Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why. (1 point) Responses No, not all of the ratios are proportional or have equivalence. No, not all of the ratios are proportional or have equivalence. No, you can’t bike 12 miles in an hour. No, you can’t bike 12 miles in an hour. No, none of the ratios have equivalence. No, none of the ratios have equivalence. Yes, this data table has a proportional relationship.

Question

1:12
2:26
3:30
4:48

Answer 1

To determine if the quantities in the data table represent a proportional relationship, we need to check the ratios of the two quantities for consistency.

The data in the table appears to show pairs of numbers, which we will assume are represented as (x, y):

• (1, 12)
• (2, 26)
• (3, 30)
• (4, 48)

Next, calculate the ratios \( \frac{y}{x} \) for each pair:

1. For (1, 12):
   \( \frac{12}{1} = 12 \)

2. For (2, 26):
   \( \frac{26}{2} = 13 \)

3. For (3, 30):
   \( \frac{30}{3} = 10 \)

4. For (4, 48):
   \( \frac{48}{4} = 12 \)

Now we compare the ratios:

• First ratio: 12
• Second ratio: 13
• Third ratio: 10
• Fourth ratio: 12

Since the ratios are not all equal, we can conclude that the quantities do not form a proportional relationship.

Therefore, the correct response is: No, not all of the ratios are proportional or have equivalence.