ronaldo likes to display a section of soft drinks next to the register at the lunch counter at which he works. Each day, he chooses 4 soft drinks from the 7 different soft drinks that the lunch counter sells and decides the order in which he wants to display them. For any one day, how many different arrangements of soft drinks can ronaldo display?

35 different Arrangements

Step-by-step explanation:

To solve this question, we would be using the Combination formula because is from the question, we are told that Ronaldo CHOOSES 4 soft drinks from 7 different soft drinks

Combination Formula = C(n,r) = nCr

= n!/r! (n - r)!

n = 7

r = 4

7C4 = 7!/4! (7 - 4)!

7C4 = 7!/4! 3!

7C4 = 7 × 6 × 5 × 4 × 3 × 2 × 1/(4 × 3 × 2 × 1) × (3 × 2 × 1)

7C4 = 35

Therefore, Ronaldo can display 35 different arrangements of soft drinks

6.5

step-by-step explanation:

you said it was in the question

~courtney

(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