Cates Computing Systems develops and markets commercial software for personal computers and workstations. Three situations involving compensation for possible future absences of Cates’s employees are described below. a. Cates compensates employees at their regular pay rate for time absent for military leave, maternity leave, and jury time. Employees are allowed predetermined absence periods for each type of absence. b. Members of the new product development team are eligible for three months’ paid sabbatical leave every four years. Five members of the team have just completed their fourth year of participation. c. Company policy permits employees four paid sick days each year. Unused sick days can accumulate and can be carried forward to future years. Required: 1. What are the conditions that require accrual of an expense and related liability for employees’ compensation for future absences? 2. For each of the three situations, indicate the circumstances under which accrual of an expense and related liability is warranted.

If $G$ is an abelian group and $H = \left\{ a \in G \left| a ^ { n ( a ) } = e$ for some $n ( a ) > 1$ de- \right. \right. pending on $a \} ,$ prove that $H$ is a subgroup of $G .$

Use the Divergence Theorem to compute the outward flux of the following vector fields across the given surfaces S. F=$\left\langle x ^ { 2 } , y ^ { 2 } , z ^ { 2 } \right\rangle$; S is the cylinder $\left\{ ( x , y , z ) : x ^ { 2 } + y ^ { 2 } = 4,0 \leq z \leq 8 \right\}$.

In the Planting Trees problem earlier in this lesson, you wrote equations that were models of an everyday situation. Models are usually not perfect representations, but they are useful for describing everyday behavior and for making predictions. You predicted when the two trees would be the same height. a. making predictions. You predicted when the two trees would be the same some of the assumptions of this model? b. What are an appropriate domain and range for the models of the growth of Charles's and Amy's trees?

simplify the complex number and write it in standard form. 1/i^3

Construct a truth table to prove each law.

$$p\vee(q\wedge r)\equiv(p\vee q)\wedge(p\vee r), \quad$$

the Distributive Law for $\vee$ over $\wedge$

What are the two types of interference that block memory?

Use a graph and the Location Principle to find the real zeros of the function. Give approximate values to the nearest tenth. If necessary. $P(x)=8 x^{3}-6 x^{2}-2 x+1$

Which of the series converge, and which diverge? Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)

$$\sum _ { n = 1 } ^ { \infty } \left( 1 + \frac { 1 } { n } \right) ^ { n }$$

Give the center and radius of the circle described by the equation and graph each equation.

$$x ^ { 2 } + y ^ { 2 } = 16$$

Which of the following organs is not just a digestive organ? A. stomach B. liver C. small intestine D. large intestine

$$\left. \begin{array} { l } { \text { Let } n \text { be a fixed positive integer greater than } 1 . \text { If } a \bmod n = a ^ { \prime } \text { and } } \\ { b \text { mod } n = b ^ { \prime } , \text { prove that } ( a + b ) \text { mod } n = \left( a ^ { \prime } + b ^ { \prime } \right) \bmod n \text { and } ( a b ) } \\ { \bmod n = \left( a ^ { \prime } b ^ { \prime } \right) \bmod n . }\end{array} \right.$$

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of $9.00 \times 10^{-14}$ atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of $1.00 \mathrm{cm}^{3}$? (b) How many molecules would be present at the same temperature but at 1.00 atm instead?

Evaluate each expression when $a=5$ and $b=-3$. $\quad 3a^{2} b$