# 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
Yes, the data table has a proportional relationship.Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.No, the ratios are not equivalent
.No, the ratio 6:78 is not proportional to the other ratios.No, the ratio ratio of 6 to 78 is not proportional to the other ratios.
No, the table does not count consecutively.No, the table does not count consecutively.
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 for each pair of values.
Let's calculate the ratios for each pair:
For the first pair (2 trees and 26 apples), the ratio is 26/2 = 13.
For the second pair (3 trees and 39 apples), the ratio is 39/3 = 13.
For the third pair (6 trees and 78 apples), the ratio is 78/6 = 13.
For the fourth pair (10 trees and 130 apples), the ratio is 130/10 = 13.
For the fifth pair (12 trees and 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.
So the correct response for this question 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 consistent.
Let's calculate the ratios for each row:
For 2 trees, we have 26 apples: 26/2 = 13.
For 3 trees, we have 39 apples: 39/3 = 13.
For 6 trees, we have 78 apples: 78/6 = 13.
For 10 trees, we have 130 apples: 130/10 = 13.
For 12 trees, we have 156 apples: 156/12 = 13.
Since all the ratios are equal to 13, we can conclude that the quantities in the data table are in a proportional relationship. Therefore, the correct response is:
Yes, the data table has a proportional relationship.