#### (a)

The probability that a randomly selected show will have an unacceptable sound quality is the following:

$$
p=dfrac{6+10+7}{33+59+40}=0.17
$$

#### (b)

We can notice the following:

$$
dfrac{27}{33}=dfrac{49}{59}=dfrac{33}{40}approx0.82
$$

We can notice that those probabilities are equal, so, there is no association between the sound quality and the microphone used.

a) $p=0.17$; b) there is no association.

We are given that $x$ is the area (in square miles) deforested per year.

The total area is 1400000 minus the rate times the number of years. In 50 years, the area should be “more than” or “greater than” 1200000 square miles:

$$
1400000-x(50)>1200000
$$

or

$$
color{#c34632}1400000-50x>1200000
$$

First, we find the boundary point by replacing the inequality symbol with $=$ then solve for the corresponding equation:

$$
begin{align*}
1400000-50x &=1200000\
-50x &=-200000\
x&=4000
end{align*}
$$

Next, pick a test point except for the boundary point, say $x=0$ to substitute to the inequality:

$$
begin{align*}
1400000-50(0) &> 1200000 \
1400000 &> 1200000 \
end{align*}
$$

The test point is a solution which means all points on this side of the boundary point are part of the solution, which is to the left of it:

$$
color{#c34632}x< 4000
$$

$1400000-50x>1200000$ ; $x< 4000$ or less than 4000 square miles per year

Let $t$ be the remaining time they need to book, in hours.

For Lorena, she returned 38 books and has a rate of 16 books per hour so she will book:

$$
38+16t
$$

For Glenda, she returned 52 books and has a rate of 20 books per hour so she will book:

$$
52+20t
$$

Together, they started with a total of 252 books (that must be returned) so we can write the equation:

$$
(38+16t)+( 52+20t)=252
$$

Simplify the left side:

$$
36t+90=252
$$

Subtract 90 from both sides:

$$
36t=162
$$

Divide both sides by 36:

$$
t=4.5
$$

So, they still need $text{textcolor{#c34632}{4.5 hours}}$ more to return all the books.

Let $a$ be the number of apples and $o$ be the number of oranges.

The total cost is $$0.75$ times the number of apples, plus $$0.50$ times the number of oranges. Since the money is under $$10$, or less than $$10$:

$$
color{#c34632}0.75a+0.50o<10
$$

$$
0.75a+0.50o<10
$$

#### (a)

The new equation is the following:

$$
g(x)=0.25^x+2
$$

Here we have translation for $2$ units up.

#### (b)

The new equation is the following:

$$
g(x)=0.25^x-3
$$

Here we have translation for $3$ units down.

#### (c)

The new equation is the following:

$$
g(x)=0.25^x+1.3
$$

Here we have translation for $1.3$ units up.

#### (d)

The new equation is the following:

$$
g(x)=0.25^x-18
$$

Here we have translation for $18$ units down.

a) $g(x)=0.25^x+2$; b) $g(x)=0.25^x-3$;

c) $g(x)=0.25^x+1.3$; d) $g(x)=0.25^x-18$

We can notice that the center value of National Airways is $0$

and its spread is $58$, while the center value of Jet Set is $19$

and its spread is $19$.

We can conclude that Jet Set is on tame more often than National Airways.

#### (b)

If Arin wants to summarize his findings, in this case, it is better to use median and $IQR$,

in this situation, it is better because there is a finite number of data.

a) Jet Set is on time more often; b) Better use median and $IQR$

Here we have that side $DR$ is a side of both triangles and given angles which are equal in the task, so, according to the $AAS$ condition, those triangles are congruent.