Place the indicated product in the proper location on the grid.<br><br> (ab

Svetradugi [14.3K]

$\frac{55}{100} = \frac{11\times 5}{20\times 5} = \huge{\boxed{\frac{11}{20}}}$

7 0

3 years ago

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

Find the measure of angle x in the figure below: (1 point) Two triangles are shown such that one triangle is inverted and share

Elena L [17]

75°+75°=150°
angles in a triangle add up to 180°
180°-150°=30°
c) x=30°

5 0

3 years ago

Solve the formula for the volume of a cone for the height of the cone, h. The formula is: V = 1/3 pir^2h

Kamila [148]

80085 because this is the circumference which u multiply across surface area that gives u the volume.

7 0

3 years ago

Read 2 more answers

Can i get answer and help plis

Nadya [2.5K]

Answer
101.76(i think)

Explanation
First you would change the percentage to a decimal which would be 0.25. Multiply 0.25 x 128 = 32

Subtract 32 from 128 to get 96
96 x 0.06 = 5.76
5.76+ 96 = 101.76

Let me know if it helps

7 0

2 years ago

Place the indicated product in the proper location on the grid. (ab - 9)(ab + 8)