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3 years ago

Solve the following equation for d. Show all of your work t= b + d/2f

Mathematics

1 answer:

ANTONII [103]3 years ago

6 0

Subtract b:
T-b=d/2f

Multiply by 2f:
2f(t-b)=d

Rearrange:
D=2f(t-b)

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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

What's the domain of this function graph?<br> A) (-♾, 0)<br> B) (0,♾)<br> C) (-♾,♾)<br> D) (1,♾)

Scilla [17]

Answer:

b) (0,infinity)

Step-by-step explanation:

You can look at the graph and see it starts when x=1, and continues forever in the positive direction.

4 0

3 years ago

Read 2 more answers

How do you solve this for math -3/4÷(-8/5)

Natasha2012 [34]

Answer:

15/32

Step-by-step explanation:

(-3/4)÷(-8/5)

(-3/4)×(-5/8)

15/32

6 0

4 years ago

37.33 as a percentage of 56

nika2105 [10]

Answer:

20.9048

Step-by-step explanation:

37.33% of 56 = 0.3733 × 56 = 20.9048

i hope this is what you meant. 37.33% of 56 is 20.9048

4 0

2 years ago

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Domain and range of -3x^2+16x+3

Zarrin [17]

Answer:

＜=16

Step-by-step explanation:

3 0

3 years ago