Use the table to answer the question.

# 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 ratios are not equivalent.
No, the ratios are not equivalent.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

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.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
4 hours ago

To determine if the quantities in the data table are in a proportional relationship, we can calculate the ratio of the number of apples to the number of trees for each row and see if the ratios are equivalent.

The ratios for each entry are as follows:

  1. For 2 trees and 26 apples:
    Ratio = 26 / 2 = 13

  2. For 3 trees and 39 apples:
    Ratio = 39 / 3 = 13

  3. For 6 trees and 78 apples:
    Ratio = 78 / 6 = 13

  4. For 10 trees and 130 apples:
    Ratio = 130 / 10 = 13

  5. For 12 trees and 156 apples:
    Ratio = 156 / 12 = 13

Since all of these ratios simplify to 13, they are indeed equivalent.

Therefore, the correct response is:

Yes, the data table has a proportional relationship.