Problem $2$

$\frac{4y+50\text{l}\text{v}\text{e}\text{t}\text{h}\text{e}\text{f}\text{o}\text{l}\text{l}\text{o}\text{w}\text{i}\text{n}\text{g}simultaneous\text{i}\text{n}\text{e}\text{q}\text{u}\text{a}\text{l}\text{i}\text{t}\text{i}\text{e}\text{s}\text{,}\text{a}\text{n}\text{d}\text{w}\text{r}\text{i}\text{t}\text{e}\text{d}\text{o}\text{w}\text{n}\text{t}\text{h}\text{e}\text{r}\text{a}\text{n}\text{g}\text{e}ofx}{{10}^{as}\text{a}\text{f}\text{u}\text{n}\text{c}\text{t}\text{i}\text{o}\text{n}ofy}$

$10x+3y7y+5$

$6y-5x-2x-10$

Problem $3$

Let $M$ be a function of $x$ :

$M(x)=a{x}^2+bx+c$

where $a,b,$ and $c$ are constants. What is the first$-$order derivative of $M$ with respect to $x,$ i$.$e$.\frac{dM}{dx}?$

Problem $4$

Let $M$ be a function of $x$ :

$M(x)=a{x}^2+bx+c$

where $a,b,$ and $c$ are constants. What is the value of $x$ that maximizes the value of $M(x)?$

Problem $5$

A and $B$ are two random variables. Both A and $B$ follow normal distributions as follows:

$1$