About how long is each side of a square that is 125 square miles

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

URGENT!! I NEED HELP ASAP NOT ROCKY

Anestetic [448]

Answer:

$9000

Step-by-step explanation:

Given

Monthly payment P = $300
Time t = 3 years = 36 months
Number of payments n = 36
Interest rate r = 12% PA = 1% per month = 0.01 times

Use loan payment formula:

P = r(PV) / (1 - (1 + r)⁻ⁿ),
where P- monthly payment, PV - present value (amount of the loan), r -rate of interest, n- number of payments

Substitute values and solve for PV:

300 = (0.01*PV) / (1 - (1 + 0.01)⁻³⁶)
PV = 300*(1 - 1.01⁻³⁶ )/ 0.01
PV = 9032.25 ≈ $9000 (rounded to the nearest hundred dollars)

4 0

3 years ago

in a recent year the population of califorina was about 2.52x10^7 people its land area is about 4.05x10^5 km^2 what was the aver

Oduvanchick [21]

4.05x10^5 km^2 is the answer to your question.

8 0

3 years ago

The perimeter of a rectangle is 22 inches. Find the dimensions if its length is 3 inches greater than its width.

MaRussiya [10]

Answer:

Length: 7

Width: 4

Step-by-step explanation:

We can create a system of equations for this problem, where $w$ is the width and $l$ is the length.

The perimeter of a rectangle is twice its length added to twice its width.

$2l+2w=22$

The length is 3 more than the width:

$l = w+3$

We can now substitute in $w+3$ as $l$ in the equation $2l+2w=22$ .

$2(w+3) + 2w = 22$

Distribute the first terms:

$2w+6+2w=22$

Combine like terms:

$4w+6=22$

Subtract 6 from both sides:

$4w=16$

Divide both sides by 4:

$w = 4$

Now we know that w = 4. We can now substitute this inside an equation to find $l$ .

$l = w+3\\\\l = 4+3\\\\l=7$

Hope this helped!

7 0

3 years ago

How many tenths are in a whole?

Olegator [25]

10 tenths in a whole.....

8 0

3 years ago

Read 2 more answers