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The indicated function y_1(x) is a solution of the given differential equation. Use reduction of order or the formula y_2(x) = y_1(x) \int (e^{-\int P(x)dx}/(y_1^2(x))) dx to find a second solution y_2(x). {eq}\displaystyle x^2y'' - 7xy' + 16y = 0;\quad y_1 = x^4 {/eq}
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The table given below provides the data for two inputs in the production of a good. The firm is producing the maximum amount of output and is using only 20 units of labor. Quantity of labor Units of capital Total output 18 16 210 20 18 220 22 ...
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Use the standard enthalpies of formation given below to calculate the standard enthalpy change for the following reaction: {eq}2 \rm{NO}(g) \to \rm N_2(g) + \rm O_2(g) {/eq} {eq}\rm \Delta H_f \degree [NO] = 90.37 \frac {kJ}{mol} , \;\rm \Delta H_f \degree [N_2] = 0 \frac {kJ}{mol}, \;\rm \Delta H_f \degree [O_2] = ...
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The demand for goods and services in the United States is primarily a function of _____. A. domestic production. B. personal consumption and investment. C. government spending. D. trade with other nations.
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A truck costing USD 45,000 with an estimated salvage value of USD 4,500 and an original life of five years is exchanged for a new truck. The cash price of the new truck is USD 57,000, and a trade-in allowance of USD 22,500 is received. The old truck has been depreciated for three years using the straight-line method. T...
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What is the least value of n for which the sum of the series {eq}\Sigma^{\infty}_{k=1} \frac{1}{2k+1} - \frac{1}{2k-1} {/eq} is less than -0.0001?
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Boone Hobbies, a wholesaler, has a sales budget for next month of $600,000. Cost of units sold is expected to be 40 percent of sales. All units are paid for in the month following purchase. The beginning inventory of units is $20,000, and an ending amount of $24,000 is desired. Beginning accounts payable is $152,000. ...
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Based on the following information, determine the firm's maximum rate of growth. Sales $58,000 Cost of goods sold 39,000 Depreciation 8,200 Earnings before interest and taxes 10,800 Interest paid 1,800 Taxes 3,48...
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Given a connected graph $G$, prove that either $G$ or its complement $\bar{G}$ is connected. Is this statement true, and how can we approach proving or disproving it?
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You bought 100 shares of TAN Corporation stock for $28 per share and sold them for $41 per share one year later. You paid a broker $200 to buy the stock and $300 to sell the stock. During the year, you received $600 in dividends from TAN Corporation. What was your return on investment during the year?
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With the AD curve remaining unchanged, which of the following is most likely to occur if the Fed reduces the supply of money? (a) Unemployment will decrease. (b) Unemployment will increase. (c) Unemployment will remain unchanged. (d) The relationship between unemployment and the money supply is unknown. (e) Unempl...
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Which one of the following would result in an adjustment to federal income for tax purposes but would not affect state taxable income? A. dividends received from other U.S. corporations B. A net operating loss on a federal basis C. federal income tax expense D. expenses paid to a state official for travel to a stat...
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For the dual of a dual, the new primal is: a. the original primal b. the original dual c. its dual d. None of the above e. None of the above
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Kong Company manufactures a variety of products. Last year, the company's variable costing net operating income was $109,000, and its inventory decreased by $8,000. What was the absorption costing net operating income last year?
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Determine the change in length of a thin aluminum wire 1000 ft long when it is heated from 75{eq}^\circ {/eq}F to 250{eq}^\circ {/eq}F, assuming the original length is correct at 75{eq}^\circ {/eq}F.
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Fresh Bakery, Inc., experienced a cash shortfall in 2015. In its income statement for the year ended December 31, 2015, the firm reported revenues of $1,178,840, total expenses of $1,300,000, depreciation of $53,000, and a gain on sale of equipment of $27,000. The firm also reported accounts receivable of $138,000 at t...
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Calyon Mining Corporation reported the following information for 2015: 2015 2014 Inventory $114,200 $106,100 Accounts receivable 252,800 244,300 Accounts payable 110,800 106,100 Other current liabilities 20,400 22,100 Net Credit Sales for 2015 were $1,232,400. What is the Cash Coverage Ratio for 2015?
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Use the divergence theorem to find the flux of {eq}F(x,y,z) = (x+e^y)i + (xy + sinz)j - (xz+ \sqrt{xy})k {/eq} across the total surface of the tetrahedron in the first octant formed by coordinate planes and the plane 2x+3y+z=6
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Minstrel Manufacturing uses a job-order costing system. During one month, Minstrel purchased {eq}\$172,000 {/eq} of raw materials on credit; issued materials to the production of {eq}\$197,000 {/eq} of which {eq}\$8,000 {/eq} were indirect. Minstrel incurred a factory payroll of {eq}\$151,000 {/eq} of which {eq}\$2...
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You wish to borrow $2,000,000 to finance the construction of a small multi-family investment property. A lender is willing to give you a 10 year fixed rate fully amortizing loan at 4.5%. What is your total interest expense?
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Use the reversed order of integration and the change of variable u = x + y, v = x − y to evaluate the double integral. {eq}\int_0^2 \int_y^{2y} 2\cos (\frac{x^2 - y^2}{2})dxdy{/eq} {eq}\int_\alpha^\beta \int_g^h 2cos(\frac{u^2 - v^2}{2})dudv{/eq} where, {eq}\alpha{/eq} = {eq}\beta{/eq} = {eq}g(v){/eq} = {eq}h(v)...
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Which of the following organizations has been responsible for setting U.S. accounting standards? a. Accounting Principles Board. b. Committee on Accounting Procedure. c. Financial Accounting Standards Board. d. All of the above.
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I know that any subgroup of an abelian group is abelian. How do I prove that a group of even order must have an odd number of subgroups of order 2?
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At December 31, 2014, and 2015, Gamma Company had 30,000 shares of common stock and 5,000 shares of 5%, $100 par value cumulative preferred stock outstanding. No dividends were declared on either the preferred or common stock in 2014 or 2015. Net income for 2016 was $400,000. In its 2016 financial statements, Gamma's ...
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If you purchase Large Oil Inc. for $36 and the firm pays a $3.00 annual dividend which you expect to grow at 7.5 percent, what is the implied annual rate of return on your investment? Round the answer to two decimal places.
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What is the value of 80 e-0.2t after 3 seconds?
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If a sphere of radius r has a hole of radius a drilled through its center, the volume of the resulting solid can be found by evaluating the integral V = ∫ from -a to a of 2 * π (sqrt(a^2 - y^2)) * (2 * sqrt(r^2 - y^2)) dy = 4 * π * ∫ from -a to a of (sqrt(a^2 - y^2)) * (sqrt(r^2 - y^2)) dy. By applying a suitable chang...
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Hercules Exercise Equipment Co. purchased land by issuing common stock worth $100,000. Which of the following statements is true? a. Debit Stock for $100,000. b. Credit Land for $100,000. c. Debit Land for $100,000. d. Credit Stock for $100,000.
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A company is considering buying a machine that costs $50,000. The machine will reduce the firm's cash operating costs by $10,000 per year. The machine will last 8 years with no salvage value. Use the payback method to determine whether to buy the machine. The maximum desired payback for this type of machine is 5 years....
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Find the solution of the following Non-homogeneous Partial Differential Equation by using the Method of separation of Variables: ${U}_{xx}+4{U}_{t}+4U=0$ for {eq}x\in R,t>0 {/eq} where U(x,0)=e^x for {eq}-\infty<x<\infty {/eq}
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Evaluate the double integral {eq}\iint_D xydA{/eq} where D is bounded by {eq}y=x^2{/eq} and {eq}y=2x{/eq}
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Use {eq}u = xy, v = xy^2 {/eq} to evaluate the integral {eq}\displaystyle \iint_R 10y^2 \; dA {/eq}, where {eq}R {/eq} is the region bounded by the curves {eq}xy = 6, \ xy = 9, \ xy^2 = 6, \ xy^2 = 9 {/eq}.
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How do I solve the recurrence relation $T(n) = T(\sqrt{n}) + 1$?
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Use the Laplace transform to solve the following O.D.E.: y'' - 3y' + 2y = 1 ; y(0) = y'(0) = 0
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What is the present value of $30,000 to be received at the end of each of 20 periods, assuming money is worth 10% compounded interest annually?
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New Coke Corporation (NCC) produced 125,000 cases of a new soft drink and sold 100,000 cases during the year. At the end of the year, there were 15,000 cases left in the warehouse. NCC sold 5,000 cases to customers through the mail and sold 10,000 cases in vending machines. NCC added 18,000 cases to its warehouse durin...
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Assume that 72% of a town's population supports a new fire department. If 35 citizens are randomly chosen, find the probability that no more than 20 support the new fire department.
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Let $A \in \mathbb{R}^{n \times m}$ and $x \in \mathbb{R}^m$. Consider the problem $$\sup_{||y||_2 \leq 1} y^TAx$$ I know that when $A^TAx=0$ the optimal value is $0$. If $A^TAx \neq 0$ then the optimal value is $||A^Tx||_2$. I am interested in what happens when $A^TAx$ is not defined, in particular when $A$ is not a m...
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Which of the following will not help a country to get out of a recession, but may help that country reduce inflation? a. a decrease in government spending b. a reduction in income taxes c. an increase in government spending d. a reduction in transfer payments
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Two converging lenses are placed at a distance of $D=166$ cm apart. The first lens has a focal length of $f_1=4 cm$, and the second lens has a focal length of $f_2=8 cm$. If an object is at a distance of $32 cm$ to the left of the first lens, what is the image distance in centimeters from the second lens? Round your an...
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A manager is considering buying a computer priced at $11,000. He could also lease it for 3 years at $4,000 per year, due at the beginning of each year. The manager's WACC is 14% and his tax rate is 35%. Should he buy or lease the computer? a. Lease. b. Buy. c. The manager's decision will depend on the length of the ...
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For the alternating series {eq}\sum_{n=1}^{\infty}a_n=0.23-\frac{(0.23)^3}{3!}+\frac{(0.23)^5}{5!}-\frac{(0.23)^7}{7!}+...{/eq}, how many terms do you have to compute in order for your partial sum to be within {eq}0.0000001{/eq} from the convergent value of that series?
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A company's 6% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $515.16. The company's federal-plus-state tax rate is 40%. What is the firm's after-tax component cost of debt for purposes of evaluating the WACC?
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Let C be the positively oriented circle x^2+y^2=1. Use Green's theorem to evaluate the line integral ∫_C 13y\,dx+15x\,dy.
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Consider a normal distribution with $\mu = 25$ and $\sigma = 3$. If you select a sample of $n = 12$, what is the probability that the sample mean is less than $23$?
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Which of the following is not a factor that determines equilibrium level of output? A. Marginal propensity to consume. B. Aggregate demand. C. Interest rate. D. Prices.
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A firm has a gross profit margin of 9%, a return on sales of 12%, and a 45% tax rate. This firm's common stock is selling for $36 per share and has a retention ratio of 40%. The appropriate required rate of return for this stock is 14%. Which of the following is the correct statement? a) The firm is reporting earnings...
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A call option has an exercise price of $55 and matures in six months. The current stock price is $55, and the risk-free rate is 4% per year, compounded continuously. What is the price of the call if the standard deviation of the stock is 0 percent per year?
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Find the area of the region cut from the graph of {eq}r=3\cos \theta {/eq} by the line {eq}\theta = \frac {\pi}{3} {/eq}.
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For the price level of $100, the value of the marginal product of the 100th unit of labor is $20, and the wage rate is $25. For the 101st unit of labor, the value of the marginal product is $19, and the wage rate is $25. What is the profit-maximizing choice for the firm? A) hire the 101st unit of labor because the val...
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What is the future value of $2,600 in 19 years at an interest rate of 7 percent per year? a. $7,333.42 b. $7,176.57 c. $7,811.00 d. $6,579.75 e. $7,224.89
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Mark Welsch, financial manager of Division 26 at Covington Manufacturing Corporation, is considering a proposal to purchase a new machine for $6,600,000. The machine has an expected useful life of three years and will have no residual value. The accountant responsible for preparing the proposal has gathered the followi...
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XYZ stock is currently selling for $55.3 per share. The company just paid its first annual dividend of $1.83 a share. The firm plans to increase the dividend by 5.2% per year indefinitely. What is the expected return on XYZ stock?
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You are analyzing the cost of debt for a firm. You know that the firm's 14-year maturity, 8.5 percent coupon bonds are selling at a price of $752.50. The bonds pay interest semiannually. If these bonds are the only debt outstanding for the firm, what is the after-tax cost of debt for this firm if the firm is in the 30...
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Evaluate the work done on a 4-C charge as it is moved from point A to point B along the straight-line path AB in the field of the two point charges shown in the figure. The distance d= 0.5 m. <img src="/question/image/upload/v1/q0kkf7spjlh8opduh5f2" alt="" caption="">
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The following information is available: Beginning work in process 20% Beginning work in process $5,000 Units started 18,000 Units completed 15,000 Units in ending WIP 3,000 Ending work in process 40% Manufacturing costs: Direct Material $20,000 Direct Labor $25,000 Overhead $15,000 If direct labor and overhead are t...
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A yield curve for a government's dollar-denominated bonds in terms of the U.S. dollar interest rate: a. Can be flat if the expected percentage devaluation of the government's currency is equal to the increased level of interest rates in the government's bonds. b. Cannot be flat if the expected percentage devaluation ...
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Bill's Boards has provided the following information regarding the company's single product. Direct materials cost $40 per unit Variable overhead $20 per unit Fixed manufacturing overhead $400,000 Fixed selling & administrative costs $300,000 The regular selling price of the product is $150 per unit and variable s...
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On January 1, of this year, the Utah Company acquired a 5% interest in the Missouri Corporation through the purchase of 100,000 shares of Missouri's common stock for $350,000. During the current year, Missouri paid $40,000 in dividends and reported net income of $100,000. The market price of Missouri's common stock was...
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All of the following statements regarding the inventory method best described as LIFO are true, except: a. It is the inventory method that results in the highest net income in periods of falling prices. b. It is the inventory method that results in the highest net income in periods of rising prices. c. It is the inv...
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Suppose your firm has decided to use a maximum of $42,000 in adverstising. You have to decide between radio and tv ads. Each spot on the radio costs $600 and each spot on television costs $1,500. Radio usage will reach 4,500 people per ad and television usage will reach 1,000,000 people per ad. If your company is seeki...
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Data provided for the pound poundsterling ($) exchange rate: Spot exchange rate $1.9326 2-year forward exchange rate $1.8623 What does this tell you about whether the pound is expected to be trading at a premium or discount in the future?
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Suppose a geyser has a mean time between eruptions of 100 minutes. Let the interval of time between the eruptions be normally distributed with a standard deviation of 16 minutes. What is the probability that a random sample of 16 time intervals between eruptions has a mean of less than 96 minutes?
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Business strategy concerns: A. the actions and approaches crafted by management to produce successful performance in one specific line of business. B. what set of businesses to be in and why. C. selecting a business model to use in pursuing business objectives. D. selecting a set of stretch financial and strategic ...
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The manager of time recorded the following data for the duration of a task. Best = 7.8 minutes Worst = 10.2 minutes Average most likely = 9 minutes Calculate the total time for the task using the PERT method. 7.8 - 9.0 - 10.2 minutes 6.2 - 7.8 - 9.0 minutes 8.4 - 9.6 - 10.2 minutes 6.2 - 8.4 - 10.2 minutes
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Find the error in the reasoning that the 100th partial sum of the Taylor series about 0 for e^x is 100!, given that the remainder term R_n(x) ≤ |(x^(n+1))/(n+1)!| = x^(101)/101! for x in [-2, 2] and n = 100.
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Evaluate the expressions P(X > 7) and P(X < 1), where X is a binomial random variable with n = 12 and p = 0.35. Round your answers to four decimal places. Use the normal approximation with the continuity correction.
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Why does the Cauchy-Schwarz Inequality hold for continuous functions with the inner product defined as $$\langle f, g \rangle=\int_{-1}^1 f(t) g(t)\, \mathrm{d}t?$$ Specifically, how do I prove that the norm is bounded, i.e., $||f||^2 = \langle f, f\rangle \leq \int_{-1}^1 |f(t)|^2\mathrm{d}t$?
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In 2007, Procter & Gamble reported a net income of $7,638 million. Among its expenses were $249 million of interest expenses. If its corporate tax rate was 35% and it paid $613 million in dividends, what was Procter & Gamble's taxable income for 2007? Show the formulas with explanation.
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Should I reduce my price if demand elasticity has increased from -2 to -3, given that I am currently charging $10 for my product? Given that I am currently charging $10 for my product and the demand elasticity has increased from -2 to -3 (i.e., I face more elastic demand), should I reduce my price?
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The HNH Corporation will pay a constant dividend of $10.00 per share, per year, in perpetuity. Assume all investors pay a 15% tax on dividends and that there is no capital gains tax. Suppose the other investments with equivalent risk to HNH stock offer an after-tax return of 12%. What is the price of a share of HNH sto...
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Determine a formula for the linear approximation to the function f (x) = x^2 sin(4x) near the point x = 1.
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Suppose you are running a small company that wants to produce an innovation. The probability of success in the market is 0.65. If it succeeds, you think you can sell the patent for $550,000. If it fails you can sell the patent for $10,000. You are considering whether to pay $200,000 to purchase a market study that will...
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A system has been pre-pressurized to {eq}200\ kPa {/eq} (gage) before it is pressurized again while submerged in seawater to a gage pressure of {eq}1\ MPa {/eq} at a depth {eq}h {/eq}. Determine the total force on the circular observation window, which has a diameter of {eq}0.8\ m {/eq}. Express your answer in term...
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You have just completed a $20,000 feasibility study for a new coffee shop in some retail space you own. You bought the space two years ago for $100,000, but if you sold it today, you would net $115,000 after taxes. Outfitting the space for a coffee shop would require a capital expenditure of $30,000 plus an initial inv...
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A very long insulating cylinder of charge of radius 2.00 cm carries a uniform linear density of 17.0 nC/m . If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads 190 V ? d =....cm
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One-third of the world's smokers drink wine, while half of wine drinkers smoke. Of all people who drink wine and smoke, 1 in 411 are smokers. Suppose that a person is randomly selected from the general population. Given that this person drinks wine, what is the probability that this person is a smoker?
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There are four children, ages 7, 13, 18, and 26, and the taxpayer is the only parent. Which of the following statements is false? a. The 7-year-old child may be claimed as a dependent. b. The 13-year-old child may be claimed as a dependent. c. The 18-year-old child may be claimed as a dependent. d. The 26-year-old ...
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What is the internal rate of return (IRR) for the following annual series of cash flows, given that the PV of this set of cash flows is $15,200? Cash Flow Year 0$-15,200 Year 14,400 Year 28,000 Year 32,000 a) Between 9% and 10% b) Between 14% and 15% c) Between 11% and 12% d) Between 8% and 9%
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Suppose a firm in the current period produces 100 units at $30 each and sells 80 of them at $30 each. They will add 20 more units to their inventory in the next period and will produce 110 units at $31 each in the next period. What is the firm's marginal cost for the current period? a. $270 b. $3,000 c. $3,300 d. $...
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The Baer Company sold bonds with a face value of $100,000 on January 1, 2014 for $105,000. The bonds have a stated annual interest rate of 8% paid semiannually, and were sold to yield 6% compounded semiannually. The proceeds of the bonds would be reported on the income statement for 2014 as: A) Interest Revenue. B) G...
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You own a bond with 10 years until maturity, an annual coupon rate of 7%, and a yield to maturity of 6.25%. You offer to sell the bond for $1,100. The buyer accepts your offer. The internal rate of return (to the nearest 100th of a percent) of the buyer is:
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The coordinates of the point on the graph of {eq}y= \frac{6}{x^2} {/eq} that is closest to the point {eq}(1, 2.5){/eq} is what?
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Calculate the Portfolio's average return given the returns below: Stock A is 10% -30% 40% Stock B is 18% 3% 24% Portfolio Weights are as follows: Stock A is 35% Stock B is 65%
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The Big Bubba Bucket Company manufactures plastic 5-gallon buckets for residential and commercial use. The buckets are produced in batches of 1,000 units. Each batch requires 200 pounds of plastic resin, and each bucket contains 5 pounds of plastic resin. The company's current cost and standard cost data is shown below...
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Babcock company uses a process costing system for its single product. Material A is added at the beginning of the process; in contrast, Material B is added when the units are 75% complete. The firms ending work in process inventory consists of 6,000 units that are 80% complete. Which of the following correctly expresse...
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The weighted average cost of capital is the minimum rate of return necessary to: a) Accept a project. b) Acquire new equity. c) Defend against a takeover attempt. d) Repay bondholders.
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Suppose an insurance company sells policies for a total premium of $500. Each policy has a $100 payout if the insured person dies within one year. If the insurance company does not want to face a net financial loss, what is the maximum proportion of people it can insure who are likely to die within a year? Assume that ...
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The probability that Stock A is in a bull market is 0.2. If Stock A is in a bull market the probability that it will increase in value is 0.6. If Stock A is not in a bull market the probability that it will increase in value is 0.1. What is the overall probability that Stock A will increase in value?
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A project has an initial outlay of $2,750. It has a single cash flow at the end of year 5 of $4,570. What is the internal rate of return (IRR) for the project?
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Bennett's class discussed the following example: Year 2015 Unaudited 2014 2013 Current Ratio 5 3 3 In the beginning stage of an auditor, the above ratio might suggest to the auditor which of the following: A. The company's financial picture has improved...
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Is there a closed form for the following equation: $$ \int^{T}_{0}\frac{f^{n-1}(t)}{1+(n-1)g(t)} \, dt $$ where $n$ is a positive integer and $f(t), g(t)$ are positive continuous functions, and $T>0$?
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Tran Company uses the LIFO inventory cost method. A review of the company's inventory cost for the most recently completed year revealed the following information: Bags Pcs Beginning inventory 20,000 Purchases : May 2008 40,000 October 2008 60,000 December 2008 80,000 Total 180,000 Ending Inventory 40,000 May...
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A car company's annual inventory holding cost is 14%. The desired service probability is 90%. The sales forecast is 4000 units. At the beginning of the year, there are 600 units in the warehouse. The order quantity is 800 units. Determine the order point. a. 1400 b. 1100 c. 1700 d. 1900
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Which of the following statements is correct regarding the use of PE ratios for investment decisions? A. If Company A's PE ratio is 25 and Company B's is 30, Company B's stock must have a lower price than that of Company A's stock. B. When a company has a PE ratio of 18 or 20 and the benchmark PE ratio is 15, a poten...
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At the December 31, 2011, balance sheet date, Unruh Corporation reports an accrued receivable for financial reporting purposes but not for tax purposes. When this asset is recovered in 2012, a future taxable amount will occur, and a. Unruh will record a decrease in a deferred tax liability in 2012. b. pretax financia...
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Use l'Hopital's rule to evaluate the following limit: \(\displaystyle \lim_{x\to 0} \frac{e^{2x}-e^{-2x}-2}{x\sin x}\).
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Which of the following statements is FALSE? A) In the Simplex Method, we have to look only for the entering variable. B) The optimal solution is found at a vertex of the feasibility region when solving a linear program with the Simplex Method. C) If the problem is unbounded, the Simplex Method will fail. D) If the prob...
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Given the following information about a product, at Young & Sons, Inc., what is the appropriate setup time? Setup labor cost $70.00 per hour Annual holding cost $4 per unit Daily production 1,500 units/day Annual demand 27,000 units (270 days each times a daily demand of 100 units) Desired lot size 250 units Setu...
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Assume that you are trying to value a firm that has current profits of $1 million. Assume that the opportunity cost of funds is 7% and the constant profit growth rate is 6%. What is the present value of the firm?
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