Mathematics Mock Test - 11

Maximize $Z=30x-18y$ subject to $3x+4y\le 60$ and $5x-3y\le 20$ ($x,y\ge 0$). In the feasible region, the maximum value occurs at:

Find the area between the curves $y=16x^2$ and $y=9$.

A study investigates if the average sunlight in February was greater than the annual average of $5$ units/m${}^2$. What is the null hypothesis ($H_0$) for this problem?

If $A=\left[\begin{array}{cc}6& -3\\ 4& -2\end{array}\right]$ and $B=\left[\begin{array}{cc}2& y\\ x& 7\end{array}\right]$, such that $AB=O$ (Zero matrix), find the values of $x$ and $y$.

To maximize profit, what condition must be met regarding Marginal Cost (MC) and Marginal Revenue (MR)?