Question

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.

No, the table does not count consecutively.
No, the table does not count consecutively.

No, the ratio 6 : 78 is not proportional to the other ratios.
No, the ratio 6 : 78 is not proportional to the other ratios.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
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Answer 1

#of trees #of apples
2 26
3 39
6 78
10 130
12 156

Answer 2

To determine if the quantities in a data table are in a proportional relationship, we need to check if the ratios of the corresponding quantities are equivalent.

Without the specific data from the table, I can outline what to look for:

1. **Calculate Ratios**: For each pair of corresponding values in the table, calculate the ratio. That is, if you have pairs (x1, y1), (x2, y2), ..., then you would look at ratios like y1/x1, y2/x2, etc.

2. **Compare Ratios**: Check if all the calculated ratios are equal.

- If they are all the same, then the quantities are in a proportional relationship (meaning the relationship can be expressed as y = kx, where k is a constant).
- If any of the ratios are different, then they are not proportional.

3. **Constant Differences**: If you are also considering whether the quantities count consecutively or by equal parts, in a proportional relationship, the differences between corresponding values don’t need to be consecutive, but the key is that the ratios derived from the pairs remain constant.

If you can provide the data from the table, I could analyze it further to determine the relationship accurately. Based on the responses presented, it seems there are two indications of non-proportional relationships regarding specific ratios.

Answer 3

To determine if the quantities in the data table form a proportional relationship, we will analyze the ratios of the number of apples to the number of trees.

The data provided is as follows:

| # of trees | # of apples |
|------------|-------------|
| 2 | 26 |
| 3 | 39 |
| 6 | 78 |
| 10 | 130 |
| 12 | 156 |

Now, let's calculate the ratios of # of apples to # of trees for each pair:

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

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

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

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

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

Now, we see that the ratio is consistently 13 for all pairs. This means that:

- The ratios are equal and constant.

Since all the ratios are equivalent, we conclude that the quantities in the data table **are** in a proportional relationship.

**Answer:** Yes, the data table has a proportional relationship.