one
question
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
answer
4
question
How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2
answer
infinitely many
question
Solve for n. n + 1 = 4(n - 8)
answer
n=11
question
Karissa begins to solve the equation 1/2(x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below.
answer
question
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?
answer
60t + 55t = 150
question
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?
answer
18 minutes
question
Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?
answer
Check notebook. RUN/BIKE graph
question
It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?
answer
Check notebook. HOT/COLD graph.
question
If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.
answer
1/3
question
Lea and Marie are washing all the windows in their house. It would take Lea 80 minutes to wash the windows by herself, and it would take Marie 60 minutes to wash them by herself. Lea creates a table so she can find out how long it will take to wash the windows if they work together. What is the missing value in the table that represents the rate for Marie?
answer
1/60
question
Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?
answer
0.4
question
It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?
answer
Rate (part/hour)
question
The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis. Which is an equivalent equation solved for the slope, m?
answer
m=y-b/x
question
The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = .
answer
r = 8
question
In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as f/m = a. Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.
answer
2.2 m/s^2
question
Solve for a. 7a - 2b = 5a + b
answer
a=3/2b
question
Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?
answer
S/2(pi)r - r = h
question
The goals against average (A) for a professional hockey. hich is an equivalent equation solved for g?
answer
At/60=g
question
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is
answer
C = K - 273.15
question
Solve for k. 8k + 2m = 3m + k
answer
k = m/7
question
Solve the equation for a. K = 4a + 9ab
answer
a=k/4+9b
question
Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h?
answer
h = (p/0.7- b)÷ r
question
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
answer
Notes. Line graph Name3
question
Step 1: Subtract 3 from both sides of the inequality. Step 2: __________ Step 3: Divide both sides of the inequality by the coefficient of x.What is the missing step in solving the inequality 5 - 8x < 2x + 3?
answer
Add 8x to both sides of the inequality.
question
What value of x is in the solution set of 8x - 6 > 12 + 2x?
answer
5
question
Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x?
answer
Distribute -4 to get -8x + 4 > 5 - 3x.
question
What value of x is in the solution set of 4x - 12 ≤ 16 + 8x?
answer
-7
question
What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
answer
-1
question
Which number line represents the solution set for the inequality -1/2x ≥ 4?
answer
Notes Line graph Name 8
question
What value of x is in the solution set of 3(x - 4) ≥ 5x + 2?
answer
-10
question
Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x?
answer
x ≥ 0.5
question
The solution is n = -2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?
answer
-0.8 = -0.8
question
Solve the equation. 2x − 3 + 4x = 21
answer
x=4
question
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
answer
2v + 4 = 8
question
How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12)
answer
infinitely many
question
Which number line represents the solution set for the inequality 3x < -9?
answer
Notes line graph name -3
question
What interval includes all possible values of x, where -3(6 - 2x) ≥ 4x + 12?
answer
[15, ∞)
question
Sara wants to find the input value that produces the same output for the functions represented by the tables. What is the input value that produces the same output value in both charts?
answer
2
question
What value of x is in the solution set of -2(3x + 2) > -8x + 6?
answer
6
question
The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n - 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = + 2. Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?
answer
9 sides
question
Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number"?
answer
6 + 2(x + 4) = 1/2(3 - x)
question
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? Check all that apply.
answer
230p - 1010 = 650p - 400 - p
question
What is the solution to -4(8 - 3x) ≥ 6x - 8?
answer
x ≥ 4
question
Nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. Which expression represents Nikita's distance for the second part of the race?
answer
6(0.65 - t)
question
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x - 4.75) = 629.9. She left out the description for the last step.
answer
Divide both sides of the equation by 10.4.
question
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
answer
1/4(x) = (30 + 60)
question
Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?
answer
graph in notes Name $3 ti ckets
question
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
answer
(8, 2.40)
question
Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
answer
y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
question
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let y represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, t? Is the graph of the equation continuous or discrete?
answer
t=4y+7.75; continuous
question
The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes.
answer
$100
question
What is the lowest value of the range of the function shown on the graph?
answer
See graph 3,-2 in notes -2
question
What is the range of the given function? {(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}
answer
{y | y = -9, -3, 0, 5, 7}
question
What is the range of the given function?
answer
{y | y = -7, -1, 0, 9}
question
The table shows ordered pairs of the function y = 8 - 2x. When x = 8, the value of y is
answer
Graph y=8-2x
question
What is the domain of the function shown in the mapping?
answer
{x | x = -5, -3, 1, 2, 6} Input output graph -3,4
question
What is the domain of the function on the graph?
answer
all real numbers greater than or equal to -3
question
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. What is the range of the function?
answer
all real numbers greater than or equal to 11
question
Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?
answer
(1, 3)
question
The function h(t) = -16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot. What does h(3.2) represent?
answer
the height of the rock 3.2 seconds after it is propelled
question
The table represents a function. Which value is an output of the function?
answer
-2 function table in notes
question
Which is true regarding the graphed function f(x)?
answer
f(5)=-1
question
The table represents a function. What is f(5)?
answer
-8
question
The function f(x) is given by the set of ordered pairs. {(1,0), (-10,2), (0,6), (3,17), (-2,-1)} Which equation is true?
answer
f(0)=6
question
The function V(r)=4/3(pi)r^3 can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
answer
the volume of the basketball when the radius is r
question
The table represents a function. What is f(-2)?
answer
1
question
If point (4, 5) is on the graph of a function, which equation must be true?
answer
f(4)=5
question
Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
answer
Both plans cost the same when 50 texts are sent.
question
Which statement is true regarding the functions on the graph?
answer
f(-3) = g(-3)
question
What is f(3)?
answer
9
question
Which statement is true regarding the graphed functions?
answer
f(2) = 0 and g(-2) = 0 View graph EF in notes
question
Which represents where f(x) = g(x)?
answer
f(2) = g(2) and f(0) = g(0) GRAPH EF2
question
When f(x) = -3, what is x?
answer
-1
question
Which represents where f(x) = g(x)?
answer
f(-4) = g(-4) and f(0) = g(0) graph EF3
question
If f(x) = 6x - 4, what is f(x) when x = 8?
answer
44
question
Which statement is true about the end behavior of the graphed function?
answer
As the x-values go to positive infinity, the function's values go to negative infinity.
question
Which statement is true about the graphed function?
answer
F(x) > 0 over the interval (-∞, -4)
question
What are the x-intercepts of the graphed function?
answer
(-3, 0) and (1,0)
question
Which statement is true about the end behavior of the graphed function?
answer
As the x-values go to positive infinity, the function's values go to positive infinity.
question
Which is a y-intercept of the graphed function?
answer
(0, -9) Graph 1 in analyzing graphs
question
Which interval for the graphed function contains the local maximum?
answer
[0, 2]
question
Which lists all of the y-intercepts of the graphed function
answer
(0, -3)
question
Which lists all of the x-intercepts of the graphed function?
answer
(1, 0), (2, 0), and (-3, 0)
question
Which statement is true about the graphed function?
answer
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
question
Which is a valid prediction about the continuous function f(x)?
answer
f(x) ≥ 0 over the interval [5, ∞).
question
Which is a valid prediction about the continuous function f(x)?
answer
f(x) ≥ 0 over the interval [-1, 1].
question
Which lists all of the y-intercepts of the continuous function in the table?
answer
(0, 0)
question
Which is a possible turning point for the continuous function f(x)?
answer
(0, -2)
question
Which is an x-intercept of the continuous function in the table?
answer
(3, 0)
question
Based on the table, which best predicts the end behavior of the graph of f(x)?
answer
As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.
question
Which is an x-intercept of the continuous function in the table?
answer
(-1, 0)
question
What are all of the x-intercepts of the continuous function in the table?
answer
(-4, 0), (4, 0)
question
Adita has two options for how to invest $1,000. Plan A: Put the $1,000 in an account that pays $100 per year. Plan B: Put the $1,000 in an account that pays 5 percent interest per year. Which statement is true?
answer
Plan A will be worth more than plan B after two years.
question
What type of graph is shown, and what is the growth factor?
answer
exponential function; growth factor of 4
question
Which graph represents an exponential function?
answer
LOOK IN NOTES at linear growth #1
question
Which table represents a linear function?
answer
linear growth #2
question
What kind of growth model (pattern) is shown in the table?
answer
exponential 3
question
What is the missing number in the table?
answer
1,296 #4
question
Which of the following best describes how the y values are changing over each interval?
answer
They are being multiplied by 2 each time.
question
Over which interval are the exponential and linear function approximately the same?
answer
from 0.75 to 1.0
question
The table below represents a function. Which statement would best describe the graph of the function?
answer
The graph starts flat but curves steeply upward.
question
Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research. Which insect population is growing at a faster rate?
answer
The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week
question
Which of the following describes the function shown in the table below?
answer
Comparing notes 1 exponential, there is a constant rate of decay or decrease
question
Which number is missing in the table of values below?
answer
216 g2
question
3 4 5 6 8 9 10 Which statement best describes the growth rates of the functions below?
answer
The exponential function grows faster than the quadratic function over two intervals; 2<x<4.
question
Which rule can be used to describe the growth of the y-values of the function mc018-1.jpg over each interval from mc018-2.jpg to mc018-3.jpg?
answer
multiply by 12
question
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval mc016-1.jpg?
answer
The exponential function decays at three-fourths the rate of the quadratic function.
question
Which of the following describes the growth rate of the exponential function in the graph below?
answer
For each x increase of 1, the y increases by a common factor of 3.
question
What is f(0)?
answer
unit review 1 -6 only
question
Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers. To the nearest tenth of a second, how much time would it take the penny to hit the ground?
answer
0.6 seconds
question
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
answer
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
question
Consider the function represented by the graph. What is the domain of this function?
answer
{x| x >0}
question
A ball is thrown straight up into the air. The height, in feet, h(t), of the ball collected over t seconds is shown in the table. Which statement is true?
answer
The maximum height of the ball was 2.5 seconds after it was thrown.
question
Which ordered pair could be removed so that the set of ordered pairs is a function?
answer
(4, -2)
question
According to the table, which ordered pair is a local minimum of the function, f(x)?
answer
(0, 9)
question
The graph represents a functional relationship. Which value is an input of the function?
answer
4
question
The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement is true?
answer
Seven erasers cost $3.50.
question
Which statement is true regarding the functions on the graph?
answer
f(2) = g(2)
question
Which could be the entire interval over which the function, f(x), is negative?
answer
(-∞, -6)
question
Which interval for the graphed function contains the local minimum?
answer
g2 [-3, -1]
question
Analyze the graph of the function f(x) to complete the statement.
answer
F(x) < 0 over the intervals (-∞, -3) and (-1.1,0.9)
question
Which ordered pair can be removed so that the resulting graph represents a function?
answer
(1,3)
question
Which graph represents a function?
answer
g3
question
The table below shows the amount that must be repaid, y, when x dollars are borrowed.
answer
y=5/4x+10
question
The table below shows the predicted number of words Janae can type, y, in x minutes. Which describes the pattern in the table?
answer
Janae types 30 words each minute.
question
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
answer
TAbles graph 1
question
Which table of values corresponds to the graph below?
answer
graph 2
question
The table below shows the relationship between the approximate number of hours and the corresponding number of days on Saturn.
answer
658 2/3
question
Four representations of the same data are shown below. Which two representations are considered to be only partial representations?
answer
the verbal description and the graph
question
Which table of values corresponds to the graph below?
answer
g3
question
Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states?
answer
this is a graph- points are 1,20 2,40, 3,60
question
1 2 3 4 7 8 10 The graph below represents the number of books Jaleel has read over the past x weeks. Which equation represents the graph?
answer
y = 3x
question
Anderson is a plumber and is paid a fixed amount just to make a house visit. The remainder of his fee, y, is determined by the number of hours that he works, x, as shown below. Which equation represents the graph?
answer
y = 10x + 50
question
Which table represents a linear function?
answer
Introduction g1
question
The graph shows the amount of money Miguel earns after working x hours. What is the ratio of the change in y-values to the change in x-values for this function?
answer
13:1
question
The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table?
answer
15 grapes eaten per minute
question
Which functions have an additive rate of change of 3? Check all that apply.
answer
4,6 is a point
question
The table shows the distance traveled over time while traveling at a constant speed. What is the ratio of the change in y-values to the change in x-values?
answer
1,200:1
question
Which table represents a linear function?
answer
g2
question
A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
answer
The set must have a constant additive rate of change.
question
The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
answer
$1.50
question
The table below shows measurements (in inches) from cubes with different side lengths. Which pairs of variables have a linear relationship? Check all that apply.
answer
side length and perimeter of 1 face perimeter of 1 face and area of 1 face side length and volume
question
The graph shows the increase in temperature over time in an oven. What is the change in the y-values and x-values on the graph?
answer
The change in the y-values is 40 and the change in the x-values is 1.
question
Which relationship has a zero slope?
answer
g1 slope of a line
question
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
answer
The slope of the line will be zero
question
The graph of a linear function is shown. Which word describes the slope of the line?
answer
negative
question
Which graph has a slope of 4/5?
answer
g2
question
The graph represents the balance on Harrison's car loan in the months since purchasing the car. Which statement describes the slope of the line?
answer
Harrison makes a monthly payment of $250.
question
The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height. What is the slope of the line?
answer
2
question
The graph of a linear function is shown. Which word describes the slope of the line?
answer
zero g3
question
The table represents a linear function. What is the slope of the function?
answer
-6
question
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
answer
Aaron's rate for mowing lawns is 0.5 acres per hour.
question
The sequence below represents Marisa's fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa's library fine as a function of a book that is n days overdue?
answer
f(n) = 0.15n + 0.35
question
What is the constant of variation, k, of the direct variation, y = kx, through (-3, 2)?
answer
k = -2/3
question
Three points of a function are graphed. Which statement describes the function through the points?
answer
The function is linear but is not a direct variation function.
question
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
answer
y = 7x
question
The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table. The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?
answer
9.8 m/s^2
question
Which graph represents a function with direct variation?
answer
g4
question
The table represents a bicycle rental cost in dollars as a function of time in hours. Which explains whether or not the function represents a direct variation?
answer
This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
question
A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served. If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?
answer
t = 1.8g
question
The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence?
answer
The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.
question
What is the common difference in the following arithmetic sequence? 7, 3, -1, -5, ....
answer
-4
question
Which of the following is true about the sequence graphed below?
answer
The sequence is arithmetic because the terms have a common difference.
question
Ms. Clark earned $29,600 in her third year as a banker and $32,600 in her seventh year. How much did she make in her tenth year? Assume that her yearly salaries form an arithmetic sequence.
answer
$34,850
question
What is the common difference of the arithmetic sequence graphed below?
answer
2
question
Which of the following is an arithmetic sequence?
answer
1/2,2,7/2,5,...
question
Which of the following is true regarding the sequence graphed below?
answer
The sequence is not arithmetic because the terms do not have a common difference.
question
What is the next term in the sequence 58, 47, 36, 25, ...?
answer
14
question
A karate studio charges $35 for the first course and $22.50 for each course after that, even if the student leaves the course early. Cena paid $170 for her son to take courses. How many courses did he take?
answer
7 courses
question
What is the explicit rule for the arithmetic sequence shown in the graph?
answer
an-9.5+2(n-1)
question
What is the common difference in the following arithmetic sequence?
answer
11
question
Which of the following is an arithmetic sequence?
answer
unit review 1
question
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
answer
-2/5
question
The table below shows the amount of money Sarah spends for a craft demonstration. Number of People Attending Cost 5$15 8$18 10$20 15$25 Sarah spends a total of $60. Based on the information in the table, how many people attended the craft demonstration
answer
50
question
The table represents a linear function. What is the slope of the function?
answer
-4 g2 unit review
question
The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?
answer
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
question
A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?
answer
y=x/3
question
Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same information, as shown below. Which piece of information does not represent the same information as the other three parts?
answer
graph
question
Based on the information in the graph, if David's bill came to $66 after the coupon was applied, how much would his bill have been if he hadn't used the coupon?
answer
$68
question
A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?
answer
The line does not represent a direct variation because it does not go through the origin.
question
Which table represents a linear function?
answer
g3
question
What is the constant of variation, k, of the line y = kx through (3,18) and (5,30)?
answer
6
question
Mrs. Jackson gives the table below to her students. In order for the function to be linear, what must m be and why?
answer
m = 20 because the rate of change is -3.
question
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
answer
m = 90 - 6d
question
The table represents the function f(x). Which function of t has the same slope and y-intercept as f(x)?
answer
f(t) =2/3 t + 4
question
What are the slope and y-intercept of the linear function graphed to the left?
answer
slope: -1/2; y-intercept: 1
question
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
answer
graph with point 8,12
question
A store offers packing and mailing services to customers. This table is given to customers to help them estimate the cost of shipping a box based on its weight in pounds, and a flat rate of $5 for packing. Which equation represents the shipping cost as a function of x, the weight in pounds?
answer
f(x) = 2.25x + 5
question
What is the slope of the line represented by the equation y = -1/2-x +1/4 ?
answer
-1/2
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Which equation represents the graphed function?
answer
y=-1/3x+3
question
Which equation represents the graphed function?
answer
y=-2x+3
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Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
answer
y - 2 = 1/3(x - 3)
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What is the slope of the line?
answer
-1/2
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Which equation represents a line that passes through (5, 1) and has a slope of 1/2/?
answer
y-1=1/2(x-5)
question
Which steps should be used to graph the equation y - 4 = (x + 2)?
answer
1. Plot the point (-2,4). 2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.
question
Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?
answer
f(x) = -3x + 14
question
Alejandra correctly wrote the equation y - 3 =1/5 (x - 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
answer
y - 3 = 2(x - 10)
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Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?
answer
y-1/3+3/4(x-4)
question
What is the slope of the line?
answer
5/2 points are 0,-1 and 2,4
question
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
answer
m=90-6d
question
The table represents the function f(x). Which function of t has the same slope and y-intercept as f(x)?
answer
f(t) =2/3 t + 4
question
What are the slope and y-intercept of the linear function graphed to the left?
answer
slope:-1/2 ; y-intercept: 1
question
Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative?
answer
g1
question
Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
answer
y - 1 = 3x
question
The graph of the equation x - 2y = 5 has an x-intercept of 5 and a slope of 1/2 . Which shows the graph of this equation?
answer
:Line passes through longitude of 5 and lat of in between -2 & -3
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Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
answer
-9
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The table represents a linear equation. Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form?
answer
y + 6 =2/5 (x + 2)
question
A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = (x - 2). Which equations also represent this line? Check all that apply.
answer
y = -5/3x+10/3 3y = -5x + 10 5x + 3y = 10
question
Which linear function represents the line given by the point-slope equation y - 8 = (x - 4)?
answer
f(x) =1/2 x + 4
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Which is true of the standard form of the equation of the line graphed?
answer
The value of A can only be 1, the value of C can only be -3, and the value of B is 0.
question
How does the slope of g(x) compare to the slope of f(x)?
answer
The slope of g(x) is less than the slope of f(x).
question
What is the equation of the graphed line written in standard form?
answer
x - 4y = 4
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What is the equation of the line that is perpendicular to the line y = 6 and passes through the point (-4, -3)?
answer
x = -4
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What is the equation of the line in slope-intercept form that is perpendicular to the line y = 3/4x - 2 and passes through the point (-12, 10)?
answer
y = -4/3x - 6
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Which equation represents the graphed function?
answer
y=1/4x-2
question
Timmy writes the equation f(x) = x - 1. He then doubles both of the terms on the right side to create the equation g(x) = x - 2. How does the graph of g(x) compare to the graph of f(x)?
answer
The line of g(x) is steeper and has a lower y-intercept.
question
Raphael graphed the functions g(x) = x + 2 and f(x) = x - 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? The y-intercept of f(x) is
answer
3
question
MOST RECENT TEST STARTS ON 245
answer
question
A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic. Which graph could represent the area of each rectangle in terms of the change in the length and width?
answer
Points located on 0.40 1,45 2,47 8,25
question
Daniel is on an airplane flying to a destination 825 miles away. After one hour, the pilot announces that the plane is 495 miles away from its destination airport. In another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles. Which equation represents the remaining distance, in miles, to the destination in terms of t, the time, in hours, since leaving the airport?
answer
d = 825 - 330t
question
The graph shows the population of a bacteria in an experiment, measured every hour. Which function represents the population of the bacteria after t hours?
answer
f(t) = 10(1.4)t
question
Alicia bought a notebook and several erasers at the student store. The graph shows the relationship between the total cost of her items and the number of erasers she purchased. What is the cost of each eraser?
answer
$1.50
question
The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours. Which function can be used to determine the approximate number of grams of the sample remaining after t hours?
answer
y = 50(0.85)x
question
Sophia plots points on a graph to represent the shape of a concave lens. Which type of function should Sophia use to model the shape of the lens?
answer
quadratic
question
If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?
answer
Ppoints 0,15 1,25
question
Teddy is preparing to sell some wooden blocks at a garage sale. Before pricing individual bags of blocks, he decides to determine the approximate number of blocks per pound by researching the weights of different sets of blocks. The graph shows his data. About how many blocks are there per pound? Round to the nearest block.
answer
20 blocks
question
Amanda is studying relationships between the values and ages of different items. She decides to ask teachers at her school to estimate the values and ages of their cars. She will exclude any antique cars and knows that the value of a car depreciates over time. Which correlation is expected between the age and value of a car?
answer
negative
question
The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. According to the line of best fit, about how many minutes will it take for the temperature to reach 100°C, the boiling point of water?
answer
5
question
Mr. Palmer does an experiment to investigate the effects of distractions on studying and learning. He gives each participant a line with 10 words to memorize in 5 minutes. Some of the participants are interrupted during the 5 minutes with text messages from friends. The graph shows the number of words remembered after 5 minutes and the number of text messages sent to the participants as distractions. According to the line of best fit, about how many words would a person remember if he or she is distracted by 7 text messages?
answer
5 words
question
The table shows the ages and weights of babies at a hospital. What is the correlation between age and weight as shown in the table?
answer
positive
question
Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data. According to the line of best fit, about how many times would the coin land heads up in 100 flips?
answer
53
question
Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian. The table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude. Which statement describes the slope of the line of best fit for the data?
answer
The temperature decreases by about 1.7° for each 1 degree increase north in latitude.
question
Which table shows a negative correlation?
answer
graph 1 in most recent
question
Which is most likely the correlation coefficient for the set of data shown?
answer
0.19
question
Which r-value represents the strongest negative correlation?
answer
-0.7
question
Which is most likely the correlation coefficient for the set of data shown?
answer
-0.91
question
Which r-value represents the weakest correlation?
answer
0.11
question
Which relationships would most likely be causal? Check all that apply.
answer
a positive correlation between the number of homework assignments completed and the grade on the exam a positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers
question
What is the correlation coefficient for the data shown in the table?
answer
R=1
question
Which r-value represents the most moderate correlation?
answer
0.56
question
Which relationships would most likely be causal? Check all that apply.
answer
a negative correlation between the temperature and the amount of snow still on the ground a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
question
The table shows the time a patient spends at the dentist and the amount of the bill. What is the correlation coefficient for the data in the table?
answer
0.93
question
The table shows the relationship between time spent running and distance traveled. Which type of model best describes the relationship?
answer
linear, because the r value for the linear model is closest to 1
question
Janna is making a prediction of the frequency of a key that is 12 keys from middle C. Which best describes her prediction?
answer
extrapolation, because a key that is 12 keys from middle C is outside the data set
question
Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments. She calculates two regression models. Which is true?
answer
The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.
question
The table compares x, the number of minutes of television Sam watched each day, to y, the number of minutes she spent exercising. The function y = -0.78x + 95 models the data in the table. Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?
answer
72 minutes
question
The quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the road. What does the graph of the regression model show?
answer
The height of the surface decreases from the center out to the sides of the road.
question
Marta's mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days?
answer
6,271
question
The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C. Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C?
answer
49.44
question
The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000. For which year would this model most likely be sufficient to make a prediction of the population?
answer
2005
question
The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?
answer
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
question
The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants. According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5?
answer
13
question
The table shows the height of a candle as it is continuously burned. Which statement describes the candle?
answer
The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.
question
Which is most likely the correlation coefficient for the set of data shown?
answer
-0.21
question
A line of best fit is drawn for the set of points shown on the graph. Which point is an approximate extrapolation for x = 30 from the line of best fit?
answer
(30, 38)
question
The table shows the value of a savings bond that doubles in value after 5 years. Which statement describes the bond?
answer
The bond had an original value of $50 and grows at a rate of 15%.
question
The graph shows the exponential regression model for data representing a rabbit population after x years. Which is true of the regression model?
answer
The graph of the regression model is limited to whole-number values for y
question
The data in the table represents the predicted price of a gallon of milk, y, for number of years, x. Which form of an equation was used to model the price of a gallon of milk?
answer
y = abx
question
What function models the data shown on the graph?
answer
f(x) = -2(x - 5)(x - 1)
question
The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table. Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?
answer
20
question
Which best describes the strength of the model with an r-value of -0.93?
answer
a strong negative correlation
question
The table shows the average number of hours of daylight per day for the last four months of the year. What is the correlation coefficient for the data in the table?
answer
-0.993
question
The table shows the shoe sizes of women of different ages. Which best describes the strength of the model?
answer
a weak positive correlation
question
The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = -16x2 + 100 models the data in the table. For which value of x would this model make the least sense to use?
answer
-2.75
question
The table shows a company's profit based on the number of pounds of food produced. Using the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?
answer
$5,300
question
Consider the function represented by the graph. What is the domain of this function?
answer
{x| x >0}
question
Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?
answer
20
question
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C(f)=5/9(f-32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
answer
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
question
What is the equation of the line in slope-intercept form that is perpendicular to the line y = x - 2 and passes through the point (-12, 10)?
answer
y = -4/3x - 6
question
Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
answer
-9
question
Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school. What does the slope of the graph mean?
answer
Tracie's bus travels towards her home at an average speed of 1/2 mile per minute.
question
The graph represents a functional relationship. Which value is an input of the function?
answer
4
question
Which explains how the table can be used to predict the cost of any number of students attending the game?
answer
The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.
question
Which is most likely the correlation coefficient for the set of data shown?
answer
-0.21
question
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
answer
$2.50
question
Which equation can be used to find h, the number of hours Lindsay worked last week?
answer
1/15(10h+60)=1/10(10h)
question
Which graph represents a function?
answer
Sideways porabla
question
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
answer
-2/5
question
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? Check all that apply.
answer
2.3p - 10.1 = 6.49p - 4 230p - 1010 = 650p - 400 - p
question
What is the value of r, the part of the tile that Hector could install in 1 hour?
answer
1/18
question
According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5?
answer
13
question
Which form of an equation was used to model the price of a gallon of milk?
answer
y=ab^x
question
To the nearest tenth of a second, how much time would it take the penny to hit the ground?
answer
0.6
question
Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
answer
y - 1 = 3x
question
How much money will she have if she doesn't buy any packs of baseball cards?
answer
$20
question
A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?
answer
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground
question
The explicit rule for an arithmetic sequence is mc023-1.jpg What is the value of the 47th term? Round to the nearest tenth, if necessary.
answer
-55.7
question
How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12)
answer
infinitely many
question
F(x) < 0 over the intervals (-∞, -3) and
answer
(-1.1, 0.9)
question
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
answer
1/4(x) = x(30 + 60)