To determine if the table represents a proportional relationship, we need to check if there is a constant ratio between the hours and the money.
First, let's find the ratio by dividing the money by the hours for each value in the table:
For the first entry, since 9/1 = 9, the ratio is 9.
For the second entry, 18/2 = 9, which is the same ratio as the first entry.
For the third entry, 27/3 = 9, which is again the same ratio.
For the fourth entry, 36/4 = 9, which is consistent with the previous ratios.
Therefore, since the ratio between the money and the hours is consistent and equal to 9 for all values in the table, we can conclude that the table represents a proportional relationship.
The quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship. (2 points)
Hours: 1, 2, 3, 4
Money: 9, 18, 27, 36
13 answers
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?
Hours:1/4, 1/2, 3/4, 1
Miles:1, 2, 3, 4
Hours:1/4, 1/2, 3/4, 1
Miles:1, 2, 3, 4
To determine at which ratio the constant of proportionality appears, we need to find the ratio between the miles and the hours for each value in the table.
For the first entry, 1/2 divided by 1/4 is equal to 2, which is the ratio.
For the second entry, 2 divided by 1/2 is also equal to 4, which is the same ratio as the first entry.
For the third entry, 3 divided by 3/4 is again equal to 4, the same ratio as the previous entries.
For the fourth entry, 4 divided by 1 is, once again, equal to 4, consistent with the previous ratios.
Therefore, the constant of proportionality appears at a ratio of 4.
For the first entry, 1/2 divided by 1/4 is equal to 2, which is the ratio.
For the second entry, 2 divided by 1/2 is also equal to 4, which is the same ratio as the first entry.
For the third entry, 3 divided by 3/4 is again equal to 4, the same ratio as the previous entries.
For the fourth entry, 4 divided by 1 is, once again, equal to 4, consistent with the previous ratios.
Therefore, the constant of proportionality appears at a ratio of 4.
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?
Hours:1/4, 1/2, 3/4, 1
Miles:1, 2, 3, 4
Answers: (1/4, 1) (4, 1) (1, 4)(1, 1/4)
Hours:1/4, 1/2, 3/4, 1
Miles:1, 2, 3, 4
Answers: (1/4, 1) (4, 1) (1, 4)(1, 1/4)
To determine at which ratio the constant of proportionality appears, we need to find the ratio between the miles and the hours for each value in the table.
For the first entry, 1 divided by 1/4 is equal to 4, not 1/4, so (1/4, 1) is not the correct ratio.
For the second entry, 2 divided by 1/2 is equal to 4, not 1, so (4, 1) is not the correct ratio.
For the third entry, 3 divided by 3/4 is equal to 4, not 1, so (1, 4) is not the correct ratio.
For the fourth entry, 4 divided by 1 is equal to 4, not 1/4, so (1, 1/4) is not the correct ratio.
Therefore, none of the given answer choices represent the correct ratio for the constant of proportionality.
For the first entry, 1 divided by 1/4 is equal to 4, not 1/4, so (1/4, 1) is not the correct ratio.
For the second entry, 2 divided by 1/2 is equal to 4, not 1, so (4, 1) is not the correct ratio.
For the third entry, 3 divided by 3/4 is equal to 4, not 1, so (1, 4) is not the correct ratio.
For the fourth entry, 4 divided by 1 is equal to 4, not 1/4, so (1, 1/4) is not the correct ratio.
Therefore, none of the given answer choices represent the correct ratio for the constant of proportionality.
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? (1 point) Responses (1/4,1) (4, 1) (1, 4) (1,1/4)
To determine at which ratio the constant of proportionality appears, we need to find the ratio between the miles and the hours for each value in the table.
For the first entry, 1 divided by 1/2 is equal to 2, which is the ratio.
For the second entry, 2 divided by 1/2 is also equal to 4, which is the same ratio as the first entry.
For the third entry, 3 divided by 1/2 is equal to 6, which is not the same ratio as the previous entries.
For the fourth entry, 4 divided by 1/2 is equal to 8, which is not the same ratio as the previous entries.
Therefore, the constant of proportionality appears at a ratio of (1/2, 2), which is not one of the given answer choices.
For the first entry, 1 divided by 1/2 is equal to 2, which is the ratio.
For the second entry, 2 divided by 1/2 is also equal to 4, which is the same ratio as the first entry.
For the third entry, 3 divided by 1/2 is equal to 6, which is not the same ratio as the previous entries.
For the fourth entry, 4 divided by 1/2 is equal to 8, which is not the same ratio as the previous entries.
Therefore, the constant of proportionality appears at a ratio of (1/2, 2), which is not one of the given answer choices.
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? (1 point) Responses (2, 60) (1, 30) (1/2,15) (15, 30)
To determine at what ratio the unit rate (constant of proportionality) is represented, we need to find the ratio between the number of pages and the number of minutes for each value in the table.
For the given information:
Ruth can read 15 pages in 30 minutes.
To find the unit rate, we can divide the number of pages by the number of minutes:
15 divided by 30 is equal to 1/2.
Therefore, the unit rate is represented at a ratio of (1/2, 15), which matches the fourth answer choice: (1/2, 15).
For the given information:
Ruth can read 15 pages in 30 minutes.
To find the unit rate, we can divide the number of pages by the number of minutes:
15 divided by 30 is equal to 1/2.
Therefore, the unit rate is represented at a ratio of (1/2, 15), which matches the fourth answer choice: (1/2, 15).
Determine if the data in the table represents a proportional relationship. If not, indicate why. (1 point) Responses
Yes, the data represents a proportional relationship.
Yes, the data represents equivalent ratios.
No, the ratios are not all equivalent.
No, the ratios cannot be simplified.
Yes, the data represents a proportional relationship.
Yes, the data represents equivalent ratios.
No, the ratios are not all equivalent.
No, the ratios cannot be simplified.
To determine if the data in the table represents a proportional relationship, we need to check if there is a constant ratio between the values in the table.
Unfortunately, the table has not been provided in the question. Therefore, I am unable to determine if the data represents a proportional relationship or not. Please provide the table so that I can analyze it and provide a more accurate response.
Unfortunately, the table has not been provided in the question. Therefore, I am unable to determine if the data represents a proportional relationship or not. Please provide the table so that I can analyze it and provide a more accurate response.
Determine if the data in the table represents a proportional relationship. If not, indicate why. (1 point) Responses Yes, the data represents a proportional relationship. Yes, the data represents equivalent ratios. No, the ratios are not all equivalent. No, the ratios cannot be simplified.
Hours:1,2,3,4
Miles Traveled: 12,24,36,48
Hours:1,2,3,4
Miles Traveled: 12,24,36,48
To determine if the data in the table represents a proportional relationship, we need to check if there is a constant ratio between the hours and the miles traveled.
Let's calculate the ratio by dividing the miles traveled by the hours for each value in the table:
For the first entry, 12 divided by 1 is equal to 12.
For the second entry, 24 divided by 2 is equal to 12, which is the same ratio as the first entry.
For the third entry, 36 divided by 3 is equal to 12, consistent with the previous ratios.
For the fourth entry, 48 divided by 4 is equal to 12, which is also consistent with the previous ratios.
Therefore, since there is a constant ratio of 12 between the hours and the miles traveled for all values in the table, we can conclude that the data represents a proportional relationship.
The response is: Yes, the data represents a proportional relationship.
Let's calculate the ratio by dividing the miles traveled by the hours for each value in the table:
For the first entry, 12 divided by 1 is equal to 12.
For the second entry, 24 divided by 2 is equal to 12, which is the same ratio as the first entry.
For the third entry, 36 divided by 3 is equal to 12, consistent with the previous ratios.
For the fourth entry, 48 divided by 4 is equal to 12, which is also consistent with the previous ratios.
Therefore, since there is a constant ratio of 12 between the hours and the miles traveled for all values in the table, we can conclude that the data represents a proportional relationship.
The response is: Yes, the data represents a proportional relationship.