Answer:
a) Var[z] = 1600
D[z] = 40
b) Var[z] = 2304
D[z] = 48
c) Var[z] = 80
D[z] = 8.94
d) Var[z] = 80
D[z] = 8.94
e) Var[z] = 320
D[z] = 17.88
Step-by-step explanation:
In general
V([x+y] = V[x] + V[y] +2Cov[xy]
how in this problem Cov[XY] = 0, then
V[x+y] = V[x] + V[y]
Also we must use this properti of the variance
V[ax+b] =
V[x]
and remember that
standard desviation = ![\sqrt{Var[x]}](https://tex.z-dn.net/?f=%5Csqrt%7BVar%5Bx%5D%7D)
a) z = 35-10x
Var[z] =
Var[x] = 100*16 = 1600
D[z] =
= 40
b) z = 12x -5
Var[z] =
Var[x] = 144*16 = 2304
D[z] =
= 48
c) z = x + y
Var[z] = Var[x+y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] =
= 8.94
d) z = x - y
Var[z] = Var[x-y] = Var[x] + Var[y] = 16 + 64 = 80
D[z] =
= 8.94
e) z = -2x + 2y
Var[z] = 4Var[x] + 4Var[y] = 4*16 + 4*64 = 320
D[z] =
= 17.88
(12z^2 + 25z + 12)/(3z^2 - 2z - 8)
You have to factor it. You know how to factor it right?
(12z^2 + 16z + 9z + 12)/(3z^2 - 6z + 4z - 8)
(4z(3z + 4) + 3(3z + 4))/(3z(z - 2) + 4(z - 2))
((4z + 3)(3z + 4))/((3z + 4)(z - 2))
(4z + 3)/(z - 2)
Sum/5 = 90
so Sum = 450 which should be divided by 6
450/6 = 75 as the real average.
Answer:

Step-by-step explanation:
Given: 
To choose: the correct option
Solution:
Power refers to a number of times, a number is multiplied by itself. Another name for power is exponent.
As per rule of exponents, 
Here,

Therefore,
![(-32)^{(\frac{3}{5}) }=[(-2)^5]^{(\frac{3}{5}) }=(-2)^{5(\frac{3}{5}) }](https://tex.z-dn.net/?f=%28-32%29%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%5B%28-2%29%5E5%5D%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E%7B5%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D)
Here, 
So,
![(-32)^{(\frac{3}{5}) }=[(-2)^5]^{(\frac{3}{5}) }=(-2)^{5(\frac{3}{5}) }=(-2)^3=-8](https://tex.z-dn.net/?f=%28-32%29%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%5B%28-2%29%5E5%5D%5E%7B%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E%7B5%28%5Cfrac%7B3%7D%7B5%7D%29%20%7D%3D%28-2%29%5E3%3D-8)