Evaluate the following to determine the value of 𝑛:
(83)n
(
8
3
)
= 812
8
12
(2 points)
Responses

n = 9
n = 9

n = 4
n = 4

n = 2
n = 2

n = 1
n = 1
The value of n is 1.
Inessa ran 3 laps in 10 minutes. How long would it take her to run 5 laps at this pace?(1 point)
Responses

1 12 minutes
1
1
2
minutes
1 12 minutes
1
1
2
minutes

15 minutes
15
minutes
15 minutes
15
minutes

16 23 minutes
16
2
3
minutes
16 23 minutes
16
2
3
minutes

20 minutes
To find the time it would take Inessa to run 5 laps at the same pace, we can use a proportion:
3 laps / 10 minutes = 5 laps / x minutes
Cross multiplying, we get:
3x = 50
Dividing both sides by 3, we find:
x = 16.67 minutes
So, it would take her approximately 16.67 minutes to run 5 laps at this pace.
Pick one of the answers
16 2/3 minutes
The table shows how many pizzas (y) kenneth can make per hour (x). Determine if the relationship is proportional and if so, its constant rate of proportionality. X 0 1 2 3 4 Y 0 4 8 12 16
To determine if the relationship is proportional, we need to see if the ratio of y to x is constant.
Looking at the values in the table, we can see that for every x increase of 1, y increases by 4.
So, the ratio of y to x is constant: 4/1 = 4.
Therefore, the relationship is proportional with a constant rate of proportionality of 4.
When 1 cup of popcorn kernels are popped, they create 5 bowls of popped corn. How many bowls of popcorn would 8 cups of kernels produce?
If 1 cup of popcorn kernels produces 5 bowls of popped corn, then we can set up a proportion to find out how many bowls of popcorn would 8 cups of kernels produce.
Let x represent the number of bowls of popcorn produced by 8 cups of kernels.
1 cup / 5 bowls = 8 cups / x bowls
To solve for x, we can cross multiply:
1 * x = 5 * 8
x = 40
Therefore, 8 cups of popcorn kernels would produce 40 bowls of popped corn.