Question

Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.
\[\begin{tabular}{|l|l|} \hline \text{Hours Biked} & \text{Miles Traveled} \ \hline 1 & 12 \ \hline 2 & 26 \ \hline 3 & 30 \ \hline 4 & 48 \ \hline \end{tabular}\] A. No, none of the ratios have equivalence. B. No, not all of the ratios are proportional or have equivalence. C. No, you can't bike 12 miles in an hour. D. Yes, this data table has a proportional relationship.

Answer 1

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 constant.

We can calculate the ratios for each entry:

1. For 1 hour biked: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \)
2. For 2 hours biked: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \)
3. For 3 hours biked: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \)
4. For 4 hours biked: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \)

Now let's summarize the ratios:
- 1 hour: 12
- 2 hours: 13
- 3 hours: 10
- 4 hours: 12

Since the ratios are not the same (they differ: 12, 13, 10, 12), the quantities do not have a proportional relationship.

Thus, the correct option is:
B. No, not all of the ratios are proportional or have equivalence.