Use the table to answer the question.
Raspberry | Lemonade
1 2.5
2 5
4 10
6 15
Rosie is planning to make raspberry lemonade for a party. She needs to add 2 scoops of raspberry to every 5 cups of lemonade. The data table shows the ratios needed. At what ratio does the constant of proportionality appear?
A. (2.5, 1)
B. (5, 2)
C. (1, 2.5)
D. (2, 5)
The constant of proportionality appears when the ratio of scoops of raspberry to cups of lemonade remains the same. Looking at the table, we can see that as the number of scoops of raspberry doubles, the number of cups of lemonade also doubles. Therefore, the constant of proportionality appears at the ratio (2, 5).
The answer is D. (2, 5).
Use the table to answer the question.
# of Trees | # of Apples
2 26
3 39
6 78
10 130
12 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
A. Yes, the data table has a proportional relationship.
B. No, the ratio 6 : 78 is not proportional to other ratios.
C. No, the table does not count consecutively.
D. 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 we can create equivalent ratios.
Let's check:
26/2 = 13
39/3 = 13
78/6 = 13
130/10 = 13
156/12 = 13
Since all the ratios are equal to 13, the quantities in the data table are in a proportional relationship.
The answer is A. Yes, the data table has a proportional relationship.
If a graph is proportional, what characteristic does it display?
A. It will have y-values larger than their corresponding x-values
B. It will climb rapidly, indicating a steep slope
C. It will pass through the point (0, 0).
D. It will curve.
If a graph is proportional, it will display the characteristic of passing through the point (0, 0), which is the origin.
The answer is C. It will pass through the point (0, 0).
If Chase runs 5 miles in 60 minutes, how far will he run in 3 hours if he continues to run at the same rate?
A. 1/4 miles
B. 36 miles
C. 0.067 miles
D. 15 miles
If Chase runs 5 miles in 60 minutes, we can determine his running rate by dividing the distance by the time.
Running rate = Distance / Time = 5 miles / 60 minutes
To calculate how far he will run in 3 hours (180 minutes) at the same rate, we can multiply his running rate by the new time:
Distance = Running rate x Time = (5 miles / 60 minutes) x 180 minutes = 15 miles
Therefore, Chase will run 15 miles in 3 hours if he continues to run at the same rate.
The answer is D. 15 miles.
A whale swims 200 miles in 5 days. Identify which equation could be used to find how many miles it swims in 16 days.
A. y= 40 x 16
B. y=200 x 16 x 5
C. y=200 x 16
D. 200= 16x
To find out how many miles the whale swims in 16 days, we need to determine the relationship between the number of miles and the number of days.
Since the whale swims 200 miles in 5 days, we can determine its average daily swimming distance by dividing the total distance by the number of days:
Average daily swimming distance = Total distance / Number of days = 200 miles / 5 days = 40 miles per day.
To find the total distance the whale swims in 16 days, we can multiply the average daily swimming distance by the number of days:
Total distance = Average daily swimming distance x Number of days = 40 miles/day x 16 days = 640 miles.
Therefore, the equation that could be used to find how many miles the whale swims in 16 days is:
A. y= 40 x 16
The answer is A.
Which ratio is equivalent to 9 over 78?
A. 1/8
B. 3/26
C. 3/18
D. 1/3