1. the graph shows the frequency distribution of a list of randomly generated integers between 0 and 10. what is the mean of the list of numbers?
2. the table below shows the number of cats and dogs that were seen at a veterinarian’s office last friday. if an animal receiving shots is chosen at random, what is the probability that the animal is a dog? write your answer as a reduced fraction.
3. a right circular cylinder has a base diameter of 22 cm and a height of 6 cm. what is the volume of the cylinder? (v = πr²h)
4. in the figure shown below, m∠pqr = 132 and m∠prs = 163. what is m∠qpr? show all work.
5. if 6x + 15 = 27, what is the value of 2x + 5?
6. a car speeds down the interstate at 85 miles per hour. what is this speed in miles per minute?
7. the enrollment of a community college last year was 4500 students. it increased by 5% this year. what is the enrollment this year at the community college?
8. a gaming system is on sale for 25% off its original price. if the sale price of the system is $412.50, what was the original price of the system?

Question

Accepted Answer

### 1.
# Explanation:
## Step1: Calculate sum of products
From the frequency - distribution graph:
$$
\begin{align*}
&(0\times1)+(1\times1)+(2\times1)+(3\times1)+(4\times3)+(5\times2)+(6\times1)+(7\times1)+(8\times1)+(9\times1)+(10\times1)\
=&0 + 1+2 + 3+12+10+6+7+8+9+10\
=&68
\end{align*}
$$
## Step2: Calculate total frequency
The total frequency is $1 + 1+1+1+3+2+1+1+1+1+1=13$
## Step3: Calculate the mean
The mean $\bar{x}=\frac{68}{13}\approx5.23$

# Answer:
$\frac{68}{13}$

### 2.
# Explanation:
## Step1: Identify number of dogs getting shots and total number of animals getting shots
The number of dogs getting shots is 6, and the total number of animals getting shots is $6 + 3=9$
## Step2: Calculate the probability
The probability $P=\frac{6}{9}=\frac{2}{3}$

# Answer:
$\frac{2}{3}$

### 3.
# Explanation:
## Step1: Find the radius
Given the diameter $d = 22$ cm, the radius $r=\frac{d}{2}=\frac{22}{2}=11$ cm
## Step2: Use the volume formula
The volume formula of a cylinder is $V=\pi r^{2}h$, with $r = 11$ cm and $h = 6$ cm. So $V=\pi\times11^{2}\times6=\pi\times121\times6 = 726\pi$ $cm^{3}$

# Answer:
$726\pi$ $cm^{3}$

### 4.
# Explanation:
## Step1: Use the exterior - angle property of a triangle
The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In $\triangle PQR$, $\angle PRS$ is an exterior angle. Let $\angle QPR=x$. Then $\angle PRS=\angle QPR+\angle PQR$
## Step2: Solve for $\angle QPR$
We know that $\angle PQR = 132^{\circ}$ and $\angle PRS=163^{\circ}$. So $x=\angle PRS-\angle PQR=163 - 132=31^{\circ}$

# Answer:
$31^{\circ}$

### 5.
# Explanation:
## Step1: Solve the first equation for $x$
Given $6x + 15=27$, subtract 15 from both sides: $6x=27 - 15=12$, then $x = 2$
## Step2: Substitute $x$ into the second expression
Substitute $x = 2$ into $2x+5$, we get $2\times2+5=4 + 5=9$

# Answer:
9

### 6.
# Explanation:
## Step1: Convert hours to minutes
Since there are 60 minutes in 1 hour, to convert 85 miles per hour to miles per minute, divide 85 by 60. $85\div60=\frac{85}{60}=\frac{17}{12}\approx1.42$ miles per minute

# Answer:
$\frac{17}{12}$ miles per minute

### 7.
# Explanation:
## Step1: Calculate the increase factor
The enrollment increased by 5%, so the increase factor is $1+\frac{5}{100}=1.05$
## Step2: Calculate the new enrollment
Multiply the original enrollment of 4500 by the increase factor: $4500\times1.05 = 4725$

# Answer:
4725

### 8.
# Explanation:
## Step1: Let the original price be $x$
If the item is 25% off, then the sale price is $(1 - 0.25)x=0.75x$
## Step2: Solve for $x$
We know that $0.75x = 412.50$. Divide both sides by 0.75: $x=\frac{412.50}{0.75}=550$

# Answer:
$550$

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QUESTION IMAGE

Question

Explanation:

1.

Step1: Calculate sum of products

Step2: Calculate total frequency

Step3: Calculate the mean

Step1: Identify number of dogs getting shots and total number of animals getting shots

Step2: Calculate the probability

Step1: Find the radius

Step2: Use the volume formula

Answer:

2.