A student has taken 4 regular tests in a science class, scoring 82, 88, 91, and 85. The upcoming final exam is worth exactly twice as much as a regular test. If the student wants to earn a final weighted average of exactly 90 for the class, what score must they earn on the final exam?

\( A =
\begin{bmatrix}
2 & −1 \\
3 & 4 \\
\end{bmatrix}
\ \ \ B =
\begin{bmatrix}
5 \\
−2 \\
\end{bmatrix}
\)

What is the resulting product matrix \(AB\) ?

What is the solution set for the following rational equation?

\(\dfrac{2 }{ x − 4} + \dfrac{3 }{ x + 4} = \dfrac{16} {x^2 − 16}\)

A student committee of 3 people is to be chosen at random from a group of 5 seniors and 4 juniors. What is the probability that the committee will consist of exactly 2 seniors and 1 junior?

In the standard \((x,y)\) coordinate plane, vector \(u\) has components \(\lt3, −4\gt\) and vector \(v\) has components \(\lt−1, 6\gt\). What is the magnitude of the vector \(2u + v\) ?

A circle has a radius of 12 centimeters. What is the area, in square centimeters, of a sector of this circle that is intercepted by a central angle measuring \(\frac{5\pi}{6}\) radians?

Working alone at a constant rate, Pump A can fill a community swimming pool in 6 hours. Pump B, working alone at a constant rate, can fill the same pool in 4 hours. If both pumps are turned on at the exact same time, how many hours will it take them to fill the pool together?

Given \(f(x) = x^2 + 2x + 2, \, f(x + h) = \, ?\)

A geometric designer is drafting a new tile layout using identical regular polygons. If the measure of each interior angle of the regular polygon is exactly 144 degrees, how many sides does the polygon have?

The graph of the function \(g(x)\) is obtained by taking the base quadratic function \(f(x) = x^2\), translating it to the left by 3 units, stretching it vertically by a factor of 2, and finally shifting it down by 5 units. Which of the following equations accurately defines \(g(x)\)?