What does it mean for a point to be the solution to two equations
1 answer:
Answer:
It means the point will satisfy both the equations.
Step-by-step explanation:
If we consider a point P which is the solution of two equations ax + by + c = 0 and px + qy + r = 0, then it conveys the information that both the equations will be satisfied by this point.
That means and
At the same time if we consider the geometric interpretation then, the graph of the equations ax + by + c = 0 and px + qy + r = 0 will always pass through the common point P. (Answer)
You might be interested in
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