Samanca Cabinets makes custom wooden cabinets for high-end stereo systems from specialty woods. The company uses a job-order costing system. The capacity of the plant is determined by the capacity of its constraint, which is time on the automated handsaw that makes finely beveled cuts in wood according to the preprogrammed specifications of each cabinet. The handsaw can operate up to 150 hours per month. The estimated total manufacturing overhead at capacity is $11,000 per month. The company bases its predetermined overhead rate on capacity, so its predetermined overhead rate is$74 per hour of bandsaw use. The results of a recent month's operations appear below:

$$\begin{matrix} \text{Sales} & \text{\$ 39.860}\\ \text{Beginning inventories} & \text{\$ 0}\\ \text{Ending inventories} & \text{\$ 0}\\ \text{Direct materials} & \text{\$ 4.820}\\ \text{Direct labor (all variable)} & \text{\$ 9.640}\\ \text{Manufacturing overhead incurred} & \text{\$ 10.870}\\ \text{Selling and administrative expense} & \text{\$ 9.350}\\ \text{Actual hours of bandsaw use} & \text{124}\\ \end{matrix}$$

1. Prepare an income statement following the example in Appendix 4B in which any under-applied overhead is directly recorded on the income statement as an expense. 2. Why is overhead ordinarily underapplied when the predetermined overhead rate is based on capacity?

In a poll, gymnasts were asked, "How many seconds long was your longest handstand on the balance beam?" Use the results below. Find P(6 - 30 seconds).

$$\begin{matrix} \text{Duration (seconds)} & \text{0-2} & \text{3-5} & \text{6-10} & \text{11-20} & \text{21-30} & \text{31-60} & \text{>60} & \text{Total}\\ \text{Number of Respondents} & \text{14} & \text{27} & \text{19} & \text{18} & \text{13} & \text{15} & \text{24} & \text{130}\\ \end{matrix}$$

In Game 3 of the 1970 NBA championship series, the L.A. Lakers were down by two points with three seconds left in the game. The ball was inbounded to Jerry West, whose image is silhouetted in today's NBA logo. He launched and made a miraculous shot from beyond midcourt, a distance of 60 feet, to send the game over time (there was no 3-point line at that time).

Through careful analysis of the game tape, one could determine the height at which Jerry West released the ball, as well as the amount of time that elapsed between the time the ball left his hands and the time the ball reached the basket. This information could then be used to write a rule for the ball's height $h$ in the fort as a function of time in flight $t$ in seconds.

What was the maximum height of the shot, and when did the ball reach that point?

The following chart gives average water usage for various activities for one person for one day.

a. Use the chart to calculate how much water you use each day. b. An average American uses approximately 200 L of water per day and there are approximately 310,000,000 people in the United States. On average approximately how much water is used in the United States per day?

Portable hot packs are available for skiers and people engaged in other outdoor activities in a cold climate. The air-permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. The exothermic reaction that produces the heat (the rusting of iron) is

$$4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s)$$

When the outside plastic envelope is removed, $\mathrm{O}_2$ molecules penetrate the paper, causing the reaction to begin. A typical packet contains $250 \mathrm{~g}$ of iron to warm your hands or feet for up to 4 hours. How much heat (in $\mathrm{kJ}$ ) is produced by this reaction? (Hint: See Appendix 2 for $\Delta H_{\mathrm{f}}$ values.)

In Game 3 of the 1970 NBA championship series, the L.A. Lakers were down by two points with three seconds left in the game. The ball was inbounded to Jerry West, whose image is silhouetted in today's NBA logo. He launched and made a miraculous shot from beyond midcourt, a distance of 60 feet, to send the game over time (there was no 3-point line at that time).

Through careful analysis of the game tape, one could determine the height at which Jerry West released the ball, as well as the amount of time that elapsed between the time the ball left his hands and the time the ball reached the basket. This information could then be used to write a rule for the ball's height $h$ in the fort as a function of time in flight $t$ in seconds.

Write a rule giving $h$ as a function of $t$.

A predicate is the part of a sentence that contains the main verb and states the action or condition of the subject. A compound predicate has two or more verbs or verb phrases that relate to the same subject. In this example from "The Seafarer," the subject is sea. The three verbs in the compound predicate are underlined.
Example:... the sea $\underline{\text{took}}$ me, $\underline{\text{swept}}$ me back / And forth in sorrow and fear and pain, / $\underline{\text{Showed}}$ me suffering in a hundred ships,...
As you can see in the example above, compound predicates can be used to create an effect of movement or drama by "piling up" events.
Identify the verbs or verb phrases in the following compound predicate.
"The soul... knows nothing / Of sweetness or sour, feels no pain, / Bends neither its hands nor its brain..."

Your 70-kg friend always thinks he can dominate you in contests of strength because, even though you are a very athletic gymnast, your inertia is 63 kg. This time, while the gym class watches, he has attached a pulley to the ceiling of the gym, passed a rope over it, and tied one end of the rope around his waist. He hands you the other end of the rope, which is not quite long enough to reach the floor, and bets you that you cannot lift him off the ground by pulling on the rope. You realize that gravitational forces will favor your friend if the two of you are hanging on opposite sides of the pulley, but then you recall your amazing arm strength gained from years of work on gymnastic apparatus.

In each of the following sentences, draw a line through the error in comparison. Then, above it, write the correct form. If the error is a missing word, draw a caret ($_\wedge$) where the word should be inserted and then write the word above the caret.

Examples

1. Of the two of you, she is clearly $\overset{\textit{\color{#c34632}{taller}}}{\sout{\text{tallest}}}$.

2. Rhode Island is smaller than $\overset{\textit{\color{#c34632}{other}}}{{\text{any state\ last}}}$.

Your brother is the more handsome senior I know.

Air molecules stuck inside an inflated balloon are perpetually colliding with the inner surface of the balloon. Each collision provides a little push outward on the balloon. All the many collisions working together is what keeps the balloon inflated. To get a "feel" for what's happening here, add about a tablespoon of tiny beads to a large balloon (pellets, beans, BBs, grains of rice, etc., also work). Inflate the balloon to its full size and tie it shut. Hold the balloon in the palms of both hands and shake rapidly. Can you feel the collisions? As you shake the balloon wildly, the flying beads represent the gaseous phase. How should you move the balloon so that the beads represent the liquid phase? The solid phase?

You and your tean1 are designing a device that can be used to position a small, plastic object in the region between the plates of a parallel-plate capacitor. A small plastic sphere of mass $m=1.20 \times 10^{-2}$ kg carries a charge $q=+0.200 \mu \mathrm{C}$ and hands vertically (along the y direction) from a massless, insulating thread (length l=10.0 cm) between two vertical capacitor plates. When there is no electric field, the object resides at the midpoint between the plates (at x=0). However, when there is a field between plates (in the $\pm x$ direction) the object moves to a new equilibrium position.

To what value should you set the field if you want the object to be located at x=2.10 cm?

Portable hot packs are available for skiers and people engaged in other outdoor activities in a cold climate. The air-permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. The exothermic reaction that produces the heat is a very common one - the rusting of iron:

$$\begin{align*} 4\;\mathrm{Fe}(s)+3\;\mathrm{O_2}(g)&\rightarrow2\;\mathrm{Fe_2O_3}(s) \end{align*}$$

When the outside plastic envelope is removed, $\mathrm{O_2}$ molecules penetrate the paper, causing the reaction to begin. A typical packet contains 250 g of iron to warm your hands or feet for up to 4 hours. How much heat (in kJ) is produced by this reaction? (Hint: See Appendix 2 for $\Delta H_f°$ values.)

A survey was done of men’s and women’s hands to see if the ring finger appeared longer than the index finger or not. Yes means the ring finger is longer, and No means the ring finger appears shorter or the same length as the index finger. The students in this survey were not told the theory that men are more likely to have a longer ring finger than women due to more testosterone.

a. What percentage of the men said Yes?
b. What percentage of the women said Yes?
c. What percentage of the people who said Yes were men?
d. If a large group of $250$ men had the same rate of responses as the men in this sample, how many men of the $250$ would say yes?

Involve a deck of $52$ cards.

A poker hand consists of five cards.

$$\textbf{a.}\hspace{10pt}\text{Find the total number of possible five-card poker hands.}$$

$$\textbf{b.}\hspace{10pt}\text{Find the number of ways in which four aces can be selected.}$$

$$\textbf{c.}\hspace{10pt}\text{Find the number of ways in which one king can be selected.}$$

$$\textbf{d.}\hspace{10pt}\text{Use the Fundamental Counting Principle and your answers from parts (b) and (c) to find the number of ways getting four aces and one king.}$$

$$\textbf{e.}\hspace{10pt}\text{Find the probability of getting a poker hand of four aces and one king.}$$