A regular hexagon has a radius of 20 in. what is the approximate area of the hexagon
2 answers:
Remark
You need 2 facts to solve this
1. The area of a hexagon is
A = 3*(sqrt(3) ) * a^2/2
Just to make this clear, I'll put it in Latex
2. The second fact you need to know is that the radius = the length of the side a.
Givens
r = 20 in
a = r where a is the length of the side of a hexagon.
Formula Substitute and solve.
A = 3*(sqrt(3) * a^2 ) / 2
A = 3*(sqrt(3) * 20^2) / 2
A = 3*sqrt(3) * 400 / 2
A = 3*sqrt(3) * 200
A = 3*1.7321 * 200
A = 1039 square inches.
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Answer:
The probability is 0.971032
Step-by-step explanation:
The variable that says the number of components that fail during the useful life of the product follows a binomial distribution.
The Binomial distribution apply when we have n identical and independent events with a probability p of success and a probability 1-p of not success. Then, the probability that x of the n events are success is given by:
In this case, we have 2000 electronics components with a probability 0.005 of fail during the useful life of the product and a probability 0.995 that each component operates without failure during the useful life of the product. Then, the probability that x components of the 2000 fail is:
(eq. 1)
So, the probability that 5 or more of the original 2000 components fail during the useful life of the product is:
P(x ≥ 5) = P(5) + P(6) + ... + P(1999) + P(2000)
We can also calculated that as:
P(x ≥ 5) = 1 - P(x ≤ 4)
Where P(x ≤ 4) = P(0) + P(1) + P(2) + P(3) + P(4)
Then, if we calculate every probability using eq. 1, we get:
P(x ≤ 4) = 0.000044 + 0.000445 + 0.002235 + 0.007479 + 0.018765
P(x ≤ 4) = 0.028968
Finally, P(x ≥ 5) is:
P(x ≥ 5) = 1 - 0.028968
P(x ≥ 5) = 0.971032