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.
A. Yes, this data table has a proportional relationship
B. No, none of the ratios have equivalence.
C. No, you can't bike 12 miles in an hour.
D. No, not all of the ratios are proportional or have equivalance.
D. No, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the "Hours biked" and "Miles traveled" remains constant. Let's calculate the ratios for each set of data:
Ratio for the first set of data: 1 hour / 12 miles = 1/12
Ratio for the second set of data: 2 hours / 26 miles = 2/26 = 1/13
Ratio for the third set of data: 3 hours / 30 miles = 3/30 = 1/10
Ratio for the fourth set of data: 4 hours / 48 miles = 4/48 = 1/12
Since the ratios are not constant, we can see that the quantities in the data table are not in a proportional relationship. Therefore, the correct answer is:
D. No, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table are in a proportional relationship, we need to compare the ratios of miles traveled to hours biked for each data point.
Let's calculate the ratios for each data point:
- For the first data point, the ratio is 12 miles traveled / 1 hour biked = 12/1 = 12.
- For the second data point, the ratio is 26 miles traveled / 2 hours biked = 26/2 = 13.
- For the third data point, the ratio is 30 miles traveled / 3 hours biked = 30/3 = 10.
- For the fourth data point, the ratio is 48 miles traveled / 4 hours biked = 48/4 = 12.
To determine if the ratios are equal, we compare them. We can see that the first and fourth ratios are equal at 12, but the second and third ratios are not equal to the first or fourth ratio.
Since all the ratios are not equal, we can conclude that the quantities in the data table do not have a proportional relationship. Therefore, the answer is D. No, not all of the ratios are proportional or have equivalence.