To answer this item, we let x be the measure of angle Y. If we say supplement, it is understood that when we sum up the measures of the two angles (angle Y and its supplement) the answer should be 180. Therefore the other angle is 180-x. Going back to the condition given in this item, we will be able to generate an equation,
x = 3(180 - x)
The value of x from the equation is 135. Thus, m∠Y is 135°.
Answer:
The correct approach will be "the likelihood of cashing the coupon".
Step-by-step explanation:
- That what's being examined as well as calculated throughout the experiment or observational study seems to be the dependent variable (almost always widely recognized as that of the responding variable). As a consequence of the modifications to something like the independent variable, that's what modifications.
- Whether large you are really at various ages would be an illustration of some kind of dependent variable.
286. you just subtract the two numbers
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
Answer:
P = 7
Step-by-step explanation:
We have 21 total cards and out of those 21 cards, 14 of those are birthday cards. So that means that the amount of cards that are not birthday cards is the number of cards subtracted by the number of birthday cards, also shown as 21 - 14. So 21 - 14 = P, so now we solve what 21 - 14 is which is 7, so that means P = 7.
Let me know if you have any questions.
