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 12
3 36
5 60
10 120
The constant of proportionality appears in the ratio (1, 12) in the data table.
To determine the ratio at which the constant of proportionality appears, we need to check if there is a consistent ratio between the number of paper towel rolls and the number of cases.
Let's divide the number of cases by the number of paper towel rolls for each data point:
For (1, 12):
12 / 1 = 12
For (3, 36):
36 / 3 = 12
For (5, 60):
60 / 5 = 12
For (10, 120):
120 / 10 = 12
From the calculations above, we can see that the ratio between the number of cases and the number of paper towel rolls is consistently 12. This means that the constant of proportionality appears at a ratio of (1, 12).
To determine the constant of proportionality in the data table, we need to find the ratio between the number of cases and the amount of paper towel rolls.
For the given data:
1 case corresponds to 12 rolls
3 cases correspond to 36 rolls
5 cases correspond to 60 rolls
10 cases correspond to 120 rolls
Let's calculate the ratios for each pair:
(1, 12): 12/1 = 12
(3, 36): 36/3 = 12
(5, 60): 60/5 = 12
(10, 120): 120/10 = 12
As you can see, the ratio is consistently 12 for each data point, indicating that the constant of proportionality is 12.
Therefore, the ordered pair representing the constant of proportionality is (1, 12).
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. (1 point)
To determine the constant of proportionality in the data table, we need to find the ratio between the number of people and the number of buses.
Given that the company plans to use 4 buses and the combined capacity of the buses is 140 people, we can calculate the people-to-bus ratio for each data point in the table:
(10, 2): 10 / 2 = 5
(30, 4): 30 / 4 = 7.5
(40, 6): 40 / 6 = 6.67
(70, 10): 70 / 10 = 7
As we can see, the ratio is not consistent for each data point. Therefore, in this data table, there is no constant of proportionality present.
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. (1 point)
0 0
1 35
2 70
3 105
4 140
To determine the constant of proportionality in the data table, we need to find the ratio between the number of people and the number of buses.
Given that the company plans to use 4 buses and the combined capacity of the buses is 140 people, we can calculate the people-to-bus ratio for each data point in the table:
For (0, 0):
0 / 0 = undefined
For (1, 35):
35 / 1 = 35
For (2, 70):
70 / 2 = 35
For (3, 105):
105 / 3 = 35
For (4, 140):
140 / 4 = 35
As we can see, the ratio is consistently 35 for each data point. Therefore, the constant of proportionality appears at a ratio of (1, 35).
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. (1 point)
1 1/2
2 1
3 1 1/2
4 2
To determine the constant of proportionality in the data table, we need to find the ratio between the amount of flour and the number of loaves of bread.
Let's calculate the ratio for each pair:
For (1, 1/2):
(1/2) / 1 = 1/2
For (2, 1):
1 / 2 = 1/2
For (3, 1 1/2):
(3/2) / 3 = 1/2
For (4, 2):
2 / 4 = 1/2
As we can see, the ratio is consistently 1/2 for each data point. Therefore, the constant of proportionality appears at a ratio of (1, 1/2).
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.
1 75
2 150
3 225
5 375
10 750
100 7500