Answer:
Step-by-step explanation:
Given is a system of equations as
We have 5 variables and 3 equations
a) coefficient matrix of this system is
1 -4 0 -1 0\\
0 1 0 -2 0\\
0 0 0 1 2\\
We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as
1 -4 -1 0\\
0 1 -2 0\\
0 0 1 2\\
b) Augmented matrix is
1 -4 -1 0\\ 7
0 1 -2 0\\
3
0 0 1 2\\3
c) For row operations to ehelon form
we can do R1+4R2 = R1
We get
1 0 -9 0 \\ 19
0 1 -2 0 \\ 3
0 0 1 2 \\ 3
Now let us do R1 = R1+9R3 and R2 = R2+2R3
1 0 0 0 \\ 46
0 1 0 0 \\ 9
0 0 1 2 \\ 3
d) We find that there are infinite solutions to the system in parametric form, since x4 and x5 are linked with only one equation
e) x1 = 46, x2 = 9, x4+2x5 =3
Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution
Answer:
The expected value for the insurance company is $200
Step-by-step explanation:
In order to calculate the expected value for the insurance company we would have to make the following calculation:
expected value for the insurance company=expected value live+expected value die
expected value live=Net gain*probability of living
expected value live=$300*0.999=$299.70
expected value die=Net gain*probability of die
expected value die=(-$100,000 + $300)*0.001
expected value die=$-99.70
Therefore, expected value for the insurance company=$299.70-$99.70
expected value for the insurance company=$200
The expected value for the insurance company is $200
<span>Identities that come from sums, differences, multiples, and fractions of angles</span>
Answer:
x = 7.535 and y = 0.307
Step-by-step explanation:
Given that,
Two equations,
2x + 3y = 8 ...(1)
x – 5y = 6....(2)
Multiply equation (2) by -2.
-2x + 10y = -12....(3)
Now, adding equations (1) and (2),
2x + 3y -2x + 10y = 8-12
13y = 4
y = 0.307
Put the value of y in equation (2).
x – 5(0.307) = 6
x = 6 + 1.535
x = 7.535
So, the solutions of the given equation are x = 7.535 and y = 0.307.
