Question

Time(min): 1. 2 3 7. 10
Water used(gal): 5. 10 15 35. 50

Determine if the quantities in the data table in a proportional relationship if they do not have a proportional relationship indicate why a know the ratio 7:35 is not proportional to the other ratios B yes the data table has a proportional relationship see know the table does not count consecutively D know the ratios are not equivalent

Answer 1

To determine if the quantities in the data table have a proportional relationship, we need to check if the ratios of water used to time are equivalent for each pair of values.

The data table is as follows:

| Time (min) | Water used (gal) |
|------------|------------------|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 7 | 35 |
| 10 | 50 |

Now, let's calculate the ratios of water used to time for each entry:

1. For 1 min: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
2. For 2 min: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
3. For 3 min: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
4. For 7 min: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
5. For 10 min: \( \frac{50 \text{ gal}}{10 \text{ min}} = 5 \)

Since all of these ratios are equal to 5, the quantities in the data table **do represent a proportional relationship**.

So the answer is **B**: Yes, the data table has a proportional relationship.