Answer:
D.]
Step-by-step explanation:
We will find the standard deviation and variance:
Variance= E
-[![[E(x)]^{2}](https://tex.z-dn.net/?f=%5BE%28x%29%5D%5E%7B2%7D)
E[x] = 3.462
E[{x}^2]= 31.86
Var(x)= 31.86-(3.462)^2 = 28.4
Standard deviation = 
= 
= 5.833 = 6(aproximately)
Therefore, the chances of winning are equal in each lane.
Rational exponents work as follows:
![a^{\frac{b}{c}}=\sqrt[c]{a^b}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Csqrt%5Bc%5D%7Ba%5Eb%7D)
So, in your case, we have
![(x^3y^5)^{\frac{4}{3}} = \sqrt[3]{(x^3y^5)^4}=\sqrt[3]{x^{12}y^{20}}=\sqrt[3]{x^{12}y^{18}\cdot y^2}}=x^4y^6\sqrt[3]{y^2}](https://tex.z-dn.net/?f=%28x%5E3y%5E5%29%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%28x%5E3y%5E5%29%5E4%7D%3D%5Csqrt%5B3%5D%7Bx%5E%7B12%7Dy%5E%7B20%7D%7D%3D%5Csqrt%5B3%5D%7Bx%5E%7B12%7Dy%5E%7B18%7D%5Ccdot%20y%5E2%7D%7D%3Dx%5E4y%5E6%5Csqrt%5B3%5D%7By%5E2%7D)
Your equation to solve is 108-(12×4).
This is 108-48 which is 60.
There were 60 cords at the hotel before the order. Since you need to find the boxes you do 60/12 which is 5.
There were 5 boxes.
10 different pairs. Since there are 5 different brands you simply add 4+3+2+1 to get 10.
