Use the table to answer the question.
Time(Hours) / Pages Read
T:1/2 PR:15
T:1 PR:30
T:1 1/2 PR:45
T:2 PR:60
Ruth can read 15 pages in 30 minutes. she decides to create a table to keep track of her progress. from a data provided, at what ratio is the constant of proportionality
A (1 1/2, 30)
B (1, 30)
C (15, 1/2)
D (2, 60)
To find the ratio of the constant of proportionality, we can divide the pages read by the time in hours for each entry in the table.
For the first entry, we have 15 pages read in 0.5 hours, which gives a ratio of 15/0.5 = 30.
For the second entry, we have 30 pages read in 1 hour, which gives a ratio of 30/1 = 30.
For the third entry, we have 45 pages read in 1.5 hours, which gives a ratio of 45/1.5 = 30.
For the fourth entry, we have 60 pages read in 2 hours, which gives a ratio of 60/2 = 30.
Therefore, the constant of proportionality is 30 in all cases. None of the given options match this result, so none of the options are correct.
what is the closest answer?
From the given options, the closest answer in terms of the ratio and the constant of proportionality is option B: (1, 30).
use the table to answer the question.
Hours Biked: 1 Miles Traveled: 12
Hours Biked: 2 Miles Traveled: 26
Hours Biked: 3 Miles Traveled: 30
Hours Biked: 4 Miles Traveled: 48
determine if the quantity is in the data table or in a proportional relationship. if they do not have a proportional relationship, indicate why
A no, you can't buy 12 miles in an hour
B yes, this data table has a proportional relationship.
C no, none of the ratios have equivalence
D no, not all of the ratios are proportional or have equivalence.
To determine if the quantities in the data table have a proportional relationship, we need to check if the ratios of miles traveled to hours biked are consistent.
For the first entry, we have 12 miles traveled in 1 hour, giving us a ratio of 12/1 = 12.
For the second entry, we have 26 miles traveled in 2 hours, giving us a ratio of 26/2 = 13.
For the third entry, we have 30 miles traveled in 3 hours, giving us a ratio of 30/3 = 10.
For the fourth entry, we have 48 miles traveled in 4 hours, giving us a ratio of 48/4 = 12.
Since the ratios are not consistent and do not have equivalence, the quantities in the data table do not have a proportional relationship.
Therefore, the correct answer is option C: no, none of the ratios have equivalence.
To find the ratio constant of proportionality, we need to examine the relationship between time and pages read.
Let's calculate the ratio of pages read per hour for each time interval:
T:1/2 PR:15 - Pages read per hour: 15 / 0.5 = 30
T:1 PR:30 - Pages read per hour: 30 / 1 = 30
T:1 1/2 PR:45 - Pages read per hour: 45 / 1.5 = 30
T:2 PR:60 - Pages read per hour: 60 / 2 = 30
As we can see, the ratio of pages read per hour remains constant at 30 for each time interval.
Therefore, the correct answer is B) (1, 30), where the ratio constant of proportionality is 30.
To determine the constant of proportionality, we need to look for the relationship between time and pages read. Let's analyze the given data:
Time (Hours) / Pages Read
T:1/2 PR:15
T:1 PR:30
T:1 1/2 PR:45
T:2 PR:60
Looking at the data, we can observe that the pages read are increasing at a consistent rate with time. From the given values, we can see that for every 30 minutes (or half an hour) she reads 15 pages.
We can also see that for every additional 30 minutes, the number of pages she reads increases by 15.
Therefore, the constant of proportionality can be found by determining how many pages she reads in one hour.
To do this, we need to double the number of pages she reads in 30 minutes (15 pages) to get the number of pages she would read in one hour. So the constant of proportionality is 30 pages for one hour.
Looking at the options provided, the closest match to the constant of proportionality is:
B) (1, 30)
Therefore, the correct answer is B) (1, 30), which means for every hour (1), Ruth can read 30 pages.