Evaluate the linear equation, y=4x-7,at the value x=2. y=?

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
${\displaystyle P\left(x\right)=-12x^2+2136x-41000}$
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?

Use polar coordinates to find the limit. [Hint: Let ${\displaystyle x=r\cos \text{and}y=r\sin }$ , and note that (x, y) (0, 0) implies r 0.] ${\displaystyle \underset{(x,y)\to (0,0)}{lim}\frac{x^2-y^2}{\sqrt{x^2+y^2}}}$

1) A group of preschooters has 63 boys and 27 girl. What is the ratio of boys to all children?

Answer the following questions about an ANOVA analysis involving three samples.
a. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
b. State the null and alternate hypotheses for a three-sample ANOVA analysis.
c. What sample statistics must be known to conduct an ANOVA analysis?
d. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

Prove multivariable function is surjective
The function is ${\displaystyle f:{\mathbb{N}}^2\to \mathbb{N}}$ such that ${\displaystyle f(a,b)=a^b}$

Let $x_1,...,x_{25}>0$ be such that $\sum _{i=1}^{25}{x}_i=4350$ and $\sum _{i=1}^{25}{x}_i^2=757770.25$.
From the first equality alone, we know that at least one of the $x_i$'s must be less than or equal to $\frac{4350}{25}=174$. From the second equality alone, we know that at least one of the $x_i$'s must be less than or equal to $\sqrt{\frac{757770.25}{25}}=174.1$, which is less useful than the first bound. My question is whether we can get a better bound, i.e. to find the least upper bound of $min\{x_1,...,x_{25}\}$, when we use both equalities together. I appreciate any comments or hints.

Solve each problem and simplify it with no variables
$A=\left[\begin{array}{cc}a& -2\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}4& -5\\ b& 7\end{array}\right]$
what is ${\displaystyle A+B^2}$?
What is ${\displaystyle A^2-B}$?