# of Trees # of Apples
2|26
3|39
6|78
10|130
12|156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
(1 point)
Responses
No, the table does not count consecutively.
No, the ratios are not equivalent.
Yes, the data table has a proportional relationship.
No, the ratio 6:78 is not proportional to the other ratios.
No, the data table does not have a proportional relationship. The ratios between the number of trees and the number of apples are not equivalent.
which response is correct
The correct response is: No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the number of trees and the number of apples are equivalent or not.
Let's calculate the ratios for each pair of values:
Ratio for 2 trees and 26 apples: 26 ÷ 2 = 13
Ratio for 3 trees and 39 apples: 39 ÷ 3 = 13
Ratio for 6 trees and 78 apples: 78 ÷ 6 = 13
Ratio for 10 trees and 130 apples: 130 ÷ 10 = 13
Ratio for 12 trees and 156 apples: 156 ÷ 12 = 13
As we can see, all the ratios are equal to 13. Therefore, the ratios are equivalent, and the quantities in the data table are in a proportional relationship.
So, the correct response is: Yes, the data table has a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the number of trees and the number of apples are equivalent for all the entries.
To do this, calculate the ratios for each entry by dividing the number of apples by the number of trees:
- For the first entry (2 trees, 26 apples), the ratio is 26/2 = 13.
- For the second entry (3 trees, 39 apples), the ratio is 39/3 = 13.
- For the third entry (6 trees, 78 apples), the ratio is 78/6 = 13.
- For the fourth entry (10 trees, 130 apples), the ratio is 130/10 = 13.
- For the fifth entry (12 trees, 156 apples), the ratio is 156/12 = 13.
Since all the ratios are equal to 13, the quantities in the data table are in a proportional relationship.
Therefore, the correct response is: Yes, the data table has a proportional relationship.