Mathematics, 02.07.2020 01:01 peno211

A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

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Answer from: fatimaacarrillo2005

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

54% of the school's graduates move to a different state after graduating.

This means that p = 0.54

7 randomly selected graduates

This means that n = 7

Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Either none moves, or at least one does. The sum of the probabilities of these events is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{7,0}.(0.54)^{0}.(0.46)^{7} = 0.0044$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0044 = 0.9956$

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Answer from: Quest

step-by-step explanation:

yuo ned the activity or vertical angle of the form of 1,7 but 2,2 has a c4,2 as it verticie so i not have a car

Answer from: Quest

(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

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