Question

The University of Central Florida's cheerleading team has eighteen males and twenty-one females. If h represents the height of a team member, the inequality 260 ≤ 4h + 28 < 324 , represents the range of heights of the cheerleaders, in inches. Select all possible heights for the University of Central Florida's cheerleaders.

Answer 1

The possible heights for cheerleaders range from 58 to 74 inches, based on the inequality 260 ≤ 4h + 28 < 324, after subtracting 28 and dividing by 4.

Step-by-step explanation:

The range of possible heights for the University of Central Florida's cheerleaders can be determined by solving the inequality 260 ≤ 4h + 28 < 324. To find the range of h, we first subtract 28 from all parts of the inequality to isolate the term with h. This gives us 232 ≤ 4h < 296. Next, we divide all parts of the inequality by 4 to solve for h. The result is 58 ≤ h < 74, meaning the heights of the cheerleaders range from 58 inches to 74 inches, but do not include 74 inches.

The range of possible heights would include values like 60 inches, 65 inches, and 72 inches. They would not include values like 57 inches, which is below the minimum, or 75 inches, which is above the maximum.

Answer 2

The range of heights of the cheerleaders is the interval [58, 74)

All real numbers greater than or equal to 58 inches and less than 74 inches

Step-by-step explanation:

we have

`260 \leq 4h+28 <324`

Divide the compound inequality into two inequalities

`260 \leq 4h+28` -----> inequality A

`4h+28 <324` -----> inequality B

Solve inequality A

`260 \leq 4h+28`

Subtract 28 both sides

`232 \leq 4h`

Divide by 4 both sides

`58 \leq h`

Rewrite

`h \geq 58\ in`

Solve the inequality B

`4h+28 <324`

Subtract 28 both sides

`4h <296`

Divide by 4 both sides

`h <74\ in`

therefore

The range of heights of the cheerleaders is the interval [58, 74)

All real numbers greater than or equal to 58 inches and less than 74 inches