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:
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For 4.25 thousand customers: \[ \text{Ratio} = \frac{187}{4.25} \] Calculation: \[ \frac{187}{4.25} = \frac{187 \times 100}{425} = \frac{18700}{425} \approx 44 \]
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For 5.25 thousand customers: \[ \text{Ratio} = \frac{231}{5.25} \] Calculation: \[ \frac{231}{5.25} = \frac{231 \times 100}{525} = \frac{23100}{525} \approx 44 \]
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For 6.25 thousand customers: \[ \text{Ratio} = \frac{275}{6.25} \] Calculation: \[ \frac{275}{6.25} = \frac{275 \times 100}{625} = \frac{27500}{625} \approx 44 \]
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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. \( \frac{4,250}{187} = \frac{y}{440} \)