5+ [x - {2y-(6x + y - 4) + 2x} - {x -(y

Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

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.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

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

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

How many solutions does the system y = -7x + 3 and y + 7x = 10 have? Explain.

Vaselesa [24]

Answer:

i believe its infinitely

Step-by-step explanation:

i say this because the equation is similar on both sides

4 0

3 years ago

Need answeer ASAP. please

mario62 [17]

Answer:

The answer to your question is below

Step-by-step explanation:

Process

1.- Transform the inequality to a line

2x - y < 4

2x - y = 4

2.- Find the x and y-intercepts

If x = 0, 2(0) - y = 4

0 - y = 4

y = -4 (0, -4)

If y = 0 2x - 0 = 4

2x = 4

x = 2 (2, 0)

3.- Do not consider graphs 1 and 2 because do not go through (0, -4).

4.- The answer is graph three because of the inequality "<", we look for the shaded region below the line.

4 0

3 years ago

Amber, Bernie, and Carlos are working on a problem together. Their goal is to correctly apply the difference of cubes formula to

NeX [460]

Answer: Carlos is correct

Step-by-step explanation:

2x^5-250x^2

The first step is to factorize out 2x^2

2x^2(x^3-125)

This can be rewritten as

2x^2(x^3-5^3),

Recall, difference if cube (a^3-b^3)

= (a-b)(a^2 +ab + b^2)

from our equation,

a= x

b = 5.

So the difference of cubes will be

2x^2[(x-5) (x^2 + 5x + 5^2)]

=2x^2[(x-5) (x^2 + 5x + 25)]

Carlos followed these steps. So he is correct. Carlos is correct because he correctly factored the GCF, identified a and b, and applied the difference of cubes method.

Amber is incorrect because 125 is equal to b3, not b.

Bernie is incorrect because x2 is not the GCF of the polynomial. The GCF is 2x^2.

6 0

3 years ago

Given that g(x) = 3x - 5, evaluate g(4 + h) <br> ————<br> h

ElenaW [278]

Answer:

3h+7/h

Step-by-step explanation:

the parenthesis in g(4+h) is saying that is x. plug in 4+h in the x and evaluate.

so you would get 3(4+h)-5. distribute the 3 and get 12+3h-5. combine like terms to get 3h+7!

then it's just over h because you can't simplify anymore. so the real answer is 3h+7/h!!

8 0

3 years ago

Read 2 more answers

5+ [x - {2y-(6x + y - 4) + 2x} - {x -(y - 2)}solve it.​

5+ [x - {2y-(6x + y - 4) + 2x} - {x -(y - 2)}solve it.