Answer:
-0.4
B. The answer is the same irrespective of the sample sizes.
Step-by-step explanation:
Given that an article in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively
Let X be the sample average lifetime of 81 Duracell and Y be the sample average lifetime of 81 Eveready Energizer batteries.
Now we have sample mean difference does not depend about the sample sizes.
This is because
E(X-Y) = E(X)-E(Y) for all X and Y
Mean of X-Y = ![4.1-4.5=-0.4](https://tex.z-dn.net/?f=4.1-4.5%3D-0.4)
This does not depend on the specified sample sizes
B. The answer is the same irrespective of the sample sizes.
Answer:
I don't know but 4 could be it
Step-by-step explanation:
Answer:
? ≈ 37°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? =
=
, then
? =
(
) ≈ 37° ( to the nearest degree )
Answer:
a) ![\frac{74}{10025}](https://tex.z-dn.net/?f=%5Cfrac%7B74%7D%7B10025%7D)
b) ![\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
c) ![\frac{-24x^2+32x-2}{(8x^2+x)^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-24x%5E2%2B32x-2%7D%7B%288x%5E2%2Bx%29%5E2%7D)
Step-by-step explanation:
For total cost function
, average cost is given by
i.e., total cost divided by number of units produced.
Marginal average cost function refers to derivative of the average cost function i.e., ![\left ( \frac{c(x)}{x} \right )'](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bc%28x%29%7D%7Bx%7D%20%5Cright%20%29%27)
Given:![c(x)=\frac{3x-2}{8x+1}](https://tex.z-dn.net/?f=c%28x%29%3D%5Cfrac%7B3x-2%7D%7B8x%2B1%7D)
Average cost = ![\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%28x%29%7D%7Bx%7D%3D%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
a)
At x = 50 units,
![\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%2850%29%7D%7B50%7D%3D%5Cfrac%7B150-2%7D%7B50%28400%2B1%29%7D%3D%5Cfrac%7B148%7D%7B50%28401%29%7D%3D%5Cfrac%7B74%7D%7B10025%7D)
b)
Average cost = ![\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%28x%29%7D%7Bx%7D%3D%5Cfrac%7B3x-2%7D%7Bx%288x%2B1%29%7D)
c)
Marginal average cost:
Differentiate average cost with respect to ![x](https://tex.z-dn.net/?f=x)
Take ![f=3x-2\,,\,g=8x^2+x](https://tex.z-dn.net/?f=f%3D3x-2%5C%2C%2C%5C%2Cg%3D8x%5E2%2Bx)
using quotient rule, ![\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bf%7D%7Bg%7D%20%5Cright%20%29%27%3D%5Cfrac%7Bf%27g-fg%27%7D%7Bg%5E2%7D)
Therefore,
![\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cfrac%7Bc%28x%29%7D%7Bx%7D%20%5Cright%20%29%27%3D%5Cleft%20%28%20%5Cfrac%7B3x-2%7D%7B8x%5E2%2Bx%7D%20%5Cright%20%29%27%5C%5C%3D%5Cleft%20%28%20%5Cfrac%7B3%288x%5E2%2Bx%29-%2816x%2B1%29%283x-2%29%7D%7B%288x%5E2%2Bx%29%5E2%7D%20%5Cright%20%29%5C%5C%3D%5Cfrac%7B24x%5E2%2B3x-48x%5E2-3x%2B32x%2B2%7D%7B%288x%5E2%2Bx%29%5E2%7D%5C%5C%3D%5Cfrac%7B-24x%5E2%2B32x-2%7D%7B%288x%5E2%2Bx%29%5E2%7D)
IF
2=5 ;
3=9 ; 3*5 - 3*2
4=48 ; 4*9 + 4*3
5=220 ; 5*48 - 5*4
6=1,350 6*220 + 6*5
7= 9408 7*1350 - 7*6
THEN 8 = 8*9408 + 8*7 = 75320