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 $\triangle ABC$?

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

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

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

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

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

K.B. is a 65 -year-old man admitted to the hospital after a 5-day episode of "the flu" with symptoms of dyspnea on exertion, palpitations, chest pain, insomnia, and fatigue. K.B. was diagnosed with Graves'disease 6 months ago and placed on methimazole (Tapazole) $15 \mathrm{mg} /$ day. His other past medical history includes heart failure and hypertension requiring antihypertensive medications; however, he says that he has not been taking these medications on a regular basis. Vital signs (VS) are 150/90, 124 irregular, $20,100.2^{\circ} \mathrm{F}$ (37.9 $\left.9^{\circ} \mathrm{C}\right)$. Admission assessment findings are height $5 \mathrm{ft}, 8$ in $(173 \mathrm{~cm})$; weight $132 \mathrm{lb}(60 \mathrm{~kg})$; appears anxious and restless; loud heart sounds; 1+ pitting edema noted in bilateral lower extremities; diminished breath sounds with fine crackles in the posterior bases. K.B. begins to cry when he tells you he recently lost his wife; you notice someone has punched several more holes in his belt so he could tighten it.

Laboratory Test Results:

$$\begin{array}{ll}\text { Hemoglobin (Hgb) } & 11.8 \mathrm{~g} / \mathrm{dL}(118 \mathrm{~g} / \mathrm{L}) \\ \text { Hematocrit (Hct) } & 36 \% \\ \text { Erythrocyte sedimentation rate (ESR) } & 48 \mathrm{~mm} / \mathrm{hr} \\ \text { Sodium } & 141 \mathrm{mEq} / \mathrm{L}(141 \mathrm{mmol} / \mathrm{L}) \\ \text { Potassium } & 4.7 \mathrm{mEq} / \mathrm{L}(4.7 \mathrm{mmol} / \mathrm{L}) \\ \text { Chloride } & 101 \mathrm{mEq} / \mathrm{L}(101 \mathrm{mmol} / \mathrm{L}) \\ \text { Blood urea nitrogen (BUN) } & 33 \mathrm{mg} / \mathrm{dL}(11.78 \mathrm{mmol} / \mathrm{L}) \\ \text { Creatinine } & 1.9 \mathrm{mg} / \mathrm{dL}(168 \mathrm{mcmol} / \mathrm{L}) \\ \text { Free thyroxine }\left(\mathrm{T}_{+}\right) & 14.0 \mathrm{ng} / \mathrm{dL}(180 \mathrm{pmol} / \mathrm{L}) \\ \text { Triiodothyronine }\left(\mathrm{T}_3\right) & 230 \mathrm{ng} / \mathrm{dL}(353 \mathrm{nmol} / \mathrm{L})\end{array}$$

Physician's Orders:

Propranolol (Inderal) $20 \mathrm{mg}$ PO q6hr Dexamethasone $10 \mathrm{mg}$ IV q $6 \mathrm{hr}$ Methimazole (Tapazole) $15 \mathrm{mg} /$ day twice daily Verapamil (Calan SR) $120 \mathrm{mg} /$ day PO Furosemide $80 \mathrm{mg}$ IV push now, then $40 \mathrm{mg} /$ day IV push Diet as tolerated Stat ECG and echocardiogram Up ad lib IV of D5W at $125 \mathrm{~mL} / \mathrm{hr}$ Daily weights with intake and output (I&0)

Later in your shift, you note that K.B. is extremely restless and disoriented to person, place, and time. VS are 174/82, 180 and irregular, 32 and labored, $104^{\circ} \mathrm{F}\left(40^{\circ} \mathrm{C}\right)$. His ECG shows atrial fibrillation. What actions do you need to take first?

A. Look at the picture below of Universidad Troyana. Based on the picture, circle the activities in the bank that people do there.

$$\begin{array}{|llll|} \hline \text { leer } & \text { estudiar } & \text { repetir } & \text { dormir } \\ \text { bailar } & \text { almorzar } & \text { pedir } & \text { poder } \\ \text { jugar } & \text { esquiar } & \text { servir } & \text { cocinar } \\ \hline \end{array}$$

B. Now, using the verbs above, complete the ad below that some students are writing to attract people to the Universidad Troyana. ¡La Universidad Troyana es la mejor! Aquí, nosotros... $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____. Para aprender más sobre nuestra universidad, lee lo que dice una de nuestras estudiantes: "¡Hola! Yo soy Catalina, una estudiante de primer año aquí en la Universidad Troyana. Me encanta la vida aquí. Todos los días yo.... $\cdot$ _____ $\cdot$ _____ $\cdot$ _____ $\cdot$ _____. Realmente es la mejor universidad."

Newspaper Ad Revenue The table lists U.S. print newspaper advertising revenue (in billions of dollars).

$$\begin{array}{l|c|c|c|c} \text { Year } & 2006 & 2008 & 2010 & 2012 \\ \hline \begin{array}{l} \text { Revenue } \\ \text{ (\$ billions) } \end{array} & 48 & 35 & 22 & 10 \end{array}$$

• (a) Find the point-slope form of the line that passes though $(2006,48)$ and $(2010,22)$. Let $\left(x_1, y_1\right)$ be (2006, 48). (b) Find the point-slope form of the line that passes though $(2008,35)$ and $(2012,10)$. Let $\left(x_1, y_1\right)$ be $(2008,35)$. (c) Interpret the slope of the line from part (b). (d) Use equations from parts (a) and (b) to predict the revenue for 2009 .

K.B. is a 65 -year-old man admitted to the hospital after a 5-day episode of "the flu" with symptoms of dyspnea on exertion, palpitations, chest pain, insomnia, and fatigue. K.B. was diagnosed with Graves'disease 6 months ago and placed on methimazole (Tapazole) $15 \mathrm{mg} /$ day. His other past medical history includes heart failure and hypertension requiring antihypertensive medications; however, he says that he has not been taking these medications on a regular basis. Vital signs (VS) are 150/90, 124 irregular, $20,100.2^{\circ} \mathrm{F}$ (37.9 $\left.9^{\circ} \mathrm{C}\right)$. Admission assessment findings are height $5 \mathrm{ft}, 8$ in $(173 \mathrm{~cm})$; weight $132 \mathrm{lb}(60 \mathrm{~kg})$; appears anxious and restless; loud heart sounds; 1+ pitting edema noted in bilateral lower extremities; diminished breath sounds with fine crackles in the posterior bases. K.B. begins to cry when he tells you he recently lost his wife; you notice someone has punched several more holes in his belt so he could tighten it.

Laboratory Test Results:

$$\begin{array}{ll}\text { Hemoglobin (Hgb) } & 11.8 \mathrm{~g} / \mathrm{dL}(118 \mathrm{~g} / \mathrm{L}) \\ \text { Hematocrit (Hct) } & 36 \% \\ \text { Erythrocyte sedimentation rate (ESR) } & 48 \mathrm{~mm} / \mathrm{hr} \\ \text { Sodium } & 141 \mathrm{mEq} / \mathrm{L}(141 \mathrm{mmol} / \mathrm{L}) \\ \text { Potassium } & 4.7 \mathrm{mEq} / \mathrm{L}(4.7 \mathrm{mmol} / \mathrm{L}) \\ \text { Chloride } & 101 \mathrm{mEq} / \mathrm{L}(101 \mathrm{mmol} / \mathrm{L}) \\ \text { Blood urea nitrogen (BUN) } & 33 \mathrm{mg} / \mathrm{dL}(11.78 \mathrm{mmol} / \mathrm{L}) \\ \text { Creatinine } & 1.9 \mathrm{mg} / \mathrm{dL}(168 \mathrm{mcmol} / \mathrm{L}) \\ \text { Free thyroxine }\left(\mathrm{T}_{+}\right) & 14.0 \mathrm{ng} / \mathrm{dL}(180 \mathrm{pmol} / \mathrm{L}) \\ \text { Triiodothyronine }\left(\mathrm{T}_3\right) & 230 \mathrm{ng} / \mathrm{dL}(353 \mathrm{nmol} / \mathrm{L})\end{array}$$

Physician's Orders:

Propranolol (Inderal) $20 \mathrm{mg}$ PO q6hr Dexamethasone $10 \mathrm{mg}$ IV q $6 \mathrm{hr}$ Methimazole (Tapazole) $15 \mathrm{mg} /$ day twice daily Verapamil (Calan SR) $120 \mathrm{mg} /$ day PO Furosemide $80 \mathrm{mg}$ IV push now, then $40 \mathrm{mg} /$ day IV push Diet as tolerated Stat ECG and echocardiogram Up ad lib IV of D5W at $125 \mathrm{~mL} / \mathrm{hr}$ Daily weights with intake and output (I&0)

Describe 4 priority problems that will guide K.B.'s nursing care.

In $2006,$ for passengers who made early reservations, American Airlines offered lower prices on one-way fares from New York to various cities. Fourteen of the cities are listed in the following table, with the distances from New York to the cities included. Source: American Airlines

$$\begin{array}{|c|c|c|}\hline {\text{City}}& {\text { Distance }(x)} & {\text { Price }(y)} \\ & {\text { (miles) }} & {\text { (dollars) }} \\ \hline \text { Boston } & {206} & {95} \\ \hline \text { Chicago } & {802} & {138} \\ \hline \text { Denver } & {1771} & {228} \\ \hline \text { Kansas City } & {1198} & {209} \\ \hline \text { Little Rock } & {1238} & {269} \\ \hline \text { Los Angeles } & {2786} & {309} \\ \hline {\text { Minneapolis }} & {1207} & {202} \\ \hline \text { Nashville } & {892} & {217} \\\hline {\text { Phoenix }} & {2411} & {109} \\\hline {\text { Portland }} & {2885} & {434}\\\hline {\text { Reno }} & {2705} & {399} \\\hline {\text { St. Louis }} & {948} & {206} \\\hline {\text { San Diego }} & {2762} & {239} \\\hline {\text { Seattle }} & {2815} & {329}\\\hline\end{array}$$

$a.$ Plot the data. Do the data points lie in a linear pattern? $b.$ Find the correlation coefficient. Combining this with your answer to part a, does the cost of a ticket tend to go up with the distance flown? $c.$ Find the equation of the least squares line, and use it to find the approximate marginal cost per mile to fly. $d.$ For similar data in a January $2000)$ New York Times ad, the equation of the least squares line was $Y=113+0.0243 x$.Source: The New York Times. Use this information and your answer to part $b$ to compare the cost of flying American Airlines for these two time periods. $e.$ Identify the outlier in the scatterplot. Discuss the reason why there would be a difference in price to this city.

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.

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.

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

tissue _________.

The total output of loudspeaker systems of the Acrosonic Company at their three production facilities for May and June is given by the matrices A and B, respectively, where

$$A=\begin{array}{l} \text{Location I}\\ \text{Location II}\\ \text{Location III} \end{array}\overset{\normalsize \text{Model}}{\overset{\normalsize \quad \text{A\phantom{ss}}\quad\text{B\phantom{ss}}\quad\text{C\phantom{ss}}\quad\text{D\phantom{ss}}}{\left[\begin{array}{cccc} 320 & 280 & 460 & 280 \\ 480 & 360 & 580 & 0 \\ 540 & 420 & 200 & 880 \end{array}\right]}}$$

$$B=\begin{array}{l} \text{Location I}\\ \text{Location II}\\ \text{Location III} \end{array}\overset{\normalsize \text{Model}}{\overset{\normalsize \quad \text{A\phantom{ss}}\quad\text{B\phantom{ss}}\quad\text{C\phantom{ss}}\quad\text{D\phantom{ss}}}{\left[\begin{array}{cccc} 210 & 180 & 330 & 180 \\ 400 & 300 & 450 & 40 \\ 420 & 280 & 180 & 740 \end{array}\right]}}$$

The unit production costs and selling prices for these loudspeakers are given by matrices $C$ and $D$, respectively, where

$$C = \begin{array}{l} \text{Model A}\\ \text{Model B}\\ \text{Model C}\\ \text{Model D} \end{array} \left[\begin{array}{l} 120 \\ 180 \\ 260 \\ 500 \end{array}\right]$$

and

$$D = \begin{array}{l} \text{Model A}\\ \text{Model B}\\ \text{Model C}\\ \text{Model D} \end{array} \left[\begin{array}{l} 160 \\ 250 \\ 350 \\ 700 \end{array}\right]$$

Compute the following matrices, and explain the meaning of the entries in each matrix.

a. AC

b. AD

c. BC

d. BD

e. (A+B)C

f. (A+B)D

g. A(D-C)

h. B(D-C)

i. (A+B)(D-C)

K.B. is a 65 -year-old man admitted to the hospital after a 5-day episode of "the flu" with symptoms of dyspnea on exertion, palpitations, chest pain, insomnia, and fatigue. K.B. was diagnosed with Graves'disease 6 months ago and placed on methimazole (Tapazole) $15 \mathrm{mg} /$ day. His other past medical history includes heart failure and hypertension requiring antihypertensive medications; however, he says that he has not been taking these medications on a regular basis. Vital signs (VS) are 150/90, 124 irregular, $20,100.2^{\circ} \mathrm{F}$ (37.9 $\left.9^{\circ} \mathrm{C}\right)$. Admission assessment findings are height $5 \mathrm{ft}, 8$ in $(173 \mathrm{~cm})$; weight $132 \mathrm{lb}(60 \mathrm{~kg})$; appears anxious and restless; loud heart sounds; 1+ pitting edema noted in bilateral lower extremities; diminished breath sounds with fine crackles in the posterior bases. K.B. begins to cry when he tells you he recently lost his wife; you notice someone has punched several more holes in his belt so he could tighten it.

Laboratory Test Results:

$$\begin{array}{ll}\text { Hemoglobin (Hgb) } & 11.8 \mathrm{~g} / \mathrm{dL}(118 \mathrm{~g} / \mathrm{L}) \\ \text { Hematocrit (Hct) } & 36 \% \\ \text { Erythrocyte sedimentation rate (ESR) } & 48 \mathrm{~mm} / \mathrm{hr} \\ \text { Sodium } & 141 \mathrm{mEq} / \mathrm{L}(141 \mathrm{mmol} / \mathrm{L}) \\ \text { Potassium } & 4.7 \mathrm{mEq} / \mathrm{L}(4.7 \mathrm{mmol} / \mathrm{L}) \\ \text { Chloride } & 101 \mathrm{mEq} / \mathrm{L}(101 \mathrm{mmol} / \mathrm{L}) \\ \text { Blood urea nitrogen (BUN) } & 33 \mathrm{mg} / \mathrm{dL}(11.78 \mathrm{mmol} / \mathrm{L}) \\ \text { Creatinine } & 1.9 \mathrm{mg} / \mathrm{dL}(168 \mathrm{mcmol} / \mathrm{L}) \\ \text { Free thyroxine }\left(\mathrm{T}_{+}\right) & 14.0 \mathrm{ng} / \mathrm{dL}(180 \mathrm{pmol} / \mathrm{L}) \\ \text { Triiodothyronine }\left(\mathrm{T}_3\right) & 230 \mathrm{ng} / \mathrm{dL}(353 \mathrm{nmol} / \mathrm{L})\end{array}$$

Physician's Orders:

Propranolol (Inderal) $20 \mathrm{mg}$ PO q6hr Dexamethasone $10 \mathrm{mg}$ IV q $6 \mathrm{hr}$ Methimazole (Tapazole) $15 \mathrm{mg} /$ day twice daily Verapamil (Calan SR) $120 \mathrm{mg} /$ day PO Furosemide $80 \mathrm{mg}$ IV push now, then $40 \mathrm{mg} /$ day IV push Diet as tolerated Stat ECG and echocardiogram Up ad lib IV of D5W at $125 \mathrm{~mL} / \mathrm{hr}$ Daily weights with intake and output (I&0)

Later in your shift, you note that K.B. is extremely restless and disoriented to person, place, and time. VS are 174/82, 180 and irregular, 32 and labored, $104^{\circ} \mathrm{F}\left(40^{\circ} \mathrm{C}\right)$. His ECG shows atrial fibrillation. You need to call the resident regarding K.B.'s status. Using SBAR, what will you report?

Consider the system of equations AX = 0 where

$$A=\left[\begin{array}{ll}{a} & {b} \\ {c} & {d}\end{array}\right]$$

is a $2 \times 2$ matrix over the field F. Prove the following. (a) If every entry of A is 0, then every pair $\left(x_{1}, x_{2}\right)$ is a solution of AX = 0. (b) If $a d-b c \neq 0$, the system AX = 0 has only the trivial solution $x_{1}=x_{2}=0$. (c) If ad - bc = 0 and some entry of A is different from 0, then there is a solution $\left(x_{1}^{0}, x_{2}^{0}\right)$ such that $\left(x_{1}, x_{2}\right)$ is a solution if and only if there is a scalar y such that $x_{1}=y x_{1}^{0}, x_{2}=y x_{2}^{0}$.

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

excess, beyond _________.

The matrices A, B, C, D, E, F, G and H are defined as follows.

$$A = \left[ \begin{array} { r r } { 2 } & { - 5 } \\ { 0 } & { 7 } \end{array} \right] \quad B = \left[ \begin{array} { r r r } { 3 } & { \frac { 1 } { 2 } } & { 5 } \\ { 1 } & { - 1 } & { 3 } \end{array} \right] \quad C = \left[ \begin{array} { r r r } { 2 } & { - \frac { 5 } { 2 } } & { 0 } \\ { 0 } & { 2 } & { - 3 } \end{array} \right]$$

$$D = \left[ \begin{array} { l l } { 7 } & { 3 } \end{array} \right] \quad E = \left[ \begin{array} { l } { 1 } \\ { 2 } \\ { 0 } \end{array} \right] \quad F = \left[ \begin{array} { l l l } { 1 } & { 0 } & { 0 } \\ { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

$$G = \left[ \begin{array} { r r r } { 5 } & { - 3 } & { 10 } \\ { 6 } & { 1 } & { 0 } \\ { - 5 } & { 2 } & { 2 } \end{array} \right] \quad H = \left[ \begin{array} { r r } { 3 } & { 1 } \\ { 2 } & { - 1 } \end{array} \right]$$

Carry out the indicated algebraic operation, or explain why it cannot be performed. (a) AD (b) DA