discrete math functions pigeonhole principle How many numbers in

Finding upper confidence limit without mean and sd
So the question I'm trying to answer looks like this:
We are interested in p, the population proportion of all people who are currently happy with their cell phone plans. In a small study done in 2012, it was found that in a sample of 150 people, there were 90 who were happy with their cell phone plans.
Find the upper confidence limit of an 82% confidence interval for p.
I know the formula is $\mathrm{estimate}\pm \left(\mathrm{criticalvalue}\right)(\mathrm{standard} \mathrm{error})$

How many injective functions are there from a set with 3^10 elements to a set with 2^20 elements

A system for a random amount of time X (in units of months) is given by a density ;

$$\begin{gathered} f\left(x\right) = \frac{1}{4}x{e}^{-\frac{x}{2}} ; x > 0 \\ 0; x\le 0 \end{gathered}$$

(a) Find the moment generating function of X . Hence, compute the variance of X . 

(b) Deduce the expression for the k th moment. 

(c)Obtain the distribution function of X . Hence, compute that the probability that, 7 of such system, at least 4 will function for at least 6 units of months. State the assumptions that you make. 

Determine whether g(x)= x lxl is even or odd or neither function.

Given that the polynomial f(x) has 8 x-intercepts, which of the following most accurately describes the degree of the polynomial f(x)?

Determine the lowest common multiple (LCM) of the following 4𝑥2𝑦2 , 6𝑥𝑦 , 10𝑥𝑦2 
 

A quadratic function has its vertex at the point (−7,2)${\displaystyle (-7,2)}$. The function passes through the point (8,3)${\displaystyle (8,3)}$. When written in vertex form, the function is f(x)=a(x−h)2+k${\displaystyle f\left(x\right)=a{(x-h)}^2+k}$, where: