Applying pythagorean theorem:-
Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables 
with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that 
We need to proof that 
by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
![Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2](https://tex.z-dn.net/?f=%20Var%28Z%29_%20%3D%20E%28N%29%20Var%28X%29%20%2B%20Var%20%28N%29%20%5BE%28X%29%5D%5E2%20)
![Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5Bp%281-p%29%5D%20%2B%20Mq%281-q%29%20p%5E2)
And if we take common factor 
we got:
![Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]](https://tex.z-dn.net/?f=%20Var%28Z%29%20%3DMpq%20%5B%281-p%29%20%2B%20%281-q%29p%5D%3D%20Mpq%5B1-p%20%2Bp-pq%5D%3D%20Mpq%5B1-pq%5D)
And as we can see then we can conclude that
<u>Answer:</u>
The correct answer option is B. Construct a line perpendicular to XP through point A.
<u>Step-by-step explanation:</u>
We are given an incomplete figure of construction of a perpendicular line and we are to determine whether which of the given answer options is the next step in the construction.
From the given marks, we can deduce that a perpendicular line to XY is being constructed, passing through P.
So the next step must be to construct a line perpendicular to XP through point A to complete the construction.
Answer:
C
Step-by-step explanation:
We can use process of elimination
D is incorrect because the roots are 3 and -4 and there are no negative roots visible
B is wrong because the roots -3 and -6 are both negative
You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6
For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate
