Use the table to answer the question.

Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.

(1 point)
Responses

No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.

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

No, none of the ratios have equivalence.
No, none of the ratios have equivalence.

No, you can’t bike 12 miles in an hour.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To determine if the quantities in the data table (Hours Biked and Miles Traveled) are in a proportional relationship, we need to check if the ratios of Miles Traveled to Hours Biked are constant.

Let's calculate the ratios for each entry in the table:

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

Now, we can see the ratios:
- First hour: 12
- Second hour: 13
- Third hour: 10
- Fourth hour: 12

Since the ratios are not constant (12, 13, 10, 12), the data does not indicate a proportional relationship.

Therefore, the correct response is:
**No, not all of the ratios are proportional or have equivalence.**