Question
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.
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
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
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
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
Answers
GPT-4o mini
To answer the questions about the relationship between the number of cell phone towers and the number of customers, let's analyze the provided data.
### Part 1
a. To determine if the relationship is proportional, we can compare the ratios of towers to customers for each case. Let's calculate these ratios:
1. For 4.25 thousand customers:
\[
\text{Ratio} = \frac{187}{4.25}
\]
Calculation:
\[
\frac{187}{4.25} = \frac{187 \times 100}{425} = \frac{18700}{425} \approx 44
\]
2. For 5.25 thousand customers:
\[
\text{Ratio} = \frac{231}{5.25}
\]
Calculation:
\[
\frac{231}{5.25} = \frac{231 \times 100}{525} = \frac{23100}{525} \approx 44
\]
3. For 6.25 thousand customers:
\[
\text{Ratio} = \frac{275}{6.25}
\]
Calculation:
\[
\frac{275}{6.25} = \frac{275 \times 100}{625} = \frac{27500}{625} \approx 44
\]
4. For 8.25 thousand customers:
\[
\text{Ratio} = \frac{363}{8.25}
\]
Calculation:
\[
\frac{363}{8.25} = \frac{363 \times 100}{825} = \frac{36300}{825} \approx 44
\]
Since all ratios are approximately equal 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
b. To find out how many customers correspond to 440 towers, we can use a proportion that relates the number of towers to the number of customers.
Let's use the first data point from the table for our proportion:
\[
\frac{4,250 \text{ customers}}{187 \text{ towers}} = \frac{y \text{ customers}}{440 \text{ towers}}
\]
Thus, the correct proportion is:
**A. \( \frac{4,250}{187} = \frac{y}{440} \)**
### Summary of Answers:
- Part 1: A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of \( \frac{44}{1} \).
- Part 2: A. \( \frac{4,250}{187} = \frac{y}{440} \)
### Part 1
a. To determine if the relationship is proportional, we can compare the ratios of towers to customers for each case. Let's calculate these ratios:
1. For 4.25 thousand customers:
\[
\text{Ratio} = \frac{187}{4.25}
\]
Calculation:
\[
\frac{187}{4.25} = \frac{187 \times 100}{425} = \frac{18700}{425} \approx 44
\]
2. For 5.25 thousand customers:
\[
\text{Ratio} = \frac{231}{5.25}
\]
Calculation:
\[
\frac{231}{5.25} = \frac{231 \times 100}{525} = \frac{23100}{525} \approx 44
\]
3. For 6.25 thousand customers:
\[
\text{Ratio} = \frac{275}{6.25}
\]
Calculation:
\[
\frac{275}{6.25} = \frac{275 \times 100}{625} = \frac{27500}{625} \approx 44
\]
4. For 8.25 thousand customers:
\[
\text{Ratio} = \frac{363}{8.25}
\]
Calculation:
\[
\frac{363}{8.25} = \frac{363 \times 100}{825} = \frac{36300}{825} \approx 44
\]
Since all ratios are approximately equal 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
b. To find out how many customers correspond to 440 towers, we can use a proportion that relates the number of towers to the number of customers.
Let's use the first data point from the table for our proportion:
\[
\frac{4,250 \text{ customers}}{187 \text{ towers}} = \frac{y \text{ customers}}{440 \text{ towers}}
\]
Thus, the correct proportion is:
**A. \( \frac{4,250}{187} = \frac{y}{440} \)**
### Summary of Answers:
- Part 1: A. Yes. The ratios of towers to customers (thousands) are all equivalent to a unit rate of \( \frac{44}{1} \).
- Part 2: A. \( \frac{4,250}{187} = \frac{y}{440} \)