Question

Use the table to answer the question.
# of Trees # of Apples
23
6
110
12
$gd 8 8|
130
156
Determine if the quantities in the data table are in a proportional relationship. Explain your answer If they are not in a proportional relationship, indicate why. No answer provided for this one.
Describe as a 7th grader short enough to fit in a small text box.

Answer 1

can you shorten it more.

Answer 2

To determine if the quantities in the table are in a proportional relationship, we need to check if the ratio of apples to trees is the same for each pair. A proportional relationship means that when you divide the number of apples by the number of trees, you get the same answer each time.

Looking at the numbers, we see they are:
- 23 trees : 6 apples
- 110 trees : 12 apples
- 8 trees : 8 apples
- 130 trees : 130 apples
- 156 trees : (number of apples not provided)

Calculating the ratios:
1. For 23 trees, \(\frac{6}{23} \approx 0.26\)
2. For 110 trees, \(\frac{12}{110} \approx 0.11\)
3. For 8 trees, \(\frac{8}{8} = 1\)
4. For 130 trees, \(\frac{130}{130} = 1\)

Since the ratios are different (some are around 0.26, 0.11, and 1), we see that the amount of apples does not grow consistently with the number of trees. So, the quantities in the table are not in a proportional relationship.

Answer 3

To see if the numbers are proportional, we check if the ratio of apples to trees is the same.

1. 23 trees : 6 apples → \(\frac{6}{23} \approx 0.26\)
2. 110 trees : 12 apples → \(\frac{12}{110} \approx 0.11\)
3. 8 trees : 8 apples → ratio = 1
4. 130 trees : 130 apples → ratio = 1

Since the ratios are different (0.26, 0.11, 1), the quantities are not proportional.