The answer is 29 and 31 because by the definition of a prime number it is a natural number that is greater than 1 and has no positive divisors other than 1 and itself.
Let a, b be two odd integers. Then both can be written as
a=2k-1, k is an integer
b=2m-1, m is an integer
So,
a-b=2k-1-(2m-1)=2k-2m-2=2(k-m-1)
Since, k and m and 1 are all integers, then (k-m-1) is also an integer. Hence, 2(k-m-1) is an even integer.
Thus, a-b is even.
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
Answer:
b=bh
Step-by-step explanation:
Answer:
The answer is supposed to be (2,-3), but for some reason I don't see it as one of the choices.
(Please don't get mad or report this answer, the work is below, so you may see for yourself.)
Step-by-step explanation:
Since y equals both -6x + 9 and -3x + 3, we will simply write them into one equation:
-6x + 9 = -3x + 3
Next we will solve for x by isolating it:
So, first subtract 3 on both sides to get -6x + 6 = -3x. Next add 6x on both sides to get 6 = 3x. Then finally divide by 3 on both sides to get 2 = x or you can flip it to be x = 2.
Now that we know what x is, we can plug it back into one of the original equations. In this case we'll plug it into y = -3x + 3:
y = -3(2) + 3
-3 × 2 = -6 and -6 + 3 = -3
So: y = -3
Now we can plug each into an ordered pair (x,y), and your answer is (2,-3).
As always, don't forget to check your work (It's correct btw, I already checked) and I hope this helps you :)
