Answer:
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.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
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 
What is the risk that the levee will NEVER fail in the next 20 years?
This is 
when 
. So
66.76% probability that the levee will NEVER fail in the next 20 years.
Answer:
C(N(h)) = 1400h +530
Step-by-step explanation:
x = N(h), so substitute in the expression for N(h) to get x
C(N(h)) = 35(40h) + 530
=> 1400h + 530
now pray for my lazy brain to check work it is correct
LHS ⇒ RHS:
Identities:
[1] cos(2A) = 2cos²(A) - 1 = 1 - 2sin²(A)
[2] sin(2A) = 2sin(A)cos(A)
[3] sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
[4] cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
cos(x) - cos(x + 2Θ)
= cos(x) - (cos(x)cos(2Θ) - sin(x)sin(2Θ)) [4]
= cos(x) - cos(x)(1 - 2sin²(Θ)) + sin(x)(2sin(Θ)cos(Θ)) [1] [2]
= cos(x) - cos(x) + 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin(Θ)(sin(Θ)cos(x) + sin(x)cos(Θ))
= 2sin(Θ)sin(x + Θ)
If the triangle has the angle of 90°, 89° and 1° then 1 side length can be 3 in but all the side lengths cannot be 3 in.
<u>Explanation:</u>
The sum of all the angles of a triangle = 180°
So, if 1 angle is 90° and the 2nd angle is 89°, then the third angle will be 1°
and length of 1 side = 3 in
a = 3 in
Using the Sine rule,
On substituting the value:
Therefore, if the triangle has the angle of 90°, 89° and 1° then 1 side length can be 3 in and the triangle will be very acute but all the side lengths cannot be 3 in.
