To determine if the quantities in the data table are in a proportional relationship, we can examine the ratios of miles traveled to hours biked.
We will 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, let's summarize the results:
- The ratio for 1 hour is \(12\)
- The ratio for 2 hours is \(13\)
- The ratio for 3 hours is \(10\)
- The ratio for 4 hours is \(12\)
Since not all of the ratios are the same (\(12\), \(13\), \(10\)), this indicates that the quantities do not have a proportional relationship.
The correct conclusion based on this analysis is:
No, not all of the ratios are proportional or have equivalence.