uses objective e
in 17–21, calculate the rate for the given situation.
17. hurricane helene traveled 480 miles in 48 hours.
a. miles per hour
b. miles per minute
18. anastasia spent $42.50 on 5 movie tickets.
19. zanobia is paying $22,860 for her car over
a period of 60 months.
20. ten inches of snow fell in 12 hours.
21. the word “the” is the most used word in the english
language. at what rate is it used in the following famous quote
from carl friedrich gauss?
mathematics is the queen of the sciences.
in 22–26, solve the problem.
22. in 2005, california’s total population of 36,132,147
ranked number one in the united states. california has
155,959 square miles of land. if its population were
distributed evenly throughout the state, how many people
would live in each square mile of land?
23. printer a prints 450 pages in 15 minutes. printer b prints
875 pages in 25 minutes. which printer prints at a faster rate?
24. in 2003, researchers believed that by 2008 over
90 million additional laptops and pdas will have
wireless capabilities to access the internet. what
is the yearly rate of increase for these technology
tools to have wireless capabilities?
25. a 42-ounce carton of oatmeal costs $3.20. an 18-ounce
carton costs $1.25 on sale. which size of oatmeal is
the better buy?
26. a 1-ounce serving of toasted chips has 130 calories of which
40 calories are from fat. a 1-ounce serving of potato chips has
150 calories of which 90 calories are from fat. which chips have
a lower rate of fat in relationship to total number of calories?

Question

uses objective e
in 17–21, calculate the rate for the given situation.
17. hurricane helene traveled 480 miles in 48 hours.
    a. miles per hour
    b. miles per minute
18. anastasia spent $42.50 on 5 movie tickets.
19. zanobia is paying $22,860 for her car over
    a period of 60 months.
20. ten inches of snow fell in 12 hours.
21. the word “the” is the most used word in the english
    language. at what rate is it used in the following famous quote
    from carl friedrich gauss?
    mathematics is the queen of the sciences.
in 22–26, solve the problem.
22. in 2005, california’s total population of 36,132,147
    ranked number one in the united states. california has
    155,959 square miles of land. if its population were
    distributed evenly throughout the state, how many people
    would live in each square mile of land?
23. printer a prints 450 pages in 15 minutes. printer b prints
    875 pages in 25 minutes. which printer prints at a faster rate?
24. in 2003, researchers believed that by 2008 over
    90 million additional laptops and pdas will have
    wireless capabilities to access the internet. what
    is the yearly rate of increase for these technology
    tools to have wireless capabilities?
25. a 42-ounce carton of oatmeal costs $3.20. an 18-ounce
    carton costs $1.25 on sale. which size of oatmeal is
    the better buy?
26. a 1-ounce serving of toasted chips has 130 calories of which
    40 calories are from fat. a 1-ounce serving of potato chips has
    150 calories of which 90 calories are from fat. which chips have
    a lower rate of fat in relationship to total number of calories?

Accepted Answer

### Question 17a:
# Explanation:
## Step1: Recall the formula for rate (speed)
The formula for speed (rate) is $ \text{rate} = \frac{\text{distance}}{\text{time}} $. Here, the distance is 480 miles and the time is 48 hours.
## Step2: Substitute the values into the formula
$ \text{rate} = \frac{480 \text{ miles}}{48 \text{ hours}} $
## Step3: Perform the division
$ \frac{480}{48} = 10 $
# Answer:
10 miles per hour

### Question 17b:
# Explanation:
## Step1: Convert hours to minutes
We know that 1 hour = 60 minutes, so 48 hours = $ 48\times60 = 2880 $ minutes.
## Step2: Use the rate formula
The distance is still 480 miles and the time is now 2880 minutes. So $ \text{rate} = \frac{480 \text{ miles}}{2880 \text{ minutes}} $
## Step3: Simplify the fraction
$ \frac{480}{2880}=\frac{1}{6}\approx0.1667 $
# Answer:
$ \frac{1}{6} $ (or approximately 0.1667) miles per minute

### Question 18:
# Explanation:
## Step1: Recall the rate formula for cost per ticket
The rate (cost per ticket) is $ \text{rate}=\frac{\text{total cost}}{\text{number of tickets}} $
## Step2: Substitute the values
Total cost is $42.50 and number of tickets is 5. So $ \text{rate}=\frac{42.50}{5} $
## Step3: Perform the division
$ 42.50\div5 = 8.5 $
# Answer:
$8.50 per movie ticket

### Question 19:
# Explanation:
## Step1: Recall the rate formula for cost per month
The rate (cost per month) is $ \text{rate}=\frac{\text{total cost}}{\text{number of months}} $
## Step2: Substitute the values
Total cost is $22,860 and number of months is 60. So $ \text{rate}=\frac{22860}{60} $
## Step3: Perform the division
$ 22860\div60 = 381 $
# Answer:
$381 per month

### Question 20:
# Explanation:
## Step1: Recall the rate formula for snowfall
The rate (snowfall rate) is $ \text{rate}=\frac{\text{amount of snow}}{\text{time}} $
## Step2: Substitute the values
Amount of snow is 10 inches and time is 12 hours. So $ \text{rate}=\frac{10 \text{ inches}}{12 \text{ hours}} $
## Step3: Simplify the fraction
$ \frac{10}{12}=\frac{5}{6}\approx0.8333 $
# Answer:
$ \frac{5}{6} $ (or approximately 0.8333) inches per hour

### Question 21:
# Explanation:
## Step1: Count the number of "the" and total words
The quote is "Mathematics is the queen of the sciences". Let's count:
- Number of "the": 2
- Total number of words: Let's list them: Mathematics, is, the, queen, of, the, sciences. So 7 words.
## Step2: Use the rate formula
The rate (number of "the" per word) is $ \text{rate}=\frac{\text{number of "the"}}{\text{total number of words}} $
## Step3: Substitute the values
$ \text{rate}=\frac{2}{7}\approx0.2857 $
# Answer:
$ \frac{2}{7} $ (or approximately 0.2857) times per word

### Question 22:
# Explanation:
## Step1: Recall the population density formula
Population density (people per square mile) is $ \text{density}=\frac{\text{total population}}{\text{total land area}} $
## Step2: Substitute the values
Total population is 36,132,147 and total land area is 155,959 square miles. So $ \text{density}=\frac{36132147}{155959} $
## Step3: Perform the division
$ 36132147\div155959\approx231.7 $ (rounded to one decimal place)
# Answer:
Approximately 231.7 people per square mile

### Question 23:
# Explanation:
## Step1: Find the rate for Printer A
For Printer A, pages printed = 450, time = 15 minutes. Rate $ r_A=\frac{450}{15}=30 $ pages per minute.
## Step2: Find the rate for Printer B
For Printer B, pages printed = 875, time = 25 minutes. Rate $ r_B=\frac{875}{25} = 35 $ pages per minute.
## Step3: Compare the two rates
Since $ 35>30 $, Printer B has a faster rate.
# Answer:
Printer B

### Question 24:
# Explanation:
## Step1: Determine the time period
From 2003 to 2008, the number of years $ t = 2008 - 2003=5 $ years.
## Step2: Use the rate formula
The rate (yearly increase) is $ \text{rate}=\frac{\text{total increase}}{\text{number of years}} $
## Step3: Substitute the values
Total increase is 90 million and number of years is 5. So $ \text{rate}=\frac{90 \text{ million}}{5 \text{ years}} $
## Step4: Perform the division
$ \frac{90}{5}=18 $
# Answer:
18 million per year

### Question 25:
# Explanation:
## Step1: Find the cost per ounce for each carton
For the 42 - ounce carton: Cost per ounce $ c_1=\frac{3.20}{42}\approx0.0762 $ dollars per ounce.
For the 18 - ounce carton: Cost per ounce $ c_2=\frac{1.25}{18}\approx0.0694 $ dollars per ounce.
## Step2: Compare the two costs per ounce
Since $ 0.0694<0.0762 $, the 18 - ounce carton has a lower cost per ounce, so it is a better buy.
# Answer:
18 - ounce carton

### Question 26:
# Explanation:
## Step1: Find the fat - to - calorie rate for toasted chips
For toasted chips, fat calories = 40, total calories = 130. Rate $ r_1=\frac{40}{130}=\frac{4}{13}\approx0.3077 $
## Step2: Find the fat - to - calorie rate for potato chips
For potato chips, fat calories = 90, total calories = 150. Rate $ r_2=\frac{90}{150}=\frac{3}{5} = 0.6 $
## Step3: Compare the two rates
Since $ 0.3077<0.6 $, toasted chips have a lower rate of fat in relation to total calories.
# Answer:
Toasted chips

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 17a:

Step1: Recall the formula for rate (speed)

Step2: Substitute the values into the formula

Step3: Perform the division

Step1: Convert hours to minutes

Step2: Use the rate formula

Step3: Simplify the fraction

Step1: Recall the rate formula for cost per ticket

Step2: Substitute the values

Step3: Perform the division

Answer:

Question 17b: