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gayaneshka [121]
1 year ago
8

What number makes the expressions equivalent? Enter your answer in the box. 1/2(–1.4m + 0.4) =__m + 0.2A) -1.4B) 1.4C) -0.7D) 0.

7
Mathematics
1 answer:
Snowcat [4.5K]1 year ago
6 0

Answer:

C. -0.7

Explanation:

Given the equation:

\frac{1}{2}(-1.4m+0.4)=\boxed{\square}_{}m+0.2​

First, distribute the bracket on the left-hand side:

\begin{gathered} \frac{1}{2}(-1.4m)+\frac{1}{2}(0.4) \\ =-0.7m+0.2 \end{gathered}

The number that makes the given expressions equivalent is -0.7.

The correct choice is C.

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3 years ago
What is the variance of a portfolio invested 21 percent each in a and b and 58 percent in c?
victus00 [196]
Given the following information:

\begin{tabular}&#10;{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}&#10;\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] &#10;\multicolumn{1}{|p{1.5cm}|}{}\multicolumn{1}{|p{2.6cm}|}{}\multicolumn{1}{|c|}{Stock A}&StockB&Stock C\\[2ex]&#10;\multicolumn{1}{|p{1.5cm}|}{Boom}\multicolumn{1}{|p{2.6cm}|}{0.66}\multicolumn{1}{|p{1.27cm}|}{0.09}&0.03&0.34\\&#10;\end{tabular}
\begin{tabular}&#10;{|p{1.5cm}|p{1.5cm}|p{1.2cm}|p{1.2cm}|p{1.2cm}|}&#10;\multicolumn{1}{|p{1.5cm}|}{Bust}\multicolumn{1}{|p{2.6cm}|}{0.34}\multicolumn{1}{|p{1.27cm}|}{0.23}&0.29&-0.14\\&#10;\end{tabular}

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\%}



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

0.66(0.2224-0.1563)^2+0.34(0.028-0.1563)^2 \\  \\ =0.66(0.0661)^2+0.34(-0.1283)^2=0.66(0.00437)+0.34(0.01646) \\  \\ =0.00288+0.0056=\bold{0.00848}
4 0
3 years ago
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