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.

Rebecca bought a game in Miami. The game was $30. Miami has a 7% sales tax. How much money did Rebecca pay for the video game including sales tax?