Answer:
a. 12/13
Step-by-step explanation:
Sin is opposite over hypotenuse.
Opposite side of K is 12 and your hypotenuse is 13
To find the unit rate, 391/17 gives us 23$ per hour time 13 hours is 299$ total.
Answer:
The length of the yard is 102
Step-by-step explanation:
If the width of the yard is 100 feet, and it's a rectangular, that means the other side of the rectangle is also equal to 100 feet. So so far we have 200 feet of the yard covered. Then we do 404-200=204. So the combined length of both the sides is 204. Since they both equal the same length, we can then do 204/2 to get 102. So one side length is 102 and the L, W, L, W of the rectangle is 102, 100, 102, 100. In other words, the rectangle is 102 by 100.
Notice that 
for 
implies that 
elsewhere, since
where 
is a random variable representing cable lengths according to the PDF 
.
a. By definition of expectation, the mean is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x\,\mathrm dx=1205](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf%28x%29%5C%2C%5Cmathrm%20dx%3D0.1%5Cint_%7B1200%7D%5E%7B1210%7Dx%5C%2C%5Cmathrm%20dx%3D1205)
The variance is
![\operatorname{Var}[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2](https://tex.z-dn.net/?f=%5Coperatorname%7BVar%7D%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2)
where
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f(x)\,\mathrm dx=0.1\int_{1200}^{1210}x^2\,\mathrm dx=\frac{4,356,100}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf%28x%29%5C%2C%5Cmathrm%20dx%3D0.1%5Cint_%7B1200%7D%5E%7B1210%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B4%2C356%2C100%7D3)
so that the variance is 
, making the standard deviation 
.
b. The proportion of cables within specs is
