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.
The quantities in the data table do not have a proportional relationship.
To determine if two quantities are proportional, their ratio should remain the same throughout the data set.
In this case, if we calculate the ratio of water used to time for each data point, we get:
Ratio for 1st data point: 5/1 = 5
Ratio for 2nd data point: 10/2 = 5
Ratio for 3rd data point: 15/3 = 5
Ratio for 4th data point: 35/7 = 5
Ratio for 5th data point: 50/10 = 5
As we can see, all the ratios are equal to 5. Hence, the quantities in the data table are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we can check if the ratio of water used to time is constant.
Ratio of water used to time for each entry:
1 minute: 5 gallons
2 minutes: 10 gallons (ratio = 10/2 = 5 gallons per minute)
3 minutes: 15 gallons (ratio = 15/3 = 5 gallons per minute)
7 minutes: 35 gallons (ratio = 35/7 = 5 gallons per minute)
10 minutes: 50 gallons (ratio = 50/10 = 5 gallons per minute)
Since the ratio of water used to time is constant at 5 gallons per minute for all entries, the quantities in the data table are indeed in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio of water used to time remains constant.
The ratio of water used to time can be calculated by dividing the amount of water used by the time. Let's calculate this ratio for the given data points:
For time = 1 min, water used = 5 gal
Ratio = 5/1 = 5
For time = 2 min, water used = 10 gal
Ratio = 10/2 = 5
For time = 3 min, water used = 15 gal
Ratio = 15/3 = 5
For time = 7 min, water used = 35 gal
Ratio = 35/7 = 5
For time = 10 min, water used = 50 gal
Ratio = 50/10 = 5
As we can see, the ratio of water used to time is the same for all data points, which is 5. This indicates that the quantities in the data table are indeed in a proportional relationship.
Therefore, the quantities in the data table are in a proportional relationship.