e (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 ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the table does not count consecutively.
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
No, the ratio 7:35 is not proportional to the other ratios.
No, the quantities in the data table are not in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we can check if the ratios between the two quantities are equivalent for each set of values.
Let's calculate the ratios for each pair:
For the first pair (1 min, 5 gal), the ratio is 5:1.
For the second pair (2 min, 10 gal), the ratio is 10:2, which simplifies to 5:1.
For the third pair (3 min, 15 gal), the ratio is 15:3, which simplifies to 5:1.
For the fourth pair (7 min, 35 gal), the ratio is 35:7, which also simplifies to 5:1.
For the fifth pair (10 min, 50 gal), the ratio is 50:10, which simplifies to 5:1.
As we can see, all the ratios are equivalent and simplify to 5:1. Therefore, the quantities in the data table are in a proportional relationship. So the correct response is "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 remain constant. To do this, we can calculate the ratios of water used (gal) to the corresponding time (min) for each data point.
e (min) | Water Used (gal) | Ratio
1 | 5 | 5/1 = 5
2 | 10 | 10/2 = 5
3 | 15 | 15/3 = 5
7 | 35 | 35/7 = 5
10 | 50 | 50/10 = 5
As we can see, all the ratios are equivalent to 5. Therefore, the quantities in the data table are in a proportional relationship.
The correct response is: "Yes, the data table has a proportional relationship."