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, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.
No, none of the ratios have equivalence.
No, none of the ratios have equivalence.
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.
No, not all of the ratios are proportional or have equivalence.
Answers
GPT-4o mini
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio of miles traveled to hours biked remains constant across all values.
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 let's summarize the ratios:
- 1 hour: 12
- 2 hours: 13
- 3 hours: 10
- 4 hours: 12
Since the ratios are not all the same (12, 13, 10, 12), the relationship is not proportional.
Therefore, the correct response is:
**No, not all of the ratios are proportional or have equivalence.**
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 let's summarize the ratios:
- 1 hour: 12
- 2 hours: 13
- 3 hours: 10
- 4 hours: 12
Since the ratios are not all the same (12, 13, 10, 12), the relationship is not proportional.
Therefore, the correct response is:
**No, not all of the ratios are proportional or have equivalence.**