Standard deviation is calculated by the square root of the variance. Now, how do we solve the variance? The variance is the <span>average of the </span>squared differences from the Mean. Calculating the variance, we can obtain a standard deviation of <span>3.74. Therefore, the correct answer is option A.</span>
We want to find
![\displaystyle{ \frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20)
, for
![\displaystyle{ y=(x^2+2)^3(x^3+3)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20y%3D%28x%5E2%2B2%29%5E3%28x%5E3%2B3%29%5E2)
.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:
![(fg)'=f'g+g'f](https://tex.z-dn.net/?f=%28fg%29%27%3Df%27g%2Bg%27f)
.
Thus,
![y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=y%27%3D%5B%28x%5E2%2B2%29%5E3%5D%27%5B%28x%5E3%2B3%29%5E2%5D%2B%5B%28x%5E3%2B3%29%5E2%5D%27%5B%28x%5E2%2B2%29%5E3%5D%5C%5C%5C%5C%20%3D3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
Answer: A)
![3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
.
The answer is 1.125 liquid pints
46.8 is 39% of 120. Hope this helped you!