Mathematics, 19.02.2020 04:58 zamorano75341

A levee was designed to protect against floods with an annual exceedance probability of 0.02. A larger flood would cause the levee to fail. What is the risk that the levee will NEVER fail in the next 20 years?

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Answer from: lalllda

66.76% probability that the levee will NEVER fail in the next 20 years.

Step-by-step explanation:

For each year, there are only two possible outcomes. Either a levee fails during the year, or no levees fail. In each year, the probabilities of levees failing are independent from each other. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

A levee was designed to protect against floods with an annual exceedance probability of 0.02. This means that p = 0.02

What is the risk that the levee will NEVER fail in the next 20 years?

This is P(X = 0) when n = 20 . So

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

$P(X = 0) = C_{20,0}*(0.02)^{0}*.(0.98)^{20} = 0.6676$

66.76% probability that the levee will NEVER fail in the next 20 years.

Answer from: Quest

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram. we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2. so it's not a square or a rhombus.

we check the dot product of direction vectors of adjacent sides. we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular. we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

Answer from: Quest

answer: the answer is 5/22

step-by-step explanation: if you subtract 17 from 22 the answer is 5 therefore the remainder of students are female

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A levee was designed to protect against floods with an annual exceedance probability of 0.02. A larg...