80.24796 pesos for $3.90 usd
If you add the standard deviation to the average, it is 14.84. Because Marcus's score was lower than that, he will not receive a certificate.
I think this should be right for the reason and the calculation.
Answer:
a = 1
b = - 1
Explanation:
To know the values of a and b, we need to solve the following equation:
![z=\sqrt[]{2}\lbrack\cos (\frac{-\pi}{4})+i\sin (\frac{-\pi}{4})\rbrack](https://tex.z-dn.net/?f=z%3D%5Csqrt%5B%5D%7B2%7D%5Clbrack%5Ccos%20%28%5Cfrac%7B-%5Cpi%7D%7B4%7D%29%2Bi%5Csin%20%28%5Cfrac%7B-%5Cpi%7D%7B4%7D%29%5Crbrack)
So, replacing cos(-π/4) by √2/2 and sin(-π/4) by -√2/2, we get:
![z=\sqrt[]{2}\cdot(\frac{\sqrt[]{2}}{2}+i\frac{-\sqrt[]{2}}{2})](https://tex.z-dn.net/?f=z%3D%5Csqrt%5B%5D%7B2%7D%5Ccdot%28%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D%2Bi%5Cfrac%7B-%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D%29)
Applying the distributive property:
![\begin{gathered} z=\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}-\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}i \\ z=\frac{2}{2}-\frac{2}{2}i \\ z=1-1i \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20z%3D%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%5Csqrt%5B%5D%7B2%7D%7D%7B2%7Di%20%5C%5C%20z%3D%5Cfrac%7B2%7D%7B2%7D-%5Cfrac%7B2%7D%7B2%7Di%20%5C%5C%20z%3D1-1i%20%5Cend%7Bgathered%7D)
Therefore, we can complete the equation as:
![z=1-1i=a+bi_{}](https://tex.z-dn.net/?f=z%3D1-1i%3Da%2Bbi_%7B%7D)
It means that a = 1 and b = - 1.
I promise that the answer is 1,090.80
220 + 375 + 185 + 129 * 1.2 = 1,090.80