puer Aegyptius, qui sollicitudinem mean senserit, me ad casam proximam duxit. An Egyptian boy, who had sensed my anxiousness, led me to the closest small house. The boy realized why Quintus was anxious and decided to move him away from the crowd. "domine, in hac casa habitat faber, qui Barbillum bene novit. necesse est nobis casam intrare et periculum vitare." Master, in this house lives a smith, who knows Barbillus well. We need to enter the small house and evade the danger.

The diagram shows a quadrilateral ABCD such that

AB=10 cm, AD=5 cm, BC=13 cm, BCD=$45^{\circ}$ and BAD=$30^{\circ}$.

a. Find the exact area of the triangle ABD.

b. Show that $\mathrm{BD}=5 \sqrt{5-2 \sqrt{3}}$.

c. Find the exact value of sin CDB.

d. Hence, explain why there are two possible values for the size of the angle CBD, stating the relationship between the two possible values.

Trapezoid $ABCD$ is shown. A diagonal is drawn from point $B$ to point $D$. Sides $BC$ and $AD$ are parallel. Sides $BA$ and $CD$ are congruent. Angle $CBD$ is $24$ degrees and angle $BAD$ is $116$ degrees. What is the measure of angle $ABD$ in trapezoid $ABCD$?

A) $24\degree$; B) $40\degree$; C) $64\degree$; D) $92\degree$.

Use the following matrices. $$ A=\left[\begin{array}13&1\\-1&0\end{array}\right] $$ $$ B=\left[\begin{array}14&2\end{array}\right] $$ $$ C=\left[\begin{array}10\\-2\end{array}\right] $$ $$ D=\left[\begin{array}15&0\\1&2-\end{array}\right] $$ For each part, either do the calculation or explain why it does not make sense. a. $3D$ b. $A+B$ c. $A-D$ d. $B\cdot C$ e. $A\cdot C$ f. $AB$ g. $AC$ h. $AD$

Let

$$A = \left[ \begin{array} { r r r } { 1 } & { - 1 } & { 2 } \\ { 3 } & { 1 } & { 4 } \end{array} \right] , B = \left[ \begin{array} { r r r } { 2 } & { - 1 } & { 3 } \\ { 5 } & { 1 } & { 2 } \\ { 4 } & { 6 } & { - 2 } \end{array} \right], \\C = \left[ \begin{array} { r } { 1 } \\ { - 1 } \\ { 2 } \end{array} \right] , D = \left[ \begin{array} { l l l } { 2 } & { - 2 } & { 3 } \end{array} \right], \\E = \left[ \begin{array} { c c } { 2 - i } & { 1 + i } \\ { - i } & { 2 + 4 i } \end{array} \right] , F = \left[ \begin{array} { c c } { i } & { 1 - 3 i } \\ { 0 } & { 4 + i } \end{array} \right].$$

In these problems, i denote

$$\sqrt { - 1 }.$$

For each item, decide whether or not the given expression is defined. For each item that is defined, compute the result. (a) AC, (b) DC, (c) DB, (d) AD, (e) EF

$$( { \mathrm f } ) A ^ { T } B, ( \mathrm { g } ) C ^ { 2 } , ( { h } ) E ^ { 2 },\text { (i) } A D ^ { T },\text { (j) } E ^ { T } A$$

Consider the generating functions

$$\begin{array}{ll} A=1+x+x^2, & B=1+2 x+4 x^4+x^5, \\ C=1-x^2+x^4, & D=1+x+x^2+x^3+\cdots, \\ E=1+x^3+x^6+x^9+\cdots, & F=1-x+x^2-x^3+x^4-\cdots . \end{array}$$

In exercise given below, write each indicated expression in the form

$$a_0+a_1 x+a_2 x^2+a_3 x^3+\cdots .$$

If the expression is a polynomial, then compute it completely; otherwise compute it through the $x^7$ term.

AD

The table refers to a survey of senior high school students in Dayton, Ohio. It cross-tabulates whether a student had ever smoked cigarettes and whether a student h ad ever drunk alcohol and shows counts and the conditional distributions of alcohol use.

	Alcohol
Cigarettes	Yes	No	Total
Yes	1449 (97%)	46 (3%)	1495 (100%)
No	500 (64%)	281 (36%)	781 (100%)

Find the odds of having used alcohol for users and non- users of cigarettes. Interpret each. Then, describe the strength of association, using the odds ratio.

You are in the market for a new couch and have found two advertisements for the kind of couch you want to buy. One seller notes in her ad that she is selling because she is moving to a smaller apartment, and the couch won't fit in the new space. The other seller says he is selling because the couch doesn't match his other furniture. Which seller do you expect to buy from? Why? (Hint: Think who would be the more motivated seller.)

$$\begin{aligned} &\text { Match the following word elements with the definitions. }\\ &\begin{array}{llll} \text { Combining Forms } & \text { } & \text { Suffixes } & \text { Prefixes } \\ \text { caud/o } & \text { kary/o } & \text {-genesis } & \text { ad- } \\ \text { dist/o } & \text { leuk/o } & \text {-gnosis } & \text { infra- } \\ \text { dors/o } & \text { morph/o } & \text {-graphy } & \text { ultra- } \\ \text { eti/o } & \text { poli/o } & & \\ \text { hist/o } & \text { somat/o } & & \\ \text { idi/o } & \text { viscer/o } & & \\ \text { jaund/o } & \text { xer/o } & & \end{array} \end{aligned}$$

tissue _________.

Diogenes statim ad armarium contendit. in armadio erant quinque fustes, quod Diogenes extraxit et nobis tradidit. Diogenes immediately hurried to the closet. In the closet there were five clubs, which Diogenes drew out and gave to us. Diogenes had prepared for an eventual attack by stacking his closet with weapons. To be prepared for battle means to expect a battle. The situation could not have been good and peaceful in their part of town. Diogenes was expecting an attack, sooner or later.

Consider the diagram and the derivation below.

Given: In $\triangle ABC$, $\overline{AD} \perp \overline{BC}$

Derive a formula for the area of $\triangle ABC$ using angle $C$.

it is given that in $\triangle ABC$, $\overline{AB} \perp \overline{BC}$. Using the definition of sine with angle $C$ in $\triangle ACD$ results in $\sin{C}=\frac{h}{b}$. Using the multiplication property of equality to isolate $h$, the equation becomes $b\sin(C)=h$.

Knowing that the formula for the area of a triangle is $A=\frac{1}{2}bh$ and using the side lengths as shown in the diagram, which expression represents the area of $\triangle ABC$?

$\bullet$ $\frac{1}{2}b\sin(C)$

$\bullet$ $\frac{1}{2}ab\sin(C)$

$\bullet$ $\frac{1}{2}cb\sin(C)$

$\bullet$ $\frac{1}{2}hb\sin(C)$

Correlative conjunctions are paired conjunctions that connect two words or groups of words of equal significance . Correlative conjunctions\ include either... or; both...and; neither... nor; whether... or; and not only...but also.
Example : For he was lord and king of all the earth, Before poor Eve h ad either life or breath,... Rewrite below item, using correlative conjunctions to combine the sentence.
Lanier believed that men had to take responsibility for sin. She believed that women also had to take responsibility.

A steel bar AD has a cross-sectional area of $0.40 \text { in. }^{2}$ and is loaded by forces $P_{1}=2700\ \mathrm{lb}$, $P_{2}=1800\ \mathrm{lb}$, and $P_{3}=1300\ \mathrm{lb}$. The lengths of the segments of the bar are a=60 in., b=24 in., and c=36 in. (a) Assuming that the modulus of elasticity $E=$ $30 \times 10^{6}$ psi, calculate the change in length $\delta$ of the bar. Does the bar elongate or shorten? (b) By what amount P should the load $P_{3}$ be increased so that the bar does not change in length when the three loads are applied?

Calculate the quantities required in the problem, where

$$\begin{aligned} &\mathbf{A}=\left[\begin{array}{rrr} {-1} & {0} & {3} \\ {2} & {1} & {2} \\ {-1} & {0} & {1} \end{array}\right], \quad \mathbf{B}=\left[\begin{array}{lll} {1} & {3} & {0} \\ {0} & {1} & {0} \\ {0} & {0} & {1} \end{array}\right]\\ &\mathbf{C}=\left[\begin{array}{ll} {1} & {0} \\ {2} & {1} \\ {1} & {3} \end{array}\right], \quad \text { and } \quad \mathbf{D}=\left[\begin{array}{rrr} {3} & {-1} & {0} \\ {2} & {1} & {2} \end{array}\right] \end{aligned}$$

or explain why they are undefined. AD