You pick a card at random. 2 3 4 What is P(4 or factor of 90)?
Write your answer as a fraction or whole number.

Sacas una carta al azar. 2 3 4
¿Cuánto es P(4 o factor de 90)?
Escribe tu respuesta como una fracción o como un número entero.

P (4 or factor of 90) = 1

Step-by-step explanation:

Given :-

Three cards numbered 2, 3, 4

To Find :-

P (4 or factor of 90)

Solving :-

4 is required and we know that 2 and 3 are both factors of 90.

Therefore, P (4 or factor of 90) = 1

Solution :-

P (4 or factor of 90) = 1

1

Step-by-step explanation:

P(2) = 1/3

P(3) = 1/3

P(4) = 1/3

2 and 3 are factors of 90

⇒ P(factor of 90) = P(2) or P(3) = 1/3 + 1/3 = 2/3

Therefore,

P(4 or factor of 90) = P(4) or P(factor of 90) = 1/3 + 2/3 = 1

(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