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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

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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

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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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Which is the leading coefficient in 2x^3 + 5x^2 - 4^x + 7 ???

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What is the degree of the polynomial in 2x^3 + 5x^2 - 4^x + 7 ???

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What is the degree of the 2nd monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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What is the degree of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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What is the coefficient of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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What is the coefficient of the fourth monomial in 2x^3 + 5x^2 - 4^x + 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

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Algebra 1 Algebra 2

Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards 12 terms

Maddison Bailey

12 terms

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Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards

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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

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Algebra 1 Algebra 2

Algebra I: Write Linear Equations – Flashcards 25 terms

Noah Thomson

25 terms

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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

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Algebra 2 Measure Of Central Tendency

AQR Unit 4 – Flashcards 70 terms

Ewan Tanner

70 terms

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AQR Unit 4 – Flashcards

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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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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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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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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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4. In how many ways can 3 singers be selected from 5 who came to an audition?

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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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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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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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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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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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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

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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

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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

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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

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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.

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22%

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7. Use the Binomial Theorem to find the binomial expansion of the expression. (d-5)^6

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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?

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479,001,600

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2. Evaluate 9P4

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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?

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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?

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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?

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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.

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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?

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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?

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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.

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0.813

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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.

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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.

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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.

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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

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30th percentile = 7 90th percentile = 19

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14. Use the Binomial Theorem to find the binomial expansion of the expression. (d + 3)7

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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.

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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?

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25 bags

STUDY

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

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What is the number of real solutions? - x² + 9x + 7 = 0

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use b^2-4ac

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What is the number of real solutions? 8x² - 11x = -3

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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

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use b^2-4ac

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What is the expression in factored form? 2x² + 16x + 30

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2(x+3)(x+5)

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What is the expression in factored form? - 4x² + 8x + 32

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__________________

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What is the expression in factored form? 3x² + 26x + 35

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__________________

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What is the expression in factored form? 9x² - 18x + 9

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__________________

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What is the expression in factored form? x² - 64

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__________________

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What are the solutions of the quadratic equation? x² - 9x + 18 = 0

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__________________

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What are the solutions of the quadratic equation? 3x² + 25X + 42 = 0

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__________________

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What are the solutions of the quadratic equation? 4x² - 18x + 20 = 0

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__________________

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Solve by using tables. Give each answer to a most two decimal places. 2x² + 5x - 3 = 0

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__________________

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Solve by using tables. Give each answer to a most two decimal places. - 7x² - 2 = -10x

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__________________

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What is the solution of each equation? 3x² = 21

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__________________

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What is the solution of each equation? 108x² =147

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__________________

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Solve the equation. x² + 18x + 81 = 25

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__________________

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Solve the equation. x² - 8x + 16 = 16

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__________________

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Solve the equation. 0.125r - 0.0625 + 0.25r = 0.25 + r

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__________________

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Solve the equation. - 5y - 9 = - ( y - 1 )

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__________________

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Solve the quadratic equation by completing the square. x² + 10x + 14 = 0

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__________________

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Solve the quadratic equation by completing the square. - 3x² + 7x = - 5

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__________________

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

__________________

STUDY

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

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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

STUDY

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

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

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

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

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

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

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

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

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

STUDY

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

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mode

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the measurement level below which half the observations fall, the 50th percentile

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median

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the sum of the observed measurements divided by the number of observations

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mean

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ability to distinguish between who has a disease and who does not

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validity

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What are two ways to measures validity?

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1. specificity 2. sensitivity

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ability of the test to determine correctly those who have the disease

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sensitivity

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ability of the test to determine correctly those who do not have the disease

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specificity

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true positive/true positive + false negative

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sensitivity

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true negative/true negative + false positive

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specificity

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the degree to which the study accurately answers the question it is intended to answer

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internal validity (study)

question

What are threats to internal validity?

answer

1. selection bias 2. information bias 3. uncontrolled confounding 4. small study sample

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the extent to which we can generalize the results of a study to a broader population beyond the study population

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external validity (generalizability)

question

What is the threats to external validity?

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1. small study sample 2. improper selection of sample

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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

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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

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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)

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negative predictive value

question

What are the factors that affect the predictive value?

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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

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intraobserver variation

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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

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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

STUDY

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.

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3. If an equation contains both addition and subtraction with neither in parenthesis, you do the first one

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first.

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4. If an equation contains both multiplication and division with neither in parenthesis, you do the first one

answer

first.

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5. The answer to an addition problem is a

answer

sum.

question

6. The answer to a subtraction problem is the

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difference.

question

7. The answer to a division problem is a

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quotient.

question

8. The answer to a multiplication problem is a

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product.

question

9. A lower case letter that stands for an unknown number is a

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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

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expression.

question

12. An expression does not contain an

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equal sign.

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13. To multiply by 10, move the decimal one place to the

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right.

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14. To multiply by 100, move the decimal two places to the

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right.

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15. To divide by 10, move the decimal one place to the

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left.

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16. To divide by 100, move the decimal two places to the

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left.

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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

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decimal.

question

19. Moving the decimal two places to the right changes a decimal number to a

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percent.

question

20. A percent can be changed to a fraction by putting the number over 100 and

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reducing to lowest terms.

question

21. When dividing a fraction to change it to a decimal, the top number goes in the

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"house".

question

22. To change a percent to a decimal, remove the percent sign and

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move the decimal two places to the left.

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23. To add or subtract fractions, you must first find a common denominator and

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change both fractions.

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24. To add or subtract decimals, you must first

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align the decimals.

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25. To multiply decimals, you multiply the problem first and then put the decimal in the answer,

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counting the same number of decimal places from the right as found in the problem.

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26. To divide by a decimal, change the divisor to a whole number and move the decimal in the dividend

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the same number of places to the right.

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27. To multiply fractions, multiply the numerators and denominators

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straight across and simplify.

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28. To divide fractions,

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flip the second fraction and multiply.

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29. A triangle with all sides congruent is

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equilateral.

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30. A triangle with two congruent sides is

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isosceles.

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31. A triangle with no congruent sides is

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scalene.

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32. Every triangle can be classified by its

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sides or angles.

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33. A triangle with two congruent angles and two congruent sides is

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isosceles.

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34. A triangle with 2 acute angles and one obtuse angle is

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obtuse.

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35. A triangle with 3 angles which measure less than 90° is

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acute.

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36. A triangle with one angle which measures exactly 90° is

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right.

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37. Two values that are the same are

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equal.

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38. Two shapes that are exactly the same are

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congruent.

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39. Two shapes that are the same shape but different sizes are

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similar.

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40. A number can be divided evenly by 2 if it is

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even.

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41. A number can be divided evenly by 5 if it ends

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in 5 or 0.

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42. A number can be divided evenly by 3 if the sum of its digits can be divided evenly by

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43. A number can be divided evenly by 9 if the sum of its digits can be divided evenly by .

answer

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44. A number can be divided evenly by 6 if it is even and can be divided by

answer

question

45. A closed figure made of straight lines is a

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polygon.

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46. A polygon with 5 sides is a

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pentagon.

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47. A polygon with 6 sides is a

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hexagon.

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48. A polygon with 7 sides is a

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heptagon.

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49. A polygon with 8 sides is an

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octagon.

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50. A polygon with 10 sides is a

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decagon.

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51. A polygon with 4 sides is a

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quadrilateral.

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52. The symbol for "is less than" is

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53. When placing numbers on a number line, negative numbers always go the

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left of zero.

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54. When comparing two numbers, the largest is always the one to the

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right on a number line.

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55. When comparing two fractions with different denominators, use the

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bottoms-up method.

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56. When comparing 3 or more fractions with different denominators, you must find a

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common denominator.

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57. When comparing decimals, write the decimals in a list,

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align the decimals, annex zeros, and compare.

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58. An angle measuring exactly 90°is a

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right angle.

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59. An angle measuring less that 90°is called

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acute.

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60. An angle measuring more than 90°is called

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obtuse.

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61. An angle measuring exactly 180°is called a

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straight angle.

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62. Two angles which are next to each other and share a leg are said to be

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adjacent.

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63. Two angles whose measurement totals 90°are

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complementary.

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64. Two angles whose measurement totals 180° are

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supplementary.

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65. When two lines cross, the two angles directly across from each other look like kissing foxes and are classified as

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vertical angles.

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66. Lines that cross are

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intersecting lines.

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67. Lines that cross at a 90° angle are

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perpendicular lines.

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68. Two lines that are in the same plane and stay the same distance apart are

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parallel lines.

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69. Two lines that are not in the same plane and never touch are

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skew lines.

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70. Numbers that only have themselves and one as factors are

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prime numbers.

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71. Numbers that are not prime are

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composite.

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72. Little numbers that are multiplied to make a product are called

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factors.

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73. Two numbers equal distance from zero are called

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opposites.

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74. The distance a number is from zero is called its

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absolute value.

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75. The smallest number in a set of data is called the

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minimum.

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76. The highest number in a set of data is called the

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maximum.

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77. The middle number in a set of data is called the

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median.

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78. The average is also called the

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mean.

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79. To solve for the variable in a one-step equation, you must do the

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inverse operation.

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80. On a coordinate plane, the horizontal number line is called the

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x-axis.

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81. On a coordinate plane, the vertical number line is called the

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y-axis.

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82. The place where the x- and y-axis cross is called the

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origin.

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83. The points on a coordinate plane are designated by two numbers in parenthesis called the

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ordered pair.

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84. In an ordered pair, the first number tells you to go left or right from the

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origin.

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85. In an ordered pair, the second number tells you to go up or down from the

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x-axis.

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86. Compound probability can be displayed by making a

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list or drawing trees.

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87. The list of all possible outcomes when figuring probability is known as a

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sample space.

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88. The result of an experiment or even is an

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outcome

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89. An outcome is always shown as a

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whole number.

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90. Probability is shown as a

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decimal or a fraction.

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91. Sliding a point or one dimensional figure on a coordinate plane is called

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translation.

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92. Flipping a point over an axis on a coordinate plane is called

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reflection.

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93. Turning a figure around a point on a coordinate plane is called

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rotation.

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94. To convert a metric measurement to a smaller unit, move the decimal to the

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right.

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95. To convert a metric measurement to a larger unit, move the decimal to the

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left.

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96. The formula for perimeter of a polygon is

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add all sides.

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97. The formula for area of a square is

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side squared. (length x width)

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98. The formula for area of a rectangle is length times

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width.

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99. The formula for area of a triangle is base times height divided by

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two.

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100. The area of a polygon is always labeled in

answer

square units.

STUDY

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

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Parabola

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

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Parent Function

answer

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

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Vertex

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the point of intersection of lines or the point opposite the base of a figure

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Axis Of Symmetry

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A line that divides a figure in half so that each half is the mirror image of the other

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Minimum Value

answer

The lowest point of a parabola (when a>0)

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Maximum Value

answer

The highest point of a parabola ( when a<0)

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Intercept Form

answer

y=a(x-p)(x-q)

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Quadratic Equation

answer

ax² + bx + c = 0

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x-intercept

answer

x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero

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Square Root

answer

√(xy) = √x · √y, a number that when multiplied by itself equals a given number

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Zero Of a Function

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a value of x that makes the function's value zero

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Roots

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the solutions to a quadratic equation

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Perfect Square

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a square of a whole number

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Linear Function

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a function in which the graph of the solutions forms a line

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Exponential Function

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a function in which an independent variable appears as an exponent

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Discriminant

answer

b²-4ac

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Perfect Square Trinomial

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a trinomial in the form a²+2ab+b² or a²+2ab+b²

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Axis of symmetry (mathematically)

answer

X = - b/2a

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vertex has a x-coordinate of

answer

X = - b/2a, (X,Y)

STUDY

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]

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A) Rate of Change [PI]

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Current Year/Base Year

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B) Price Index [PI]

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Rate of Change x 100

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Real Wage

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Wage Rate/Price Level

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Real Income

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Income/Price Level

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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

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Fixed Rates

answer

1) Payment form loan and savings 2) Doesn't change based on interest rate from inflation

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Adjusted Rates

answer

Payment could change based on interest rate from inflation

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A) Frictional Unemployment

answer

Between jobs

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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

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D) Government Spending [G]

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Spending on purchases of g/s

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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

STUDY

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

STUDY

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