Question

Question
Use the table to answer the question.

Time (min) 1 2 3 7 10
Water Used (gal) 5 10 15 35 50
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.

(1 point)
Responses

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

No, the table does not count consecutively.
No, the table does not count consecutively.

No, the ratios are not equivalent.
No, the ratios are not equivalent.

No, the ratio 7:35 is not proportional to the other ratios.
No, the ratio ratio of 7 to 35 is not proportional to the other ratios.
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Answer 1

To determine if the quantities in the table are in a proportional relationship, we need to check if the ratios of water used to time are equivalent throughout the table. A proportional relationship means that as one quantity changes, the other changes by the same factor.

Let's calculate the ratio of water used (in gallons) to time (in minutes) for each entry and see if they are equivalent:

1. For 1 min:
- Water Used: 5 gal
- Ratio: \(\frac{5}{1} = 5\)

2. For 2 min:
- Water Used: 10 gal
- Ratio: \(\frac{10}{2} = 5\)

3. For 3 min:
- Water Used: 15 gal
- Ratio: \(\frac{15}{3} = 5\)

4. For 7 min:
- Water Used: 35 gal
- Ratio: \(\frac{35}{7} = 5\)

5. For 10 min:
- Water Used: 50 gal
- Ratio: \(\frac{50}{10} = 5\)

All the ratios simplify to 5. Since all the ratios are equivalent, we can conclude that:

**Yes, the data table has a proportional relationship.**