Use the table to answer the question.%0D%0A%0D%0ATime (min)%091%092%093%097%0910%0D%0AWater Used (gal)%095%0910%0915%0935%0950%0D%0ADetermine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0ANo, the ratio 7:35%0D%0A7%0D%0A:%0D%0A35%0D%0A is not proportional to the other ratios.%0D%0ANo, the ratio ratio of 7 to 35 is not proportional to the other ratios.%0D%0A%0D%0ANo, the table does not count consecutively.%0D%0ANo, the table does not count consecutively.%0D%0A%0D%0AYes, the data table has a proportional relationship.%0D%0AYes, the data table has a proportional relationship.%0D%0A%0D%0ANo, the ratios are not equivalent.

Question

GPT-4o mini · Answer

To determine if the quantities in the table represent a proportional relationship, we need to check if the ratios of water used to time are constant throughout the table.

The given data is:

| 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 pair:

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

Since all the ratios are equal to 5, the quantities are indeed in a proportional relationship.

Thus, the correct response is:

Yes, the data table has a proportional relationship.