If $\theta$ is an acute angle and $\sin\theta = \frac{p - 6}{8 - p}$, then $p$ must satisfy:

$A$ solution of $9 \%$ acid is to be diluted by adding $3 \%$ acid solution to it. The resulting mixture is to be more than $5 \%$ but less than $7 \%$ acid. If there is $460 \text{ L}$ of the $9 \%$ solution,how many litres of $3 \%$ solution will have to be added?

$\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}$ is equal to

Find all pairs of consecutive odd positive integers,both of which are smaller than $10$,such that their sum is more than $11$.

$A$ container is filled with $1120 \text{ litres}$ of a solution containing $40 \%$ acid. How many litres of acid must be added so that the resulting mixture contains more than $40 \%$ but less than $50 \%$ water?

The region represented by the inequations $2x + 3y \leqslant 18$,$x + y \geqslant 10$,$x \geqslant 0$,$y \geqslant 0$ is