Determine how many tin atoms are contained in the tetragonal crystal lattice unit cell of $\beta$-tin. How many tin atoms are contained in the cubic crystal lattice unit cell of $\alpha$-tin?

Find the average value of the function over the given interval.

$$f(x)=\tan x ;[0, \pi / 4]$$

The element hydrogen has three isotopes. The most common has $A=1$. A rare form of hydrogen (called deuterium) has $A=2$. An unstable, radioactive form of hydrogen (called tritium) has $A=3$. Draw pictures similar to Figure 38.18 showing the structure of these three isotopes. Show all the electrons, protons, and neutrons of each.

$$A=1$$

$$A=2$$

$$A=3$$

In a nuclear fusion reaction, one deuterium atom combines with one tritium atom to form one helium atom plus a free neutron. In this reaction a huge amount of energy is released. Using Einstein's idea of mass-energy equivalence, what can you conclude about the mass of the final products compared to the mass of the initial fuel?

How to make your own deuterium-depleted water?

The reaction below can be used to produce heavy ammonia, ND$_3$.

$$\text{Li}_3\text{N}+3\text{D}_2\text{O}\rightarrow \text{ND}_3+3\text{LiOD}$$

Calculate how many grams of heavy water, D$_2$O, are required to produce 110.0 mg of ND$_3$ (g). The mass of deuterium, D, is 2.014 g/mol.

Underline any errors in the expression of numbers in the following sentence. Write the correct form in the space provided.

53 of the corporations had operating budgets that exceeded one million dollars. ________________

Which of the following statements about S corporations is most accurate?

a) Any corporation willing to pay the necessary fees and fill out the required paperwork can become an S Corporation.

b) Only large corporations with operations in more than one state can qualify to be classified as S corporations.

c) S Corporations are similar to C corporations, except that the majority of owners are foreign investors.

d) The major attraction of S corporations is that they avoid the problem of double taxation.

For the following sentence, underline any number or word that is expressed inappropriately and write the correct form in the space provided.

Example: The documentation group has prepared $\underline{\text{4 twenty-page}}$ reports. $\underline{\text{four 20-page}}$

On page forty-four of Volume two, you will see that poor employee health costs American corporations about $576,000,000,000 annually. ________________

Coyote Loco, Inc., a distributor of salsa, has the following historical collection pattern for its credit sales.

$\quad\quad$ 70 percent collected in the month of sale.

$\quad\quad$ 15 percent collected in the first month after sale.

$\quad\quad$ 10 percent collected in the second month after sale.

$\quad\quad$ 4 percent collected in the third month after sale.

$\quad\quad$ 1 percent uncollectible.

The sales on account have been budgeted for the last seven months as follows:

$$\begin{array}{lr} \text{June} & \$\hspace{5pt} 49,000\\ \text{July } &60,000\\ \text{August } &70,000\\ \text{September} &80,000\\ \text{October} & 90,000\\ \text{November } &100,000\\ \text{December } &85,000\\ \end{array}$$

Required:

1. Compute the estimated total cash collections during October from credit sales.

2. Compute the estimated total cash collections during the fourth quarter from sales made on account during the fourth quarter.

3. Build a spreadsheet: Construct an Excel spreadsheet to solve both of the preceding requirements. Show how the solution will change if the following information changes: sales in June and July were $50,000 and$65,000, respectively.

Sylvia has a jewelry collection of bracelets, necklaces, and earrings. She has 16 bracelets. The number of earrings is 2 times the number of necklaces. Which expression shows how many pieces of jewelry she has in all? How many necklaces does she have if she has 43 pieces of jewelry in all?

$$\begin{aligned} & 16+2 n+n \\ & 16+2 n+1 \end{aligned}$$

Assume that you are riding on a windowless train on perfectly smooth, straight tracks. Imagine that you have a collection of objects and measuring devices on the train. What experiment could you do to determine whether the train is moving horizontally at a constant velocity or is speeding up?

Let V be a vector space over a field F, and let $S=\left\{\alpha_i \mid i \in I\right\}$ be a nonempty collection of vectors in $V$.

Using Earlier Exercise, define the subspace of $V$ generated by $S$.

Carefully sketch the graph of the following collection of functions on the same coordinate axes

$$f(x)=x, \quad g(x)=x^2, \quad h(x)=x^3, \quad j(x)=x^4$$