Determine if the quantities in the data table are in a proportional relationship if they do not have a proportional relationship indicate why? Hours biked 1 miles treated 12. Hours biked 2 miles traveled 26. Hours biked 3 miles travelled 30 hours biked 4 miles traveld 48
To determine if the quantities are in a proportional relationship, we can check if the ratio of hours biked to miles traveled remains the same throughout the data table.
Ratio for the first set of data:
1 hour / 12 miles = 1/12
Ratio for the second set of data:
2 hours / 26 miles = 1/13
Ratio for the third set of data:
3 hours / 30 miles = 1/10
Ratio for the fourth set of data:
4 hours / 48 miles = 1/12
Since the ratios are not consistent, 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 there is a constant ratio between the hours biked and the miles traveled. If there is a constant ratio, it means that they are in a proportional relationship; if not, they do not have a proportional relationship.
Let's calculate the ratios for the given data:
- Between the 1st and 2nd entry:
Ratio of hours biked: 2/1 = 2
Ratio of miles traveled: 26/12 = 2.17
- Between the 2nd and 3rd entry:
Ratio of hours biked: 3/2 = 1.5
Ratio of miles traveled: 30/26 = 1.15
- Between the 3rd and 4th entry:
Ratio of hours biked: 4/3 = 1.33
Ratio of miles traveled: 48/30 = 1.6
As we can see, the ratios for hours biked and miles traveled are not constant. They vary from 2 to 1.15 to 1.33. Therefore, the quantities in the data table do not have a proportional relationship.
The reason they do not have a proportional relationship is that the ratio between hours biked and miles traveled changes for each progression. In a proportional relationship, the ratio between the two quantities should remain constant throughout.
To determine if the quantities in the data table are in a proportional relationship, we can compare the ratios of hours biked to miles traveled for each pair of values.
Let's calculate the ratios:
For the first pair (1 hour biked, 12 miles traveled):
Ratio = 1 hour / 12 miles = 1/12
For the second pair (2 hours biked, 26 miles traveled):
Ratio = 2 hours / 26 miles = 1/13
For the third pair (3 hours biked, 30 miles traveled):
Ratio = 3 hours / 30 miles = 1/10
For the fourth pair (4 hours biked, 48 miles traveled):
Ratio = 4 hours / 48 miles = 1/12
Since the ratios are not constant, the quantities in the data table are not in a proportional relationship. The ratios should be the same for a proportional relationship. In this case, the ratios differ, indicating that the relationship between hours biked and miles traveled is not proportional.