Answer:
$406
Step-by-step explanation:
The amount of interest that Lorenzo's account earns is given by ...
I = Prt
where P is the principal amount ($400), r is the annual rate (1.5%) and t is the number of years (1).
Lorenzo's interest is ...
I = $400·0.015·1 = $6.00
Then the balance in Lorenzo's account at the end of one year is ...
$400 +6 = $406.00
Uh sure what type of cereal?
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
Yes - they have to be similar. Since they are using the same line as the hypotenuse, the ratio of the other two sides are in the same ratio (ie, the slope of the line), the 3 inner angles will be the same. Thus, the triangles will be similar.
Answer: 14
Step-by-step explanation:
Input Data :
Point 1 (
x
A
,
y
A
) = (-4, -8)
Point 2 (
x
B
,
y
B
) = (10, -8)
Objective :
Find the distance between two given points on a line?
Formula :
Distance between two points = √
(x
B
−
x
A
)
2
+
(
y
B
−
y
A
)
2
Solution :
Distance between two points = √
(
10
− −
4
)
2
+
(
−
8
− −
8
)
2
= √
14
^2
+
0
^2
= √
196
+
0
= √
196
= 14
Distance between points (-4, -8) and (10, -8) is 14