The area of D is given by:
The average value of f over D is given by:
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B343%7D%7B3%7D%20%7D%20%20%5Cint%5Climits%5E7_0%20%20%5Cint%5Climits%5E%7Bx%5E2%7D_0%20%7B4x%5Csin%28y%29%7D%20%5C%2C%20dydx%20%20%3D%20-%5Cfrac%7B3%7D%7B343%7D%20%20%5Cint%5Climits%5E7_0%20%7B4x%5Ccos%28x%5E2%29%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D-%5Cfrac%7B3%7D%7B343%7D%20%5Cint%5Climits%5E%7B49%7D_0%20%7B2%5Ccos%28t%29%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%20%5Cleft%5B%5Csin%28t%29%5Cright%5D_0%5E%7B49%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%5Csin49)
The average value of f over D is given by:
A rectangle has a perimeter of 80 cm. If its width is x, express its length and area in terms of x, and find the maximum area.
1 answer:
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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