If six people meet, and each person shakes every other person’s hand, how many handshakes are there in all?

Calculate the value of the multiple integral $\iint_D x e^y d A$, where $D$ is bounded by $y=0, y=x^2, x=1$.

Lakes that have been acidified by acid rain can be neutralized by the addition of limestone $\left(\mathrm{CaCO}_3\right)$. How much limestone in kilograms would be required to completely neutralize a $5.2 \times 10^9-\mathrm{L}$ lake containing $5.0 \times 10^{-3} \mathrm{~g}$ of $\mathrm{H}_2 \mathrm{SO}_4$ per liter?

In this exercise, express each angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)

$$-240^{\circ}$$

Reread the chapter Big Idea and the lesson Key Concepts. We: Summarize what you have learned by converting each of the Key Concept questions into a factual answer. Lesson 1 (three Key Concepts) Lesson 2 (two Key Concepts) Lesson 3 (three Key Concepts)

Factor: $8 x+24$ Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

Suppose that there is a monthly meeting at CIA headquarters for all employees. How many handshakes will it take for every employee at the meeting to shake the hand of every other employee at the meeting once?

Complete the table to record your results.

Number of Employees	2	3	4	5	6	7	$n$
Number of Handshakes

Factor a negative number or a GCF with a negative coefficient from the given polynomial. See the discussed example.

$$-3 a^4+9 a^3-3 a^2$$

Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater $\mathrm{B}$ along a horizontal direction. Identify (e) If $A$ has a mass of $0.900$ times that of $B$, and $B$ begins to move away with a speed of $2.00 \mathrm{~m} / \mathrm{s}$, find the speed of $A$.

Suppose you work for a company that does genetic screening. Draw and write a one-page advertisement that explains genetic screening and what it both can and cannot do.

Label the following statements as true or false. In each part, V,W, and $Z$ denote vector spaces with ordered (finite) bases $\alpha, \beta,$ and $\gamma$ respectively; $T : V \rightarrow W$ and $U : W \rightarrow Z$ denote linear transformations; and $A$ and $B$ denote matrices. $\\$ (a)$[\cup T]_${\alpha}$^${\gamma}$=[T]_${\alpha}$^${\beta}$[U]_${\beta}$^${\gamma}$ $(b)$[$\mathrm{T}$(v)]_${\beta}$=[$\mathrm{T}$]_${\alpha}$^${\beta}$[v]_${\alpha} for all$v \in V $(c)$[$\mathrm{U}$(w)]_${\beta}$=[$\mathrm{U}$]_${\alpha}$^${\beta}$[w]_${\beta} for all$w \in $\mathrm{W}$ $(d)$[$\operatorname{lv}$]_${\alpha}$=I $(e)$\left[$\mathrm{T}$^{2}\right]_${\alpha}$^${\beta}$=\left([$\mathrm{T}$]_${\alpha}$^${\beta}$\right)^{2} $(e)$\left[$\mathrm{T}$^{2}\right]_${\alpha}$^${\beta}$=\left([$\mathrm{T}$]_${\alpha}$^${\beta}$\right)^{2} $(f)$A^{2}=I$implies that$A=I$or$A=-I $(g)$$\mathrm{T}$=$\mathrm{L}$_{A}$for some matrix$A .$(h)$A^{2}=O$implies that$A=O,$where$O$denotes the zero matrix.$ $(i)$L_{A+B}=L_{A}+L_{B}$.$ $(j) If$A$is square and$A_{i j}=\delta_{i j}$for all$i$and$j,$then$A=I$ .

Rainwater harvesting is becoming a viable alternative for supplying households and businesses with water. In many countries rainwater harvesters collect the runoff from roofs and store it for later use. Rain collects in gutters that channel the water into a cistern, or rain barrel. To determine the most economical cistern size, you must evaluate the annual house demand for water and the amount of rainfall in your area. For a cistern that is used in a house that is lived in year-round, the volume should be approximately 25 cubic meters. A second cistern that also holds $25 \mathrm{m}^{3}$ of water is in the shape of a rectangular prism. The function $p(x)=\frac{25}{x^{2}+2 x}$ gives the height of the cistern for a rectangular base with length x meters. a. How are the length and width of the rectangular base of the cistern related? Explain your reasoning. b. Describe the features of the graph of p(x). c. What are the domain and range of p(x) in terms of the cistern problem?

You are sitting at a baseball game when a foul ball comes in your direction. You prepare to catch it bare-handed. To catch it safely, should you move your hands toward the ball, hold them still, or move them in the same direction as the moving ball? Explain.

What is the meaning of the term genetic material?