Answer: 0.0497870 ; 0.87754
Step-by-step explanation:
Given that :
λ = 0.0003
Defining a continuous distribution function :
F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0
a. What proportion of the fans will last at least 10,000 hours?
P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870
b. What proportion of the fans will last at most 7000 hours?
P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)
1 - 0.12245642825 = 0.87754
Use present value equation.
If present value of annuity equals 400,000, then you are indifferent.

where v = 1/(1+r) and A = annual payment = 800,000/20 = 40,000
PV = 400,000
After subbing in the numbers, the equation is:

Therefore at interest rate of about 7.75% you are indifferent.
You just need pythagorean theorem c=a2+b2=72+42≈8.06226
Answer:
2x +5y = 20
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = -
x + 4
Multiply through by 5 to clear the fraction
5y = - 2x + 20 ( add 2x to both sides )
2x + 5y = 20 ← in standard form