Use the table to answer the question.
Number of Cases Ordered Number of Rolls of Paper Towels
1 12
3 36
5 60
10 120
A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
(1 point)
The ratio of the number of rolls of paper towels to the number of cases is constant at 12. Thus, the constant of proportionality appears at the ratio (12, 1).
I beileve thats wrong
Apologies for the confusion.
Let's calculate the ratio of the number of rolls of paper towels to the number of cases for each data point:
For the first data point, with 1 case and 12 rolls of paper towels, the ratio is 12/1 = 12.
For the second data point, with 3 cases and 36 rolls of paper towels, the ratio is 36/3 = 12.
For the third data point, with 5 cases and 60 rolls of paper towels, the ratio is 60/5 = 12.
For the fourth data point, with 10 cases and 120 rolls of paper towels, the ratio is 120/10 = 12.
As we can see, the ratio is constant at 12 for each data point. So the constant of proportionality appears at the ratio (12,1).
How do i write that?
Apologies once again for the confusion. The correct answer is:
The constant of proportionality appears at the ratio (number of rolls of paper towels, number of cases) of (12, 1).
Use the table to answer the question.
Buses Number of People
0 0
1 35
2 70
3 105
4 140
A tour bus company is planning a trip through Utah’s national parks. The company plans to use 4 buses. Combined, the buses can fit up to 140 people. The table provided displays the number of people-to-bus ratio. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
To find the constant of proportionality in the data table, we need to identify a ratio that remains constant throughout the table.
Let's calculate the ratio of the number of people to the number of buses for each data point:
For the first data point, with 0 buses and 0 people, the ratio is 0/0 = undefined.
For the second data point, with 1 bus and 35 people, the ratio is 35/1 = 35.
For the third data point, with 2 buses and 70 people, the ratio is 70/2 = 35.
For the fourth data point, with 3 buses and 105 people, the ratio is 105/3 = 35.
For the fifth data point, with 4 buses and 140 people, the ratio is 140/4 = 35.
As we can see, the ratio of the number of people to the number of buses is constant at 35 for each data point. Therefore, the constant of proportionality appears at the ratio (35, 1).
So, the answer is: (35, 1).
Cups of Flour Loaves of Bread
1 12
2 1
3 112
4 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
To find the constant of proportionality in the data table, we need to identify a ratio that remains constant throughout the table.
Let's calculate the ratio of the number of cups of flour to the number of loaves of bread for each data point:
For the first data point, with 1 cup of flour and 12 loaves of bread, the ratio is 12/1 = 12.
For the second data point, with 2 cups of flour and 1 loaf of bread, the ratio is 1/2 = 0.5.
For the third data point, with 3 cups of flour and 112 loaves of bread, the ratio is 112/3 = 37.333.
For the fourth data point, with 4 cups of flour and 2 loaves of bread, the ratio is 2/4 = 0.5.
As we can see, the ratio of the number of cups of flour to the number of loaves of bread is not constant for each data point. Therefore, there is no constant of proportionality in this data table.
So, the answer is: N/A
Number of Adults 1 2 3 5 10 100
Cost of Tickets ($) 75 150 225 375 750 7,500
Determine if the quantities in the data table are in a proportional relationship. If the quantities have a proportional relationship, answer 1. If the quantities do not have a proportional relationship, answer 2.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of cost of tickets to the number of adults remain constant throughout the table.
Let's calculate the ratios for each data point:
For the first data point, with 1 adult and $75, the ratio is $75/1 = 75.
For the second data point, with 2 adults and $150, the ratio is $150/2 = 75.
For the third data point, with 3 adults and $225, the ratio is $225/3 = 75.
For the fourth data point, with 5 adults and $375, the ratio is $375/5 = 75.
For the fifth data point, with 10 adults and $750, the ratio is $750/10 = 75.
For the sixth data point, with 100 adults and $7,500, the ratio is $7,500/100 = 75.
As we can see, the ratios of the cost of tickets to the number of adults are all equal to 75. Therefore, the quantities in the data table are in a proportional relationship.
So, the answer is: 1.
Pounds of Bananas Cost ($)
2 2.50
3 3.75
5 6.25
7 8.75
Determine if the quantities in the data table are in a proportional relationship. If the quantities have a proportional relationship, answer 1. If the quantities do not have a proportional relationship, answer 2.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of the cost to the pounds of bananas remain constant throughout the table.
Let's calculate the ratios for each data point:
For the first data point, with 2 pounds of bananas and $2.50, the ratio is $2.50/2 = 1.25.
For the second data point, with 3 pounds of bananas and $3.75, the ratio is $3.75/3 = 1.25.
For the third data point, with 5 pounds of bananas and $6.25, the ratio is $6.25/5 = 1.25.
For the fourth data point, with 7 pounds of bananas and $8.75, the ratio is $8.75/7 = 1.25.
As we can see, the ratios of the cost to the pounds of bananas are all equal to 1.25. Therefore, the quantities in the data table are in a proportional relationship.
So, the answer is: 1.
Hours Miles walked
1/4 1
1/2 2
3/4 3
1 4
It takes Julian 1/2 hour to walk 2 miles. He decides to start walking 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)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis
(1, 1/4)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis
(4, 1)
left parenthesis 4 comma 1 right parenthesis
(1, 4)
left parenthesis 1 comma 4 right parenthesis
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To find the constant of proportionality in the data table, we need to identify a ratio that remains constant throughout the table.
Let's calculate the ratio of the miles walked to the hours for each data point:
For the first data point, with 1/4 hour and 1 mile walked, the ratio is 1/4 / 1 = 1/4.
For the second data point, with 1/2 hour and 2 miles walked, the ratio is 2 / (1/2) = 4.
For the third data point, with 3/4 hour and 3 miles walked, the ratio is 3 / (3/4) = 4.
For the fourth data point, with 1 hour and 4 miles walked, the ratio is 4 / 1 = 4.
As we can see, the ratio of the miles walked to the hours is constant at 4 for each data point. Therefore, the constant of proportionality appears at the ratio (4, 1).
So, the answer is: (4, 1).
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?
(1 point)
Responses
(1, 30)
left parenthesis 1 comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(15, 1/2)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
(1 1/2, 30)
To find the constant of proportionality in the data table, we need to identify a ratio that remains constant throughout the table.
Let's calculate the ratio of the pages read to the time in hours for each data point:
For the first data point, with 15 pages read in 1/2 hour, the ratio is 15 / (1/2) = 30.
For the second data point, with 30 pages read in 1 hour, the ratio is 30 / 1 = 30.
For the third data point, with 45 pages read in 1 1/2 hours, the ratio is 45 / (3/2) = 30.
For the fourth data point, with 60 pages read in 2 hours, the ratio is 60 / 2 = 30.
As we can see, the ratio of the pages read to the time in hours is constant at 30 for each data point. Therefore, the constant of proportionality appears at the ratio (30, 1).
So, the answer is: (30, 1).
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.
Responses
No, the table does not count consecutively.
No, the table does not count consecutively.
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
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.
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 of water used to time remain constant throughout the table.
Let's calculate the ratios for each data point:
For the first data point, with 5 gallons of water used in 1 minute, the ratio is 5/1 = 5.
For the second data point, with 10 gallons of water used in 2 minutes, the ratio is 10/2 = 5.
For the third data point, with 15 gallons of water used in 3 minutes, the ratio is 15/3 = 5.
For the fourth data point, with 35 gallons of water used in 7 minutes, the ratio is 35/7 = 5.
For the fifth data point, with 50 gallons of water used in 10 minutes, the ratio is 50/10 = 5.
As we can see, the ratios of water used to time are all equal to 5. Therefore, the quantities in the data table are in a proportional relationship.
So, the answer is: Yes, the data table has a proportional relationship.
Use the table to answer the question.
Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.
Responses
Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.
No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.
No, none of the ratios have equivalence.
No, none of the ratios have equivalence.
No, you can’t bike 12 miles in an hour.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of miles traveled to hours biked remain constant throughout the table.
Let's calculate the ratios for each data point:
For the first data point, with 12 miles traveled in 1 hour biked, the ratio is 12/1 = 12.
For the second data point, with 26 miles traveled in 2 hours biked, the ratio is 26/2 = 13.
For the third data point, with 30 miles traveled in 3 hours biked, the ratio is 30/3 = 10.
For the fourth data point, with 48 miles traveled in 4 hours biked, the ratio is 48/4 = 12.
As we can see, the ratios of miles traveled to hours biked are not all equal. Since the ratios are not constant, the quantities in the data table do not have a proportional relationship.
So, the answer is: No, not all of the ratios are proportional or have equivalence.
Use the table to answer the question.
Hours Money ($)
1 9
2 18
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.
Responses
No, the ratio of 1 hour to $9 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
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.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of money to hours remain constant throughout the table.
Let's calculate the ratios for each data point:
For the first data point, with $9 earned in 1 hour, the ratio is $9/1 = 9.
For the second data point, with $18 earned in 2 hours, the ratio is $18/2 = 9.
For the third data point, with $27 earned in 3 hours, the ratio is $27/3 = 9.
For the fourth data point, with $36 earned in 4 hours, the ratio is $36/4 = 9.
As we can see, the ratios of money to hours are all equal to 9. Therefore, the quantities in the data table are in a proportional relationship.
So, the answer is: Yes, the ratios are in a proportional relationship.