Hi there!
For a system to have infinite solutions, the lines have to be the same. We can begin by rearranging the given equation into the format y = mx + b:
2y - 4x = 6
Move x to the opposite side:
2y = 4x + 6
Divide all terms by 2:
y = 2x + 6
The answer choice that matches this is the first one.
Answer:
1)
the mean rate of return is 17 %
the standard deviation of return is 17.06055
2)
the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325
Step-by-step explanation:
Given the data in the question;
1)
For the portfolio, the mean return and standard deviation are computed as follows;
Mean = Return = 0.65 × 10 + 0.35 × 30
= 6.5 + 10.5
= 17 %
Therefore, the mean rate of return is 17 %
Standard deviation will be;
σp = √( 0.65² × 15² + 0.35² × 40² )
= √( 0.4225 × 225 + 0.1225 × 1600 )
= √( 95.0625 + 196 )
= √291.0625
= 17.06055
Therefore, the standard deviation of return is 17.06055
2)
probability that Marvin's portfolio will make at least 20% over the next 12 months.
P( X > 20 )
we convert to a standard normal variable;
Z = )
Z = 0.17
from z table, p-value is;
p( X < 20 ) = 0.5675
P( X > 20 ) 1 - 0.5675 = 0.4325
Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325