The table shows the number of cell phone towers a company will build as the number of its customers increases. Complete a and b below.

Question

Cell Phone Towers
Customers​ (thousands)
Towers
4.25
187
5.25
231
6.25
275
8.25
363
Question content area bottom
Part 1
a. Is the relationship between number of towers and number of customers​ proportional? Explain. Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
Yes. The ratios of towers to customers​ (thousands) are all equivalent to a unit rate of
  
StartFraction 44 Over 1 EndFraction
.
Your answer is correct.B.
No. The ratios of towers to customers are not all equivalent.
Part 2
b. If there are 440 ​towers, how many customers does the company​ have? Write a proportion you can use to solve. Choose the correct proportion.
A.StartFraction 4 comma 250 Over 187 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 4 comma 250 Over 187 EndFraction equals StartFraction y Over 440 EndFraction
Your answer is correct.B.StartFraction 5.25 Over 275 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 5.25 Over 275 EndFraction equals StartFraction y Over 440 EndFraction
C.StartFraction 187 Over 4 comma 250 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 187 Over 4 comma 250 EndFraction equals StartFraction y Over 440 EndFraction
D.StartFraction 187 Over 4.25 EndFraction equals StartFraction y Over 440 EndFraction
StartFraction 187 Over 4.25 EndFraction equals StartFraction y Over 440 EndFraction
Part 3
The company has
  
enter your response here customers.
input field 1Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.Choose the correct proportion.The company hascustomers.input field 1Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.Choose the correct proportion.The company hascustomers.

Answer 1

Part 1: To determine if the relationship between the number of towers and the number of customers is proportional, we can calculate the ratios of towers to customers for each set of values.

1. For 4.25 thousand customers, the ratio is \( \frac{187}{4.25} = 44 \).
2. For 5.25 thousand customers, the ratio is \( \frac{231}{5.25} = 44 \).
3. For 6.25 thousand customers, the ratio is \( \frac{275}{6.25} = 44 \).
4. For 8.25 thousand customers, the ratio is \( \frac{363}{8.25} = 44 \).

Since all ratios are equivalent to 44, the answer is:

A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of \( \frac{44}{1} \).

Part 2: To find the proportion if there are 440 towers, we can establish a proportion based on the data we have.

The most straightforward option that relates to the original data:

• Using the first ratio, choose: A. \( \frac{4,250}{187} = \frac{y}{440} \)

Part 3: Now we can solve the proportion from Part 2 to determine how many customers \( y \) the company has when there are 440 towers.

Cross-multiplying gives us: \[ 4,250 \cdot 440 = 187 \cdot y \] \[ 1,870,000 = 187y \] \[ y = \frac{1,870,000}{187} \approx 10,000 \]

So, the company has approximately 10,000 customers.

The company has 10,000 customers.