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.
(1 point)
Responses
No, the ratio 7:35 is not proportional to the other ratios.
No, the ratio ratio of 7 to 35 is not proportional to the other ratios.
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the data table does not have a proportional relationship. The ratio of 7 to 35 is not proportional to the other ratios.
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 consistent.
The ratio between the water used and time for each pair of values is:
1 minute: 5 gallons
2 minutes: 10 gallons (ratio of 10:5 = 2:1)
3 minutes: 15 gallons (ratio of 15:10 = 3:2)
7 minutes: 35 gallons (ratio of 35:15 = 7:3. This is NOT proportional to the previous ratios)
10 minutes: 50 gallons (ratio of 50:35 = 10:7. Again, this is NOT proportional to the previous ratios)
Therefore, the quantities in the data table do not have a proportional relationship. The ratios of 7:35 and 10:50 are not consistent with the other ratios in the table.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the values remain constant.
To do this, we calculate the ratios between each pair of values in the table. Let's do that:
Ratio between 1 and 2: 10/5 = 2
Ratio between 2 and 3: 15/10 = 1.5
Ratio between 3 and 7: 35/15 = 2.333...
Ratio between 7 and 10: 50/35 = 1.428...
Since the ratios are not all the same, the quantities in the data table do not have a proportional relationship. Thus, the answer is:
No, the quantities in the data table are not in a proportional relationship.