Use the table to answer the question.
Time (hours) Pages read
1/2 15
1 30
1 1 2 45
2 60
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 find the ratio of the constant of proportionality, we need to find the ratio between the number of pages read and the time in hours.
The ratio is calculated by dividing the pages read by the time in hours.
For the first row, the ratio is 15 pages / 0.5 hours = 30 pages/hour.
For the second row, the ratio is 30 pages / 1 hour = 30 pages/hour.
For the third row, the ratio is 45 pages / 1.5 hours = 30 pages/hour.
For the fourth row, the ratio is 60 pages / 2 hours = 30 pages/hour.
Therefore, the constant of proportionality is 30 pages per hour.
Use the table to answer the question.
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.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the two quantities remains constant.
We can do this by calculating the ratios for each row in the table.
For the first row, the ratio is 5 gallons / 1 minute = 5 gallons/minute.
For the second row, the ratio is 10 gallons / 2 minutes = 5 gallons/minute.
For the third row, the ratio is 15 gallons / 3 minutes = 5 gallons/minute.
For the fourth row, the ratio is 35 gallons / 7 minutes = 5 gallons/minute.
For the fifth row, the ratio is 50 gallons / 10 minutes = 5 gallons/minute.
Since the ratio between the water used and time in minutes remains constant (5 gallons/minute), the quantities in the data table are in a proportional relationship.
We can conclude that the amount of water used is directly proportional to the time in minutes.
To find the constant of proportionality, we need to determine the ratio between the number of pages read and the time spent reading.
Let's calculate the ratios:
For the first interval (1/2 hour), the ratio is:
Pages read / Time = 15 / (1/2) = 30
For the second interval (1 hour), the ratio is:
Pages read / Time = 30 / 1 = 30
For the third interval (1 1/2 hours), the ratio is:
Pages read / Time = 45 / (3/2) = 45 * (2/3) = 30
For the last interval (2 hours), the ratio is:
Pages read / Time = 60 / 2 = 30
From the given data, we can see that the ratio of pages read to time spent reading is constant throughout all the intervals, which is 30. Therefore, the constant of proportionality is 30.
To find the ratio of the constant of proportionality, we first need to identify a pattern in the given data. Looking at the table, we can see that as the time increases, the number of pages read also increases.
Let's compare the ratio between the time and the number of pages read. We can start with the first two data points:
Time (hours) Pages read Ratio (Time/Pages)
1/2 15 1/2 ÷ 15 = 1/30
From the first two data points, the ratio of time to pages read is 1/30.
We can also calculate the ratio for the next two data points:
Time (hours) Pages read Ratio (Time/Pages)
1 30 1 ÷ 30 = 1/30
The ratio remains the same, 1/30.
Continuing with the next two data points:
Time (hours) Pages read Ratio (Time/Pages)
1 1/2 45 1 1/2 ÷ 45 = 1/30
Again, the ratio is 1/30.
Finally, for the last data point:
Time (hours) Pages read Ratio (Time/Pages)
2 60 2 ÷ 60 = 1/30
The ratio remains consistent at 1/30.
From the data given in the table, we can conclude that the constant of proportionality ratio is 1/30.