9514 1404 393
Answer:
a.
Step-by-step explanation:
For an even-index radical, ...
![\sqrt[n]{x^n}=|x|\qquad\text{n even}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5En%7D%3D%7Cx%7C%5Cqquad%5Ctext%7Bn%20even%7D)
This lets us simplify the given expression as follows:
![\sqrt[4]{81x^6y^4}-|y|\sqrt[4]{x^6}-\sqrt[4]{16x^2}=\sqrt[4]{(3xy)^4x^2}-|y|\sqrt[4]{x^4x^2}-\sqrt[4]{2^4x^2}\\\\=3|xy|\sqrt[4]{x^2}-|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}=\boxed{2|xy|\sqrt[4]{x^2}-2\sqrt[4]{x^2}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81x%5E6y%5E4%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E6%7D-%5Csqrt%5B4%5D%7B16x%5E2%7D%3D%5Csqrt%5B4%5D%7B%283xy%29%5E4x%5E2%7D-%7Cy%7C%5Csqrt%5B4%5D%7Bx%5E4x%5E2%7D-%5Csqrt%5B4%5D%7B2%5E4x%5E2%7D%5C%5C%5C%5C%3D3%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%3D%5Cboxed%7B2%7Cxy%7C%5Csqrt%5B4%5D%7Bx%5E2%7D-2%5Csqrt%5B4%5D%7Bx%5E2%7D%7D)
The answer is option "3, 40".
<span>m∠cab = 2x
m∠acb = x + 30
m∠cbd = 5x − 50
Now,
</span>m∠cab + m∠acb = m∠cbd
2x+x+30 = 5x-50
2x+x-5x = -50-30
-2x = -80
x = 40
Answer:
D 2400 ft^2
Step-by-step explanation:
His joumey maps out a right angles triangle with base 80 and height 60.
The required area = 1/2 * 80 * 60
= 2400 ft^2
The answer is b why because I had did it on the test and I had got it right HOPEFULLY IT HELPS
Let 
be the total amount of money paid by any given set of passengers. If there are 
passengers in a car, then the driver must pay a toll of 
.
Then has first moment (equal to the mean)
![E[Y]=E[0.5X+3]=0.5E[X]+3E[1]=0.5\mu_X+3=\boxed{4.35}](https://tex.z-dn.net/?f=E%5BY%5D%3DE%5B0.5X%2B3%5D%3D0.5E%5BX%5D%2B3E%5B1%5D%3D0.5%5Cmu_X%2B3%3D%5Cboxed%7B4.35%7D)
and second moment
![E[Y^2]=E[0.25X^2+3X+9]=0.25E[X^2]+3E[X]+9E[1]=0.25E[X^2]+3\mu_X+9](https://tex.z-dn.net/?f=E%5BY%5E2%5D%3DE%5B0.25X%5E2%2B3X%2B9%5D%3D0.25E%5BX%5E2%5D%2B3E%5BX%5D%2B9E%5B1%5D%3D0.25E%5BX%5E2%5D%2B3%5Cmu_X%2B9)
Recall that the variance is the difference between the first two moments:
![\mathrm{Var}[X]=E[X^2]-E[X]^2\implies E[X^2]={\sigma^2}_X+{\mu_X}^2](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5BX%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2%5Cimplies%20E%5BX%5E2%5D%3D%7B%5Csigma%5E2%7D_X%2B%7B%5Cmu_X%7D%5E2)
![\implies E[Y^2]=0.25({\sigma^2}_X+{\mu_X}^2)+3\mu_X+9\approx19.22](https://tex.z-dn.net/?f=%5Cimplies%20E%5BY%5E2%5D%3D0.25%28%7B%5Csigma%5E2%7D_X%2B%7B%5Cmu_X%7D%5E2%29%2B3%5Cmu_X%2B9%5Capprox19.22)
![\implies\mathrm{Var}[Y]=E[Y^2]-E[Y]^2=\boxed{0.3}](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%7BVar%7D%5BY%5D%3DE%5BY%5E2%5D-E%5BY%5D%5E2%3D%5Cboxed%7B0.3%7D)
