Given the following information:
![\begin{tabular} {|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|} \multicolumn{1}{|p{1.5cm}|}{State of economy}\multicolumn{1}{|p{2.6cm}|}{Probability of State of economy}\multicolumn{3}{|p{4.8cm}|}{Rate of Return if State Occurs}\\[1ex] \multicolumn{1}{|p{1.5cm}|}{}\multicolumn{1}{|p{2.6cm}|}{}\multicolumn{1}{|c|}{Stock A}&StockB&Stock C\\[2ex] \multicolumn{1}{|p{1.5cm}|}{Boom}\multicolumn{1}{|p{2.6cm}|}{0.66}\multicolumn{1}{|p{1.27cm}|}{0.09}&0.03&0.34\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cp%7B1.5cm%7D%7Cp%7B1.5cm%7D%7Cp%7B1.2cm%7D%7Cp%7B1.2cm%7D%7Cp%7B1.2cm%7D%7C%7D%0A%5Cmulticolumn%7B1%7D%7B%7Cp%7B1.5cm%7D%7C%7D%7BState%20of%20economy%7D%5Cmulticolumn%7B1%7D%7B%7Cp%7B2.6cm%7D%7C%7D%7BProbability%20of%20State%20of%20economy%7D%5Cmulticolumn%7B3%7D%7B%7Cp%7B4.8cm%7D%7C%7D%7BRate%20of%20Return%20if%20State%20Occurs%7D%5C%5C%5B1ex%5D%20%0A%5Cmulticolumn%7B1%7D%7B%7Cp%7B1.5cm%7D%7C%7D%7B%7D%5Cmulticolumn%7B1%7D%7B%7Cp%7B2.6cm%7D%7C%7D%7B%7D%5Cmulticolumn%7B1%7D%7B%7Cc%7C%7D%7BStock%20A%7D%26StockB%26Stock%20C%5C%5C%5B2ex%5D%0A%5Cmulticolumn%7B1%7D%7B%7Cp%7B1.5cm%7D%7C%7D%7BBoom%7D%5Cmulticolumn%7B1%7D%7B%7Cp%7B2.6cm%7D%7C%7D%7B0.66%7D%5Cmulticolumn%7B1%7D%7B%7Cp%7B1.27cm%7D%7C%7D%7B0.09%7D%260.03%260.34%5C%5C%0A%5Cend%7Btabular%7D)

Part A:
The expected return on an equally
weighted portfolio of these three stocks is given by:
![0.66[0.33 (0.09) + 0.33 (0.03) + 0.33(0.34)] \\ +0.34[0.33 (0.23) + 0.33(0.29) +0.33(-0.14)] \\ \\ =0.66(0.0297 + 0.0099 + 0.1122)+0.34(0.0759+0.0957-0.0462) \\ \\ =0.66(0.1518)+0.34(0.1254)=0.1002+0.0426=0.1428=\bold{14.28\%}](https://tex.z-dn.net/?f=0.66%5B0.33%20%280.09%29%20%2B%200.33%20%280.03%29%20%2B%200.33%280.34%29%5D%20%5C%5C%20%2B0.34%5B0.33%20%280.23%29%20%2B%200.33%280.29%29%20%2B0.33%28-0.14%29%5D%20%5C%5C%20%20%5C%5C%20%3D0.66%280.0297%20%2B%200.0099%20%2B%200.1122%29%2B0.34%280.0759%2B0.0957-0.0462%29%20%5C%5C%20%20%5C%5C%20%3D0.66%280.1518%29%2B0.34%280.1254%29%3D0.1002%2B0.0426%3D0.1428%3D%5Cbold%7B14.28%5C%25%7D)
Part B:
Value of a portfolio invested 21
percent each in A and B and 58 percent in C is given by
For boom: 0.21(0.09) + 0.21(0.03) + 0.58(0.34) = 0.0189 + 0.0063 + 0.1972 = 0.2224 or 22.24%.
For bust: = 0.21(0.23) + 0.21(0.29) + 0.58(-0.14) = 0.0483 + 0.0609 - 0.0812 = 0.028 or 2.8%
Expected return = 0.66(0.2224) + 0.34(0.028) = 0.1468 + 0.00952 = 0.1563 or 15.63%
The variance is given by
given the following sets.
A = {0, 1, 2, 3}
B = {a, b, c, d}
C = {0, a, 2, b}
Find B C.
Answer:
I found it! It's over here!!
Now what do I do with it?
All the numbers in this range can be written as

with

and

. Construct a table like so (see attached; apparently the environment for constructing tables isn't supported on this site...)
so that each entry in the table corresponds to the sum of the tens digit (row) and the ones digit (column). Now, you want to find the numbers whose digits add to perfect squares, which occurs when the sum of the digits is either of 1, 4, 9, or 16. You'll notice that this happens along some diagonals.
For each number that occupies an entire diagonal in the table, it's easy to see that that number

shows up

times in the table, so there is one instance of 1, four of 4, and nine of 9. Meanwhile, 16 shows up only twice due to the constraints of the table.
So there are 16 instances of two digit numbers between 10 and 92 whose digits add to perfect squares.
Answer:
http://www.cssdrive.com/
Step-by-step explanation: