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?
To determine the constant of proportionality, we need to find the ratio between the number of pages Ruth can read and the amount of time it takes her to read those pages.
We know that Ruth can read 15 pages in 30 minutes. Therefore, the ratio is 15 pages : 30 minutes.
In other words, for every 15 pages she reads, it takes her 30 minutes.
Simplifying this ratio, we find that the constant of proportionality is 15/30, which reduces to 1/2.
Therefore, the constant of proportionality is 1/2.
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
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(15, 12)
From the data provided, the ratio for the constant of proportionality 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 ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the table does not count consecutively.
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.
Yes, the data table has a proportional relationship.
From the data table, it can be observed that the ratios of water used to time are as follows:
5:1
10:2
15:3
35:7
50:10
Upon simplification, we can see that these ratios are equivalent:
5/1 = 10/2 = 15/3 = 35/7 = 50/10
Therefore, the quantities in the data table are in a proportional relationship.
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.
Yes, the ratios are in a proportional relationship.
Yes, the ratios are in a proportional relationship.
No, the ratio of 3 hours to $27 is not proportional.
No, the ratio of 3 hours to $27 is not proportional.
No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the values are equivalent.
The ratios in the given data table are:
3:27
4:36
We can simplify these ratios to check if they are equivalent:
3/27 = 1/9
4/36 = 1/9
Since the simplified ratios are the same (1/9), we can conclude that the quantities in the data table are in a proportional relationship. Therefore, the correct response is:
Yes, the ratios are in a proportional relationship.