X^2+4x divides by x

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

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.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

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

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

Chloe is saving for a laptop that cost 580 if She earns $40 each week, how long will it take her to buy the laptop

schepotkina [342]

$580 laptop/ $40 earned a week = about 14.5 weeks to buy the laptop

5 0

3 years ago

Someone please go through this with me I beg, I will award brainiest! Maths homework due in for the 8th.. ;((

enot [183]

Essentially, you're going to want to reverse the steps on x in order to isolate it from the rest of the variables. To do this, perform inverse operations on x. The first one of these is the multiplication of x and m, so divide both sides by m to cancel m out on the right side. Now we have y/m = x + b. The final thing to do in order to isolate x is to subtract b from both sides. This yields us y/m - b = x. This can be rearranged into x = y/m - b, which should be your answer.

6 0

3 years ago

Venus is about 108 kilometers from the Sun. Saturn is about 109 kilometers from the Sun. About how many times farther from the S

alexandr402 [8]

Answer:

1017.

Step-by-step explanation:

Venus is 108.11 million miles away from the sun, and Saturn is about 109 billion. Using a calculator, I tried each of the answers until I found the correct one. Hope this helped!

6 0

3 years ago

How to do this and the answers.

ANEK [815]

Answer:

I'm gonna estimate about 240 miles one way

Explanation:

You have a guide on the bottom right-hand corner of the map that tells you how many miles per that amount of distance. As you can see it is split off into tiles incremented by 30. What you do is take a ruler and measure that guide. For example, let's say the map is 9.5cm and the guide is 2cm per 60 miles. The next thing I would do is to measure the distance in centimeters of the physical map between point a and point b which is 8cm. Finally, I convert the centimeters into miles which is (8/2)*60 = 240.

8 0

2 years ago