Question

Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
A. No, the ratios are not equivalent. B. No, the ratio of 3 hours to 27isnotproportional.C.No,theratioof1hourto 9 is not proportional. D. Yes, the ratios are in a proportional relationship.

Answer 1

To determine if the quantities in your data table are in a proportional relationship, we need to analyze the ratios of the quantities.

Assuming we have two sets of quantities (for example, time and another variable), we can compute the ratios:

1. From the first pair of quantities (assuming 3 hours and 27), the ratio would be \( \frac{3}{27} = \frac{1}{9} \).

2. From the second pair (assuming 1 hour and 9), the ratio would be \( \frac{1}{9} \).

If both ratios are equal, then the quantities are in a proportional relationship.

Given your options:

- A states that the ratios are not equivalent.
- B claims that the ratio of 3 hours to 27 is not proportional.
- C claims that the ratio of 1 hour to 9 is not proportional.
- D states that the ratios are in a proportional relationship.

Since both ratios \( \frac{3}{27} \) and \( \frac{1}{9} \) are equal (\( \frac{1}{9} \)), the quantities are indeed in a proportional relationship. Therefore, the correct option would be:

**D. Yes, the ratios are in a proportional relationship.**

This means the quantities you are comparing maintain a consistent ratio to one another.