Derrick surveyed a random sample of 100 students from his middle school to learn more about what type of school lunches are preferred. the table below shows the result of the survey:   hamburgers spaghetti pizza sample #1 43 13 44 sample #2 41 20 39 which of the following inferences can be made based on the data? pizza is the most preferred lunch. spaghetti is two times more popular than pizza. hamburgers and pizza are preferred almost equally. spaghetti is two times more popular than hamburgers.

hamburgers = 43 + 41 = 84

spaghetti = 13 + 20 = 33

pizza = 44 +39 = 83

 since 83 & 84 are close the answer is:

Hamburgers and pizza are preferred almost equally.

(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