Answer:
No, with the guides in between the two ladders, it is not possible for the lower ends of the ladder to be up to 12 feet apart
Step-by-step explanation:
The given parameters are;
The length of two sides of the step ladder = 12 feet
The maximum value allowable for the included angle between the two 12 feet ladders = 58°
Therefore, the maximum value of the third side facing the included angle is given as follows;
let "a" represent the maximum value of the third side formed by the distance apart of the lower end of the ladder, by cosine rule, we have;
a² = 12² + 12² - 2 × 12 × 12 × cos(58°) = 135.383251901
∴ a = √(12² + 12² - 2 × 12 × 12 × cos(58°)) ≈ 11.64
The maximum value of the third side formed by the distance apart of the lower end of the ladder = a ≈ 11.64 feet < 12 feet
Therefore, it is not possible for the lower ends of the ladder to be up to 12 feet apart.
There are 4 possible heights and lengths. 1 and 136, 2 and 68, 4 and 34, 8 and 17 are the ones I came up with. Hope this helped.
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
2
y-intercept:
(
0
,
0
)
x
y
−
1
2
0
0
Answer:
First row. = -393 74 287
Second row = 471. 162 91
Third row =251 222 - 349
Step-by-step explanation:
For the first row
Cofactor of 12= (-8*15)-(21*13)
= -120-273
= -393
Cofactor of 23 = (11*15)-(7*13)
= 165-91
= 74
Cofactor of -6 = (11*21)-(-7*8)
= 231+56
= 287
For the second row
Cofactor of 11 = (23*15)-(21*-6)
= 345+126
= 471
Cofactor of -8 = (12*15)-(7*-6)
= 120 + 42
= 162
Cofactor of 13 (12*21)-(23*7)
= 252-161
= 91
For third row
Cofactor of 7= (23*13)-(-8*-6)
= 299-48
= 251
Cofactor of 21 = (12*13)-(11*-6)
= 156+66
=222
Cofactor of 15 = (12*-8)-(11*23)
= -96 - 253
=- 349
Calculate the total amount invested by summing up all the values of the investment.
Total = 50,000
Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.
Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%
b) Similarly,
Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605
c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio
d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%
To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.
Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.
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