Step-by-step explanation:
(7 + x) / 3 = 2x - 5
7 + x = 3(2x - 5) (multiply 3 on both sides)
7 + x = 6x - 15 (distributive property)
5x = 22 (arrange like terms)
x = 4.4 (divide 5 on both sides)
Answer:
1 s / 6 s
Step-by-step explanation:
Since you have different units of measurement (seconds and minutes) you have to get them to be the same unit.
Change the 1 minute into seconds.
1 min = 60 sec
Now simplify the new fraction.
10 s / 60 s
10 can go into both the numerator and the denominator.
1 s / 6 s
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:
134568
Step-by-step explanation:
go go go
