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.
Responses
No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour. - no response given
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship. - no response given
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence. - no response given
No, none of the ratios have equivalence.
No, none of the ratios have equivalence. - no response given
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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.
Responses
No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour. - no response given
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship. - no response given
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence. - no response given
No, none of the ratios have equivalence.
No, none of the ratios have equivalence. - no response given
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Answers
GPT-4o mini
To determine if the quantities in the data table represent a proportional relationship, we need to check if the ratio of miles traveled per hour is constant for all the given data points.
Let's calculate the ratio (miles per hour) for each entry in the table:
1. For 1 hour biked:
\[ \frac{12 \, \text{miles}}{1 \, \text{hour}} = 12 \, \text{miles per hour} \]
2. For 2 hours biked:
\[ \frac{26 \, \text{miles}}{2 \, \text{hours}} = 13 \, \text{miles per hour} \]
3. For 3 hours biked:
\[ \frac{30 \, \text{miles}}{3 \, \text{hours}} = 10 \, \text{miles per hour} \]
4. For 4 hours biked:
\[ \frac{48 \, \text{miles}}{4 \, \text{hours}} = 12 \, \text{miles per hour} \]
Now we compare the ratios:
- For 1 hour: 12 mph
- For 2 hours: 13 mph
- For 3 hours: 10 mph
- For 4 hours: 12 mph
Since the ratios are not constant (12, 13, 10, 12), the data does **not** represent a proportional relationship.
Therefore, the correct response is:
**No, not all of the ratios are proportional or have equivalence.**
Let's calculate the ratio (miles per hour) for each entry in the table:
1. For 1 hour biked:
\[ \frac{12 \, \text{miles}}{1 \, \text{hour}} = 12 \, \text{miles per hour} \]
2. For 2 hours biked:
\[ \frac{26 \, \text{miles}}{2 \, \text{hours}} = 13 \, \text{miles per hour} \]
3. For 3 hours biked:
\[ \frac{30 \, \text{miles}}{3 \, \text{hours}} = 10 \, \text{miles per hour} \]
4. For 4 hours biked:
\[ \frac{48 \, \text{miles}}{4 \, \text{hours}} = 12 \, \text{miles per hour} \]
Now we compare the ratios:
- For 1 hour: 12 mph
- For 2 hours: 13 mph
- For 3 hours: 10 mph
- For 4 hours: 12 mph
Since the ratios are not constant (12, 13, 10, 12), the data does **not** represent a proportional relationship.
Therefore, the correct response is:
**No, not all of the ratios are proportional or have equivalence.**