Multiply (x+2y)(x^2-xy+3y)

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

What is the correct answer?

Tasya [4]

Given:

The function is

$f(x)=(x+3)^2(x-5)^6$

To find:

The zeros of the given function.

Solution:

The general form of polynomial is

$P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}$ ...(i)

where, a is a constant, $c_1,c_2,...,c_n$ are zeros of respective multiplicities $m_1,m_2,...,m_n$ .

We have,

$f(x)=(x+3)^2(x-5)^6$

On comparing this with (i), we get

$c_1=-3,m_1=2$

$c_2=5,m_2=6$

It means, -3 is a zero with multiplicity 2 and 5 is a zero with multiplicity 6.

Therefore, the correct option is B.

5 0

3 years ago

What is the circumference of a circle with a radius of 5.4 inches? Enter your answer as a decimal in the box. Use 3.14 for pi. R

LenKa [72]

Hi there! The formula for circumference is π * diameter. Diameter is the length across the circle and twice the length of the radius.The radius is 5.4, so we will multiply that by 2 to get 10.8. The diameter is 10.8 inches. Now, multiply that numebr by 3.14 to find the circumference. 10.8 * 3.14 is 33.912 or 33.9 when rounded to the nearest tenth. There. The circumference is approx. 33.9 inches.

7 0

3 years ago

Read 2 more answers

Solve for x. 3x - 1 = 27

poizon [28]

X = 9
Move the 1 over to make it 3x = 28. The. 28/3 equals 9

3 0

3 years ago

Read 2 more answers

What is the volume of a cylinder with a height of 2 feet in a radius of 6 feet use 3.14 for pie

Zepler [3.9K]

Answer:226.08 cubic feet

Step-by-step explanation:

π=3.14

Radius(r)=6feet

Height(h)=2feet

volume=π x r^2 x h

Volume=3.14 x 6^2 x 2

Volume=3.14 x 6 x 6 x 2

Volume=226.08

5 0

3 years ago