Billy and Ken, the school's cross-country stars, were each running at cross-country practice. Billy was going to run $\frac{3}{4}$ of the training course, and Ken was going to run $\frac{1}{2}$ of the course. However, during practice it started raining, so they could not finish their runs. Billy had finished $\frac{1}{3}$ of his run, while Ken had finished $\frac{1}{2}$ of his run. Draw a picture to determine which cross-country star ran the farthest.

An electron traveling at $1.2 \times 10^{7} \mathrm{m} / \mathrm{sec}$ combines with an alpha particle to form a singly ionized helium atom. If the electron combined directly into the ground level, find the wavelength of the single photon emitted.

Zac is making cookies, but he does not have enough brown sugar to make a full recipe. The full recipe calls for $\frac{2}{3}$ cup of brown sugar. If Zac has enough brown sugar for $\frac{3}{5}$ of the full recipe, how much brown sugar does he have? a. Represent the $\frac{2}{3}$ cup of brown sugar the recipe calls for with a diagram. b. Represent the portion of brown sugar that Zac has if he makes only $\frac{3}{5}$ of the recipe. c. What mathematical operation should Zac use to find the amount of brown sugar he has? Write an expression and then calculate its value.

Determine whether S is a basis for $P_3$. $S=\left\{1-2 t^{2}+t^{3},-4+t^{2}, 2 t+t^{3}, 5 t\right\}$

Find the following. $\int\left(\frac{9}{x}-3 e^{-0.4 x}\right) d x$

What do microalgae produce that can be chemically converted to biodiesel?

Evaluate each definite integral. $\int_{1}^{64} \frac{\sqrt{z}-2}{\sqrt[3]{z}} d z$

Use a graphing utility to graph the function and find its average rate of change over the interval. Compare this rate with the instantaneous rates of change at the endpoints of the interval. f(t)=4t+3; [-3, 1]

If you had 2 pieces of licorice to share equally among 3 people, how much licorice would each person get? Show your thinking clearly.

Evaluate each double integral. $\int_{0}^{4} \int_{1}^{e^{x}} \frac{x}{y} d y d x$

A rock is dropped from a tower on the Brooklyn Bridge, 276 feet above the East River. Let t represent the time in seconds. (a) Find the position and velocity functions for the rock. (b) Find the average velocity over the interval [0, 2]. (c) Find the instantaneous velocities at t=2 and t=3. (d) How long will it take the rock to hit the water? (e) Find the velocity of the rock when it hits the water.

Add or subtract the following pairs of fractions and mixed numbers. $\text { a. } \frac{5}{6}+\frac{2}{3}$ $\text { b. } \frac{7}{8}-\frac{1}{2}$ $\text { c. } 1 \frac{2}{3}+1 \frac{1}{4}$ $\text { d. } 2 \frac{1}{3}-1 \frac{5}{6}$

Use integration by parts to find the integrals. $\int_{0}^{3} \frac{3-x}{3 e^{x}} d x$

Prove the statements for $m \times n$ matrices A and B and scalars c and d. $\mathbf{A}+\mathbf{B}=\mathbf{B}+\mathbf{A}$