To determine if the quantities in the data table are in a proportional relationship, we can find the ratios of water used to time for each pair of data points and check if they are equivalent.
- For \(1\) min: \(\frac{5 \text{ gal}}{1 \text{ min}} = 5\)
- For \(2\) min: \(\frac{10 \text{ gal}}{2 \text{ min}} = 5\)
- For \(3\) min: \(\frac{15 \text{ gal}}{3 \text{ min}} = 5\)
- For \(7\) min: \(\frac{35 \text{ gal}}{7 \text{ min}} = 5\)
- For \(10\) min: \(\frac{50 \text{ gal}}{10 \text{ min}} = 5\)
All these ratios are equal to \(5\). Since all the ratios of water used to time are equivalent, the data in the table represents a proportional relationship.
Therefore, the correct response is:
Yes, the data table has a proportional relationship.
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