Presented with recordings of a pair of people of the same sex speaking the same phrase, can a listener determine which speaker is taller simply from the sound of their voice? Twenty four young adults at Washington University listened to 100 pairs of speakers, and within each pair were asked to indicate which of the two speakers was the taller. Here are the number correct (out of 100) for each of the 24 participants:

$$\begin{array}{llllllllllll} 65 & 61 & 67 & 59 & 58 & 62 & 56 & 67 & 61 & 67 & 63 & 53 \\ 68 & 49 & 66 & 58 & 69 & 70 & 65 & 56 & 68 & 56 & 58 & 70 \end{array}$$

Researchers believe that the key to correct discrimination is contained in a particular type of sound produced in the lower airways or the lungs, known as subglottal resonances, whose frequency is lower for taller people. Despite the masking of these resonances by other voice sounds, researchers wondered whether the information they contained could still be heard by listeners and used to identify the taller person.

(a) Make two stemplots, with and without splitting the stems. Which plot do you prefer and why?

(b) Describe the shape, center, and variability of the distribution. Are there any outliers?

(c) If the experimental subjects are just guessing which speaker is taller, they should correctly identify the taller person about 50% of the time. Does this data support the researchers, conjecture that there is information in a person's voice to help identify the taller person? Why or why not?

Fatty acids, despite their unpleasant name, are necessary for human health. Two types of essential fatty acids, called omega-3 and omega-6, are not produced by our bodies and so must be obtained from our food. Food oils, widely used in food processing and cooking, are major sources of these compounds. There is some evidence that a healthy diet should have more omega-3 than omega-6. Table below gives the ratio of omega-3 to omega-6 in some common food oils. 25 Values greater than 1 show that an oil has more omega-3 than omega-6.

(a) Make a histogram of these data, using classes bounded by the whole numbers from 0 to 6.

(b) What is the shape of the distribution? How many of the 30 food oils have more omega-3 than omega-6? What does this distribution suggest about the possible health effects of modem food oils?

(c) Table contains entries for several fish oils (cod, herring, menhaden, salmon, sardine). How do these values support the idea that eating fish is healthy?

S.B. is a $17$-year-old man who lost control of his sport utility vehicle and struck a tree. Witnesses reported he was not restrained, and his face hit the windshield on impact. When paramedics arrived, S.B. was responsive but confused, had significant facial swelling, and complained of pain in his right wrist and left forearm. The paramedics initiated cervical spine precautions, strapped him to a backboard, started oxygen at $15 \mathrm{~L} / \mathrm{min}$ via a nonrebreather mask, and started a 16 -gauge IV with $0.9 \%$ normal saline. His vital signs were $120 / 75,125,36$, and $\mathrm{SaO}_2 94 \%$. On arrival to the local emergency department (ED) 5 minutes later, his VS were $110/62$, $110$ regular, $28$ to $32$ and shallow, and $\mathrm{SaO}_2 99 \%$. An additional 16-gauge IV was inserted and the following labs were drawn: CBC, type and crossmatch, complete metabolic panel, PT/ PTT INR, and alcohol level. The trauma physician completed a head-to-toe assessment and found the following:

Physician Note

Obeys commands, responds to voice but not oriented to time or place. Generalized facial edema with full-thickness $2$-cm cheek laceration and bilateral mandibular depressed fractures. Blood behind left tympanic membrane, edema with slight discoloration over left mastoid process. Clear drainage coming from the left nare. Mid to upper chest contusions without crepitus, breath sounds clear. Abdomen slightly firm but not tender. Catheterized for $500$ mL clear yellow urine; negative for blood, glucose, ketones. Positive deformity of right wrist and diffuse tenderness of left lower forearm.

How would you test S.B. for evidence of cerebrospinal fluid (CSF) leakage?

This trial balance of Swisher Co. does not balance.

$$\begin{array}{c} &\textbf{SWISHER CO.}\\ &\textbf{Trial Balance}\\ &\textbf{June 30, 2014}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{Debit}}&\underline{\textbf{Credit}}\\[3pt] \text{Cash}&&\text{\$\hspace{5pt}3,090}\\ \text{Accounts Receivable}&\text{\$\hspace{5pt}3,190}\\ \text{Supplies}&\text{\hspace{18pt}800}\\ \text{Equipment}&\text{\hspace{10pt}3,000}\\ \text{Accounts Payable}&&\text{\hspace{10pt}3,686}\\ \text{Unearned Service Revenue}&\text{\hspace{10pt}1,200}\\ \text{Common Stock}&&\text{\hspace{10pt}9,000}\\ \text{Dividends}&\text{\hspace{18pt}800}\\ \text{Service Revenue}&&\text{\hspace{10pt}3,480}\\ \text{Salaries and Wages Expense}&\text{\hspace{10pt}3,600}\\ \text{Utilities Expense}&\underline{\hspace{18pt}910}&\underline{\text{\hspace{34pt}}}\\ &\underline{\underline{\text{\$\hspace{1pt}13,500}}}&\underline{\underline{\text{\$\hspace{1pt}19,256}}}\\ \end{array}$$

Each of the listed accounts has a normal balance per the general ledger. An examination of the ledger and journal reveals the following errors:

 1. Cash received from a customer on account was debited for $780, and Accounts Receivable was credited for the same amount. The actual collection was for$870.
 2. The purchase of a printer on account for $340 was recorded as a debit to Supplies for$340 and a credit to Accounts Payable for $340.
 3. Services were performed on account for a client for$900. Accounts Receivable was debited for $90 and Service Revenue was credited for$900.
 4. A debit posting to Salaries and Wages Expense of $700 was omitted.
 5. A payment on account for$206 was credited to Cash for $206 and credited to Accounts Payable for$260.
 6. Payment of a $600 cash dividend to Swisher’s stockholders was debited to Salaries and Wages Expense for$600 and credited to Cash for $600.

Instructions

Prepare the correct trial balance. (Hint: All accounts have normal balances.)

In a gas at standard conditions, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about $7 \times 10^{9}$ people)?

Devise an experimental method whereby you can measure only the force required for forging the flash in impression-die forging.

A small object is placed $20 \ \mathrm{cm}$ from the first of a train of three lenses with focal lengths, in order, of $10$, $15$, and $20\ \mathrm{cm}$.. The first two lenses are separated by $30 \ \mathrm{cm}$ and the last two by $20 \ \mathrm{cm}$ . Calculate the final image position relative to the last lens and its linear magnification relative to the original object when (a) all three lenses are positive, (b) the middle lens is negative, (c) the first and last lenses are negative. Provide ray diagrams for each case.

Which of the following molecules is (are) not polar? For each polar molecule, indicate the direction of polarity-that is, which is the negative end and which is the positive end.\

$$\mathrm{BCl}_4$$

For each of the following elementary matrices, describe the corresponding elementary row operation and write the inverse.

$$\text { (a) } E = \left[ \begin{array} { l l l } { 1 } & { 0 } & { 3 } \\ { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

,

$$\text { (b) } E = \left[ \begin{array} { c c c } { 0 } & { 0 } & { 1 } \\ { 0 } & { 1 } & { 0 } \\ { 1 } & { 0 } & { 0 } \end{array} \right]$$

,

$$( \mathrm { c } ) E = \left[ \begin{array} { l l l } { 1 } & { 0 } & { 0 } \\ { 0 } & { \frac { 1 } { 2 } } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

,

$$\text { (d) } E = \left[ \begin{array} { r r r } { 1 } & { 0 } & { 0 } \\ { - 2 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

,

$$\text { (e) } E = \left[ \begin{array} { l l l } { 0 } & { 1 } & { 0 } \\ { 1 } & { 0 } & { 0 } \\ { 0 } & { 0 } & { 1 } \end{array} \right]$$

,

$$( f ) E = \left[ \begin{array} { l l l } { 1 } & { 0 } & { 0 } \\ { 0 } & { 1 } & { 0 } \\ { 0 } & { 0 } & { 5 } \end{array} \right]$$

Let $(S, \leqslant)$ and $\left(S^{\prime} , \leqslant^{\prime}\right)$ be two partially ordered sets. $(S, \leqslant)$ is isomorphic to $\left(S^{\prime}, \leqslant^{\prime}\right)$ if there is a bijection $f: S \rightarrow S^{\prime}$ such that for x, y in S, $x<y \rightarrow f(x)<^{\prime} f(y)$ and $f(x)<^{\prime} f(y) \rightarrow x<y.$ a. Show that there are exactly two nonisomorphic, partially ordered sets with two elements (use diagrams). b. Show that there are exactly five nonisomorphic, partially ordered sets with three elements. c. How many nonisomorphic, partially ordered sets with four elements are there?

Elemental phosphorus occurs as tetratomic molecules, P4. What mass of chlorine gas is needed to react completely with 455 g of phosphorus to form phosphorus pentachloride?

Find the area of parallelogram or rhombus.

Rhombus

$$\begin{aligned} & b=30 \mathrm{~m} \\ & h=15.5 \mathrm{~m} \end{aligned}$$

The trial balance for $\mathrm{K}$ and $\mathrm{J}$ Nursery, Inc., listed the following account balances at December 31 , 2018, the end of its fiscal year: cash, $\$ 16,000$; accounts receivable, $\$ 11,000$; inventories, $\$ 25,000 ;$ equipment (net), $\$ 80,000$; accounts payable, $\$ 14,000$; wages payable, $\$ 9,000$; interest payable, $\$ 1,000$; note payable (due in 18 months), $\$ 30,000 ;$ common stock, $\$ 50,000$. Calculate total current assets and total current liabilities that would appear in the company's year-end balance sheet.

On 21 $3\times 5$ cards, write the integers $-_{10}$ to 10 using one integer per card. Lay the cards on the floor to form a number line. Choose someone from your group to act like the hiker in integer addition and subtraction. Give directions to walk the number line to solve exercises 4 and 11 in Assessment 5-lA. Try other addition and subtraction problems to make sure that the number-line model is understood by everyone in your group and could be used in an elementary classroom.