Copy the following expressions on your paper and simplify them by combining like terms. Using algebra tiles may be helpful. $\text { a. } 4 x+2+2 x+x^{2}+x$ $\text { b. } 10 x+4-3+8 x+2$ $\text { c. } 4+x^{2}+3 x+2 x^{2}+4$ $\text { d. } x+4+(x-1)+3+2 x$

Explain in words what is meant by normalization of a wave function.

What is the wavelength of the most energetic photon that can be emitted from a muonic atom with Z = 1?

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.

The surface of a rock in a flowing stream will often contain a biofilm. What specific advantages could be conferred on bacteria growing in a biofilm compared with growth within the flowing stream?

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.

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

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

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]

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

Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. $f(x)=x^{3}$; [-1, 3]

Decide whether or not the given set constitutes a vector space. Assume "standard " definitions of the operations. The set of all continuous functions $f$ defined on the interval [0, 1] such that $f(0)=1$

Johanna is planting tomatoes in the school garden this year. Tomato plants come in packs of six. She needs 80 plants in the garden and already has 28. How many packs of plants will she need?

Find an arithmetic progression containing ten primes that begins with 199.