It takes Julian 1/2 hour to walk 2 miles. He decides to start working 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?
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To determine the ratio at which the constant of proportionality appears, we need to look for a pattern in the relationship between the distance Julian walks and the amount of time it takes him.
From the given information, we know that Julian can walk 2 miles in 1/2 hour. We can represent this as the ratio 2/1/2, or 4/1.
If we continue to analyze the relationship, we can observe that Julian takes the same amount of time to walk the same ratio of distance. For example, if Julian walks 4 miles, it will take him 2 hours (a ratio of 4/2). If he walks 6 miles, it will take him 3 hours (a ratio of 6/3).
From this pattern, we can conclude that the constant of proportionality is the ratio 2/1 or 4/1. This means that for every additional mile Julian walks, it will take him another 1/2 hour or 1 hour, respectively.
It takes Julian 1/2 hour to walk 2 miles. He decides to start working 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, 2)
C. (1, 4)
D. (1, 1/4)
The constant of proportionality is the ratio between the time it takes Julian to walk a certain distance and the distance itself. In this case, we are given that it takes Julian 1/2 hour to walk 2 miles.
To find the constant of proportionality, we can divide the time by the distance: (1/2) hour รท 2 miles = 1/4 hour/mile.
Therefore, the correct answer is A. (1/4, 1), as it represents the ratio 1/4 hour/mile, which is the constant of proportionality in this scenario.
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 unit rate (constant of proportionality) represented?
To find the ratio at which the unit rate (constant of proportionality) is represented, we need to consider the relationship between the number of pages Ruth reads and the amount of time it takes her.
Given that Ruth can read 15 pages in 30 minutes, we can represent this as the ratio 15 pages / 30 minutes, or 15/30.
To simplify this ratio and find the unit rate, we can divide both the numerator and denominator by their greatest common factor, which is 15:
15/30 = 1/2.
Therefore, the unit rate (constant of proportionality) is represented by the ratio 1/2, which means that Ruth can read 1 page in 2 minutes.
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 unit rate (constant of proportionality) represented?
A. (2, 60)
B. (1, 30)
C. (1/2, 15)
D. (15, 30)
To find the ratio at which the unit rate (constant of proportionality) is represented, we need to divide the number of pages by the amount of time.
Ruth can read 15 pages in 30 minutes, so the ratio to represent the unit rate is 15 pages / 30 minutes.
To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which is 15.
15 pages / 30 minutes = 1/2 pages per minute.
Therefore, the correct answer is C. (1/2, 15), as it represents the ratio 1/2 pages per minute, which is the unit rate (constant of proportionality) in this scenario.
you sure?
Apologies for the mistake. Let's re-evaluate the options:
Ruth can read 15 pages in 30 minutes, so the ratio to represent the unit rate is 15 pages / 30 minutes.
To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which is 15. This gives us:
15 pages / 30 minutes = 1/2 pages per minute.
Hence, the correct answer is C. (1/2, 15) as it represents the ratio of 1/2 pages per minute, which is the unit rate (constant of proportionality) in this scenario.
Determine if the data in the table represents a proportional relationship. If not, indicate why.
Hours Biked - Miles Traveled
1 - 12
2 - 26
3 - 30
4 - 48
A. Yes, the data represents a proportional relationship.
B. Yes, the data represents equivalent ratios.
C. No, the ratio are not all equivalent.
D. No, the ratios cannot be simplified.