Answer:
a) 
b)
c) 
Step-by-step explanation:
We want to simplify

Let :

Square both sides of the equation:

Expand the RHS;

Compare coefficients on both sides:


Solve the equations simultaneously,


Solve the quadratic equation in b²

This implies that:

When b=-3,

Therefore

We want to rewrite as a product:

as a product:
We rearrange to get:

We factor to get:

Factor again to get;

We rewrite as difference of two squares:

We factor the difference of square further to get;

c) We want to compute:

Let the numerator,

Square both sides of the equation;

Compare coefficients in both equations;

and

Put equation (2) in (1) and solve;



When b=-1, a=-2
This means that:

This implies that:

Answer:
0.0110
Step-by-step explanation:
This is a Poisson distribution problem
Poisson distribution formula is given as
P(X = x) = (e^-λ)(λˣ)/x!
where λ = mean = 3 automobiles per minute
x = variable whose probability is required = more than 9 automobiles in a minute
P(X>9) = 1 - P(X ≤ 9)
P(X ≤ x) = Σ (e^-λ)(λˣ)/x! (Summation From 0 to x)
P(X < 9) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)
So, computing this one at a time, and summing it all up
P(X ≤ 9) = 0.99620
P(X>9) = 1 - P(X ≤ 9) = 1 - 0.99890 = 0.0110
Step 1: Subtract 8 from both sides
Step 2: divide both sides by -3
Result: (x-8)/-3=y