On a separate sheet of paper, write the letter of the key term that best matches each definition below. the additional output produced when one additional unit of input is added

$$\begin{matrix} \text{a. change in quantity supplied} & \text{ g. production function }\\ \text{b. diminishing returns } & \text{h. Law of Supply }\\ \text{c. fixed costs } & \text{ i. total cost }\\ \text{d. marginal analysis } & \text{ j. change in supply }\\ \text{e. marginal product } & \text{k. overhead }\\ \text{f. marginal revenue } & \text{ l. total product}\\ \end{matrix}$$

An electrical circuit contains three resistors connected in parallel. If the resistance of each is $R_{1}, R_{2},$ and $R_{3}$ ohms, respectively, their combined resistance R is given by the formula $\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}.$ Express R as a rational expression. Evaluate R for $R_{1}=5$ ohms, $R_{2}=4$ ohms, and $R_{3}=10$ ohms.

The financial statements of Alliance News, Inc., include the following items:

$$\begin{matrix} & \text{2012} & \text{2011} & \text{2010}\\ \text{Balance sheet: }\\ \text{Cash............................................ } & \text{\$ 39,000 } & \text{\$ 45,000 }\\ \text{Short-term investments................ } & \text{12,000 } & \text{23,000 }\\ \text{Net receivables ............................} & \text{73,000 } & \text{76,000} & \text{60,000 }\\ \text{Inventory.....................................} & \text{91,000 } & \text{77,000 } & \text{62,000}\\ \text{Prepaid expenses.......................... } & \text{11,000 } & \text{5,000 }\\ \text{Total current assets......................} & \text{226,000 } & \text{226,000 }\\ \text{Accounts payable......................... } & \text{70,000 } & \text{55,000 } & \text{50,000}\\ \text{Total current liabilities.................} & \text{133,000} & \text{94,000}\\ \text{Income statement: }\\ \text{Net credit sales............................} & \text{\$491,000 } & \text{\$504,000}\\ \text{Cost of goods sold.......................} & \text{277,000} & {282,000}\\ \end{matrix}$$

Compute the following ratios for 2012 and 2011: a. Current ratio b. Quick (acid test) ratio c. Inventory turnover and days’ inventory outstanding (DIO) d. Accounts receivable turnover e. Days’ sales in average receivables or days’ sales outstanding (DSO) f. Accounts payable turnover and days’ payable outstanding (DPO) g. Cash conversion cycle (in days). (When computing days, round your answer to the nearest whole number.) Evaluate the company’s liquidity and current debt-paying ability for 2012. Has it improved or deteriorated from 2011? As a manager of this company, what would you try to improve next year?

A charged pion $\left(m_{\pi} c^{2}=139.6\ \mathrm{MeV}\right)$ at rest decays into a muon $\left(m_{\mu}=105.7\ \mathrm{MeV}\right)$ and a neutrino (whose mass is very nearly zero). Find the kinetic energy of the muon and the kinetic energy of the neutrino, in MeV $\left(1\ \mathrm{MeV}=1 \times 10^{6}\ \mathrm{eV}\right).$

How are project classifications used in the capital budgeting process?

Find the indicated number of elements by referring to the following table of enrollments in a finite mathematics class: $$ \begin{matrix} \text{} & \text{Freshmen} & \text{Sophomores}\\ \text{Arts & Sciences} & \text{19} & \text{14}\\ \text{Business} & \text{66} & \text{21}\\ \end{matrix} $$ Let the universal set U be the set of all 120 students in the class, A the set of students from the College of Arts & Sciences, B the set of students from the College of Business, F the set of freshmen, and S the set of sophomores. $n(A \cap S)$

Suppose that you wanted to know if the mean reaction time is different for U.S. Census at School seventh graders and New Zealand Census at School seventh graders. A random sample of 10 students from the population of U.S. Census at School seventh graders was selected using the random sampler on the Census at School website. The reaction times (in seconds) for these 10 students were: 0.37 0.38 0.36 0.31 0.46 0.27 0.30 0.34 0.37 0.36 A random sample of 10 students from the population of New Zealand Census at School seventh graders was also selected. The reaction times for these 10 students were: 0.38 0.34 0.36 0.37 0.34 0.34 0.31 0.38 0.33 0.45 Calculate the sample mean and MAD for each of the two samples. You can use the tables below to help organize your work for computing the MADs. United States

$$\begin{matrix} \text{Data Value} & \text{Distance from the Mean}\\ \text{0,37}\\ \text{0,38}\\ \text{0,36}\\ \text{0,31}\\ \text{0,46}\\ \text{0,27}\\ \text{0,30}\\ \text{0,34}\\ \text{0,37}\\ \text{0,36}\\ \end{matrix}$$

New Zealand

$$\begin{matrix} \text{Data Value} & \text{Distance from the Mean}\\ \text{0,38}\\ \text{0,34}\\ \text{0,36}\\ \text{0,37}\\ \text{0,34}\\ \text{0,34}\\ \text{0,31}\\ \text{0,38}\\ \text{0,33}\\ \text{0,45}\\ \end{matrix}$$

Evaluate. $\sqrt[3]{1000}$

Evaluate the cause and effect of cerebral paisy on the structure and function of cells, tissues, organs, and systems.

Solve for x to four decimal places. $\log x=-2.0144$

Reflect back to the fundamental equations of fluid motion dicussed in the early sections of this chapter. Sometimes these equations were expressed in terms of differential equations; for the most part, though, we obtained algebraic relations by integrating the differential equations. However, it is useful to think of the differential forms as relations that govern the change in flow field variables in an infinitesimally small region around a point in the flow, (a) Consider a point in an inviscid flow, where the local density is 1.1 kg/m3. As a fluid element sweeps through this point, it is experiencing a spatial change in velocity of 2 percent per millimeter. Calculate the corresponding spatial change in pressure per millimeter at this point if the velocity at the point is 100 m/s. (b) Repeat the calculation for the case in which the velocity at the point is 1000 m/s. What can you conclude by comparing your results for the low-speed flow in part (a) with the results for the high-speed flow in part (b)?

When ammonium perchlorate decomposes thermally, the products of the reaction are $N_2(g), O_2(g), H_2O(g)$ and $HCl(g)$ Write a balanced equation for the reaction. (Hint: You might find it easier to use fractional coefficients for the products.)

Solve the system using the elimination method.

$$\left. \begin{array} { l } { x + 2 y - z = 3 } \\ { - 2 x - y + z = - 1 } \\ { 6 x - 3 y - z = - 7 } \end{array} \right.$$

Write True if the statement is true. If the statement is false, change the underlined word or words to make the statement true. Immigration increases population size