To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of miles traveled to hours biked are equivalent. A proportional relationship means that the ratio (miles per hour) remains constant.
Let's calculate the ratios for each entry:
- For 1 hour: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \)
- For 2 hours: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \)
- For 3 hours: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \)
- For 4 hours: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \)
Now, we can summarize the ratios:
- 1 hour: 12 miles (ratio = 12)
- 2 hours: 26 miles (ratio = 13)
- 3 hours: 30 miles (ratio = 10)
- 4 hours: 48 miles (ratio = 12)
Since not all of the ratios are the same (12, 13, 10, and 12), we can conclude that the quantities are not in a proportional relationship.
Therefore, the correct response is:
No, not all of the ratios are proportional or have equivalence.