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2 years ago

I dont get how to do this please help me solve for the absolute value equation show your work

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

7 0

Step-by-step explanation:

$| \frac{x}{3} +{ \frac{2}{5} } | = 2$

$\frac{x}{3} = \frac{6}{5}$

$5x = 18$

$x = \frac{18}{5}$

and

x/3=-12/5

x=-36/5

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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

Simplify 3z + 4z +4 -2 -5z when Z=8

Ber [7]

Answer:

Step-by-step explanation:

3z + 4z +4 -2 -5z

Combine like terms

3z + 4z -5z +4-2

2z+2

Let z=8

2*8 +2

16+2

3 0

3 years ago

Read 2 more answers

What slope is perpendicular to m=4/5

MrRa [10]

Step-by-step explanation:

a perpendicular slope is the negative reciprocal

so the perpendicular slope is -5/4

4 0

2 years ago

Read 2 more answers

1. In which quadrant does θ lie given that sinθ>0 and cosθ<0?

expeople1 [14]

Answer:

$\theta$ is in quadrant II

Step-by-step explanation:

Given

$\sin(\theta) > 0$ and $\cos(\theta) < 0$

Required

Where is $\theta$

$\sin(\theta) > 0$ and $\cos(\theta) < 0$ imply that

$\theta$ is in quadrant II

Because that is only quadrant where $\sin(\theta) > 0$ and $\cos(\theta) < 0$ exist.

4 0

3 years ago

The sum of a number x and twenty-one

Arlecino [84]

The sum of a number.....means addition

ur expression would be : x + 21

5 0

3 years ago