Question

The table below shows the relationship between the number of calories burned and the minutes of exercise.

Minutes of
Exercise
Calories
Burned

Answer 1

This is because
`\( (25)/(3) \)` is approximately equal to 8.33, making option B the correct equation to represent the relationship between calories burned and minutes of exercise according to the given data. Therefore, option B is correct

The image shows a table of minutes of exercise and corresponding calories burned. To determine which equation relates the number of calories burned (c) to the minutes of exercise (m), we'll use the data from the table to calculate the rate at which calories are burned per minute. This will give us the slope of the line, which in a linear relationship, is the coefficient of m in the equation c = m * (slope).

Steps for Calculation:

1. Pick two points from the table to calculate the slope. For instance, use (30, 250) and (12, 100).

2. Calculate the slope (rate of calories burned per minute) using the formula for the slope of a line between two points:
`\( \text{slope} = (y_2 - y_1)/(x_2 - x_1) \)`, where (x1, y1) and (x2, y2) are the points from the table.

3. Substitute the values into the formula:
`\( \text{slope} = (250 - 100)/(30 - 12) \).`

4. Simplify to find the slope.

5. The resulting slope will be the coefficient of m in the equation.

Let's perform these calculations to find the correct equation.

The calculated slope is approximately 8.33, which suggests that for every minute of exercise, 8.33 calories are burned. This rate of calories burned per minute can be represented by the equation
`\( c = 8.33m \).`

Since the options given are in fractional form or whole numbers, we need to find the equivalent among the choices:

A.
`\( c = (3)/(25)m \)`

B.
`\( c = (25)/(3)m \)`

C.
`\( c = 150m \)`

D.
`\( c = 220m \)`

The closest option in whole number that represents the slope of 8.33 is:

B.
`\( c = (25)/(3)m \)`

This is because
`\( (25)/(3) \)` is approximately equal to 8.33, making option B the correct equation to represent the relationship between calories burned and minutes of exercise according to the given data.

Answer 2

Option B

Explanation:

Since, number of calories 'C' burned is proportional to the number of minutes (m) given to the exercise,

C ∝ m

C = km

Where k is the proportionality constant.

From the table attached,

For C = 250 calories and m = 30 minutes,

250 = 30k

k =
`(250)/(30)`

=
`(25)/(3)`

Therefore, equation representing this situation will be,

C =
`(25)/(3)m`

Option B will be the correct option.