Use the table to answer the question.
Hours Miles walked
14 1
12 2
34 3
1 4
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
(1/4, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 1/4)
The constant of proportionality appears at the ratio (1/4, 1).
r you sure
Apologies for the confusion in my previous response. Upon re-evaluating the table, it seems that there is no direct constant of proportionality based on the given data. The hours and miles walked do not have a consistent ratio, which indicates that there is no constant rate of change or proportionality between the two variables in this context. Therefore, there is no ratio where the constant of proportionality appears in this case.
Hours Miles walked
1/4 1
1/2 2
3/4 3
1 4
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
Responses
(1/4, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(1, 4)
left parenthesis 1 comma 4 right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 1/4)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
Apologies for the mistake in my previous response. In the given data table, the ratio (1/2, 2) represents the constant of proportionality.
in ratio?
Apologies for the confusion. The correct ratio that represents the constant of proportionality in this case is (1/2, 2).
so is its (1, 1/4)?
To find the constant of proportionality, we need to determine the ratio between the miles walked and the hours taken for each set of data points.
Let's calculate the ratios for each set of data:
For the first data point: 1 mile walked in 14 hours. The ratio is 1/14.
For the second data point: 2 miles walked in 12 hours. The ratio is 2/12, which simplifies to 1/6.
For the third data point: 3 miles walked in 34 hours. The ratio is 3/34, which cannot be simplified.
For the fourth data point: 4 miles walked in 1 hour. The ratio is 4/1, which simplifies to 4.
The ratio that appears as the constant of proportionality is 4, so the correct answer is:
(4, 1) - left parenthesis 4 comma 1 right parenthesis