Polly surveyed 850 teenagers to find out their favorite type of music. She found that 32% of the teenagers surveyed like hard rock. Part A: How many teenagers surveyed like hard rock? Show your work. (4 points) Part B: In another survey, Damian found that 75% of the total number of teenagers surveyed like pop music. If 150 teenagers like pop music, what is the total number of teenagers that Damian surveyed? Show your work. (4 points) Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240