It takes Julian 1/2 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?
(1 point)
Responses
(1, 1/4)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(1/4, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 4)
(1/4, 1)
The constant of proportionality in this scenario is the time it takes Julian to walk a certain distance. From the given information that it takes him 1/2 hour to walk 2 miles, we can see that the time is inversely proportional to the distance. The ratio of time to distance is 1/4 (1/2 divided by 2). Therefore, the correct answer is (1/4, 1).
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?
(1 point)
Responses
(15, 1/2)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(1, 30)
(1, 30)
The constant of proportionality in this scenario is the number of pages that Ruth can read in a certain amount of time. From the given information that she can read 15 pages in 30 minutes, we can see that the number of pages is directly proportional to the time. The ratio of pages to time is 1/2 (15 divided by 30). Therefore, the correct answer is (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.
(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.
No, the table does not count consecutively.
No, the table does not count consecutively.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.
To determine if the quantities in a data table are in a proportional relationship, we need to check if the ratios between the values are constant. In this case, we can see that the ratio of water used (gal) to time (min) changes as the values increase. For example, the ratio of 7 to 35 is not the same as the ratio of 1 to 5, 2 to 10, 3 to 15, or 10 to 50. Therefore, the correct answer is "No, the ratios are not equivalent."
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.
(1 point)
Responses
No, none of the ratios have equivalence.
No, none of the ratios have equivalence.
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.
No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.
Yes, this data table has a proportional relationship.
No, not all of the ratios are proportional or have equivalence.
To determine if the quantities in a data table are in a proportional relationship, we need to check if the ratios between the values are constant. In this case, we can see that the ratio of miles traveled to hours biked changes as the values increase. For example, the ratio of 1 to 12 is not the same as the ratio of 2 to 26, or 3 to 30, or 4 to 48. Therefore, the correct answer is "No, not all of the ratios are proportional or have equivalence."
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
Yes, the ratios are in a proportional relationship.
Yes, the ratios are in a proportional relationship.
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 $27 is not proportional.
Yes, the ratios are in a proportional relationship.
To determine if the quantities in a data table are in a proportional relationship, we need to check if the ratios between the values are constant. In this case, we can see that the ratio of Money ($) to Hours is constant. Each hour corresponds to $9, which means the ratio is consistent for each pair of values in the table. Therefore, the correct answer is "Yes, the ratios are in a proportional relationship."
To find the constant of proportionality in this scenario, we need to analyze the relationship between time (in hours) and distance (in miles) Julian can walk. According to the information given, Julian takes 1/2 hour (0.5 hours) to walk 2 miles.
To find the constant of proportionality, we can set up an equation using the formula for direct variation:
time (in hours) = constant of proportionality × distance (in miles)
Let's plug in the known values:
0.5 hours = constant of proportionality × 2 miles
To find the value of the constant of proportionality, we can solve for it using algebra:
constant of proportionality = 0.5 hours ÷ 2 miles
Simplifying this expression:
constant of proportionality = 0.25 hours/mile
Based on the given answer choices, the correct ratio for the constant of proportionality is:
(1/4, 1)
(left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis)
Therefore, the answer is (1/4, 1).