Answer:

Step-by-step explanation:
we know that

Remember the identity

step 1
Find the value of 
we have that
The angle alpha lie on the III Quadrant
so
The values of sine and cosine are negative

Find the value of sine

substitute




step 2
Find the value of 
we have that
The angle beta lie on the IV Quadrant
so
The value of the cosine is positive and the value of the sine is negative

Find the value of cosine

substitute




step 3
Find cos (α + β)

we have




substitute



Remark
You could convert base two to base 10 and then convert base 10 to base 8. That's the long way. The procedure below is the short way.
Step One
Write the base 2 number in groups of 3 starting from the right and going left
11 100 111
Step Two
Convert the base 2 numbers in groups of 3 to base 8. The largest result will be a 7
11 = 2*1 + 1 = 2 + 1 = 3
100 = 1*2^2 = 4
111 = 1*2^2 + 1*2 + 1 = 7
Step Three
Read the answer going down.
347 is the answer
Answer
347(8) = C
Use the rules of logarithms and the rules of exponents.
... ln(ab) = ln(a) + ln(b)
... e^ln(a) = a
... (a^b)·(a^c) = a^(b+c)
_____
1) Use the second rule and take the antilog.
... e^ln(x) = x = e^(5.6 + ln(7.5))
... x = (e^5.6)·(e^ln(7.5)) . . . . . . use the rule of exponents
... x = 7.5·e^5.6 . . . . . . . . . . . . use the second rule of logarithms
... x ≈ 2028.2 . . . . . . . . . . . . . use your calculator (could do this after the 1st step)
2) Similar to the previous problem, except base-10 logs are involved.
... x = 10^(5.6 -log(7.5)) . . . . . take the antilog. Could evaluate now.
... = (1/7.5)·10^5.6 . . . . . . . . . . of course, 10^(-log(7.5)) = 7.5^-1 = 1/7.5
... x ≈ 53,080.96
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
A. If the center plans to feed 700 people in 4 hours, then in order to find the average number of people the center is planning to feed each hour is 700/4 which is equal 175. So, the center is planning to feed 175 people per hour.
B. If during the first hour and a half, the center fed 270 people, find the remaining people to feed left: 700 - 270 = 430 people left to feed.
Please mark as brainliest