It takes Julian 12 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?
A. (1/4, 1)
B. (4, 1)
C. (1, 4)
D. (1, 1/4)
last one yes the ratios are in a proporttional relatationship
Hours Miles walked
1/4 1
1/2 2
3/4 3
1 4
To determine the ratio at which the constant of proportionality appears, we can divide the distance by the time for each data point in the table.
The data table is not provided in the question, so we are unable to determine the ratios. Please provide the data table.
Time (hours) Pages read
1/2 15
1 30
1 1/2 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?
A. (1, 30)
B. (1 1/2, 30)
C. (2, 60)
D. (15, 1/2)
To determine the ratio at which the constant of proportionality appears, we can divide the pages read by the time for each data point in the table.
- For the first data point, 1/2 hour and 15 pages read, the ratio is 15 pages / 1/2 hour = 30 pages per hour.
- For the second data point, 1 hour and 30 pages read, the ratio is 30 pages / 1 hour = 30 pages per hour.
- For the third data point, 1 1/2 hours and 45 pages read, the ratio is 45 pages / 1 1/2 hours = 30 pages per hour.
- For the fourth data point, 2 hours and 60 pages read, the ratio is 60 pages / 2 hours = 30 pages per hour.
Since the ratio is consistent at 30 pages per hour for each data point, the constant of proportionality appears at the ratio (1, 30).
Therefore, the correct answer is A. (1, 30).
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. Yes, the data table has a proportional relationship.
D. No, the ratio 7:35 is not proportional to the other ratios
To determine if the quantities in the data table are in a proportional relationship, we can compare the ratios of water used (gal) to time (min) for each data point.
- For the first data point, 1 min and 5 gal of water, the ratio is 5 gal / 1 min = 5 gal/min.
- For the second data point, 2 min and 10 gal of water, the ratio is 10 gal / 2 min = 5 gal/min.
- For the third data point, 3 min and 15 gal of water, the ratio is 15 gal / 3 min = 5 gal/min.
- For the fourth data point, 7 min and 35 gal of water, the ratio is 35 gal / 7 min = 5 gal/min.
- For the fifth data point, 10 min and 50 gal of water, the ratio is 50 gal / 10 min = 5 gal/min.
Since the ratio of water used to time is consistent at 5 gal/min for each data point, the quantities in the data table are in a proportional relationship.
Therefore, the correct answer is C. Yes, the data table has a proportional relationship.
Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.
A. No, not all of the ratios are proportional or have equivalence.
B. Yes, this data table has a proportional relationship.
C. No, none of the ratios have equivalence.
D. No, you can’t bike 12 miles in an hour.
To determine if the quantities in the data table are in a proportional relationship, we can compare the ratios of miles traveled to hours biked for each data point.
- For the first data point, 1 hour biked and 12 miles traveled, the ratio is 12 miles / 1 hour = 12 miles/hour.
- For the second data point, 2 hours biked and 26 miles traveled, the ratio is 26 miles / 2 hours = 13 miles/hour.
- For the third data point, 3 hours biked and 30 miles traveled, the ratio is 30 miles / 3 hours = 10 miles/hour.
- For the fourth data point, 4 hours biked and 48 miles traveled, the ratio is 48 miles / 4 hours = 12 miles/hour.
Since the ratios of miles traveled to hours biked are not consistent and do not have equivalence for all the data points, the quantities in the data table do not have a proportional relationship.
Therefore, the correct answer is A. No, not all of the ratios are proportional or have equivalence.
Question
Use the table to answer the question.
Hours Money ($)
1 9
2 18
3 27
4 36
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
(1 point)
Responses
No, the ratio of 1 hour to $9 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the ratio of 3 hours to $27 is not proportional.
No, the ratio of 3 hours to $27 is not proportional.
Yes, the ratios are in a proportional relationship.