Use the table to answer the question.
Time (min): 1 | 2 | 3 | 7 | 10 |
Water Used (gal): 5 | 10 | 15 | 35 | 50 |
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.
A. No, the ratios are not equivalent.
B. No, the table does not count consecutively.
C. No, the ratio 7 : 35 is not proportional to the other ratios.
D. Yes, the data table has a proportional relationship.
A. 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 water used and the corresponding time values are equivalent.
Let's calculate the ratios for the data given:
For Time (min) = 1, the ratio is 5/1 = 5.
For Time (min) = 2, the ratio is 10/2 = 5.
For Time (min) = 3, the ratio is 15/3 = 5.
For Time (min) = 7, the ratio is 35/7 = 5.
For Time (min) = 10, the ratio is 50/10 = 5.
As we can see, all the ratios are equal to 5. Therefore, the quantities in the data table are in a proportional relationship.
The correct answer is:
D. 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 values are equivalent.
First, we can calculate the ratios for each pair of values in the table:
- Ratio between 1 min and 2 min: 5 gal / 10 gal = 1/2
- Ratio between 2 min and 3 min: 10 gal / 15 gal = 2/3
- Ratio between 3 min and 7 min: 15 gal / 35 gal = 3/7
- Ratio between 7 min and 10 min: 35 gal / 50 gal = 7/10
Now let's check if these ratios are equivalent:
- 1/2 is not equivalent to 2/3
- 2/3 is not equivalent to 3/7
- 3/7 is not equivalent to 7/10
Since none of the ratios are equivalent to each other, we can conclude that the quantities in the data table are not in a proportional relationship.
Therefore, the correct answer is A. No, the ratios are not equivalent.