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.
No, none of the ratios have equivalence.
No, none of the ratios have equivalence.
No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.
No, this data table does not have a proportional relationship. The ratios between hours biked and miles traveled are not equivalent. For example, the ratio for the first set of data is 1:12, but the ratio for the second set of data is 2:26, which is not equal.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the hours biked and the miles traveled are consistent.
Let's calculate the ratios for all the given data points:
For 1 hour biked, the ratio is 12 miles / 1 hour = 12 miles per hour.
For 2 hours biked, the ratio is 26 miles / 2 hours = 13 miles per hour.
For 3 hours biked, the ratio is 30 miles / 3 hours = 10 miles per hour.
For 4 hours biked, the ratio is 48 miles / 4 hours = 12 miles per hour.
Since the ratios are not consistent (12, 13, 10, 12), we can conclude that the quantities in the data table do not have a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of hours biked to miles traveled are always equivalent.
To do this, we calculate the ratios for each pair of hours and miles:
For the first pair: 1 hour biked / 12 miles traveled = 1/12
For the second pair: 2 hours biked / 26 miles traveled = 2/26 = 1/13
For the third pair: 3 hours biked / 30 miles traveled = 3/30 = 1/10
For the fourth pair: 4 hours biked / 48 miles traveled = 4/48 = 1/12
Since not all of the ratios are equivalent, we can conclude that the quantities in the data table do not have a proportional relationship.
So the correct response is: No, not all of the ratios are proportional or have equivalence.