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I want to compute the determinant of a matrix $M$. The matrix $M$ is an $n\times n$ matrix where $n$ is large, e.g. $n = 10^5$. The elements in the $i$-th row are $i x$ where $x$ is an $n\times 1$ column vector. That is, $M = \begin{bmatrix}1x & 2x & 3x & \cdots & nx\end{bmatrix}$ where $x$ is the same throughout each ...
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Suppose the price of imported goods depends on the tariff rate. If {eq}x {/eq} is the tariff rate, then the price of imports will be {eq}p(x) = 3 + 4x - 2x^2 {/eq} dollars. What tariff rate should be imposed to maximize revenue for domestic producers?
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Solve: {eq}\int \frac {1}{(e^{(x)}+e^{(-x)})} dx{/eq}
arctan(e^x) + C
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The spot exchange rate for Indian Rupees is Rs 41/$. The one year forward exchange rate is Rs 42/$ the one year U.S. Interest rate is 4%. What is the implied one year interest rate in India? A) 6.77% B) 6.54% C) 6.24%
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The forecasted growth rate in dividends for Maybell's Art Gallery is 14% if the corporation's dividend payout ratio is 0.35 and its ROE is 13%. The next annual dividend will be $1.00 per share, which will be paid to investors one year from today. Investors' required rate of return for this stock is 15%. What is the est...
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R is the required rate of return for assets. If both the inflation premium (IP) and the risk-free rate (r*) increase by 2 percentage points, which of the following is true about R? a. R will increase by more than 2 percentage points if the maturity risk premium (MRP) is positive. b. R will increase by 2 percentage po...
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Given a function $f(x)$ which is never zero and always positive, such that $$\int_0^1 f(x)\ dx=1,$$ show that: $$\int_0^1 \frac{x}{1+f(x)^2}\ dx\leq\frac{1}{2}.$$ Is it correct to let $g(x):=\frac{x}{1+f(x)^2}$, observe that $g'(x)\leq 0$ on $(0,1)$, and extend $g$ by continuity at $0$ and $1$ to an odd function on $[-...
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Solve the initial-value problem: {eq}y'' + 36y = 0, \; y(0) = y'(0) = 0 {/eq}.
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X Company is considering an upgrade to its computer equipment that will cost $120,000 but result in smaller operating costs. Estimated annual operating costs are as follows: Year no upgrade upgrade 1 $-100,000 $-110,000 2 -100,000 -120,000 3 -120,000 -60,000 4 -130,000 -90,000 5 -120,000 -70,000 6 -110,00...
C
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What is the present value of a $1,000 bond that pays $200 per year for 4 years and then $2,000 at the end of 4 years, assuming a 9% discount rate?
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A charged particle moves straight down in the Earth's magnetic field, toward the Earth. The particle experiences a force from the Earth's magnetic field in which direction?
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Freman Inc., which started business at the beginning of this year, had the following data related to purchases and sales of its only product: Purchases: Date Unit Cost Units January 1 5 $110 January 10 12 $117 January 25 15 $125 January 30 14 $128 Sales: Date Units January 7 11 January 15 13 January 20 11...
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A perfectly competitive firm's demand for labor is a vertical line because: A. it is a price taker in labor markets B. it faces competition from other firms in the market C. it has no influence on wage rates D. its demand for the product the labor produces is perfectly elastic E. none of the above
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For an equity interest in a business where the owner is paid only if and when the business makes a profit, is the cost of equity highest when: A. profits are very volatile B. the owner receives a high percentage of the profits C. the business involves a high degree of risk D. profits are very volatile and the owner...
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Compute the Euler totient function $\phi(4627)$.
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Find the $\mathrm{lim\ inf}$ and $\mathrm{lim\ sup}$ of the sequence $$z_n = \frac{n}{n^2+1} + \frac{n^2}{n^3-1} + \frac{n^3}{n^4+2}.$$
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What is the probability of obtaining a sample mean greater than 1,950, given a population of $2,000 with a population mean of 1,800 and a standard deviation of 150, and a sample size of 64?
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One year ago, the Jenkins Family Fun Center deposited $5,000 in an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $6,800 to this account. They plan on making a final deposit of $9,000 to the account next year. How much will be available when they are rea...
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Bill's Boards has 20.6 million shares of common stock outstanding, 4.5 million shares of preferred stock outstanding, and 24.00 thousand bonds. If the common shares are selling for $30.50 per share, the preferred share is selling for $17.20 per share, and the bonds are selling for 95.92 percent of par, what would be th...
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Compute the limit: {eq}\lim_{(x,y) \rightarrow (0,0)} \frac{x^2y \cos(1/y)}{x^4+y^2} {/eq}
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What are the consequences to a firm if it paid the same cash wages but greater fringe benefits to its employees than the other firms in the industry do? A. Employees from the other firms would shift to that firm. B. The firm would earn less profit, would not be able to raise capital, and would shrink in size or go ou...
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The Short Co. has an investment project that will reduce expenses by $10,000 per year for 3 years. The project's cost is $15,000. If the asset's cost of capital is 16%, what is the project's MIRR? a. 17.31% b. 18.14% c. 16.02% d. 16.82% e. 14.69%
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The stock of Marzouk Inc. is selling for $50 per share and has a required rate of return of 14%. Dividends are expected to grow at a constant rate of 4%. What is the expected year-end dividend, D1?
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I am a little confused about how to use chi-squared when you are not given degrees of freedom. The problem I am working on is this: "A biology professor wanted to know whether genetics influenced color blindness, so he randomly selected 300 biology students and determined their eye color and whether or not they were co...
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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 $720.85. 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 34 ...
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A competitive advantage can be sustained if customers perceive the benefits are not readily substitutable by competitors. Which of the following examples of a competitive advantage are not easy to replicate? A. A company's free, twice weekly shipping for large orders B. The speed and convenience of services offered b...
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Suppose a firm occasionally faces a demand for short-term credit but usually has an excess of short-term capital to finance current assets. Which approach is the firm following? a. Conservative approach b. Aggressive approach c. Maturity matching approach
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In its first year of operations, Bronfren Corporation produced 1,020,000 sets and sold 980,000 sets of artificial tan lines. Assuming that Bronfren has both variable and fixed production costs, which of the following statements is true of the company's net operating income if during its second year, the company produc...
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Calculate the exact value of $$\displaystyle \int_0^1 \sum_{n = 0}^\infty \frac {(- 1)^n \displaystyle x^{2 n}}{2 n !} \ dx $$. Is it true that $$\displaystyle \int_0^1 \displaystyle \sum_{n = 0}^\infty \frac {(- 1)^n \displaystyle x^{2 n}}{2 n !} \ dx = \displaystyle \sum_{n = 0}^\infty \frac {(- 1)^n}{2 n !} \display...
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During the period of elastic deformation, an increase in confining pressure affects the shear strength of the soil by: A. increasing cohesion and angle of friction. B. increasing cohesion, but not changing the angle of friction. C. decreasing cohesion, but increasing the angle of friction. D. increasing cohesion, b...
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In 2010, Rigney Company purchased equipment that cost $160,000. The expected useful life of the equipment was eight years, and the expected residual value was $25,000. Rigney used the straight-line method of depreciation for this equipment. However, at the beginning of 2014, Rigney changed its depreciation method to th...
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The short run in macroeconomics is a period: a. in which prices do not change. b. in which output is fixed. c. in which firms cannot increase output. d. in which all factors of production are variable.
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Who believes that putting shareholders first is the wrong approach to corporate governance? Choices are: a. Freeman, b. Friedman, c. Kelly d. Halfon
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Assume that both Project 1 and Project 2 have normal cash flows, that neither project has any negative cash flows after initial outlay. However, Project 2 has a larger initial outlay than Project 1. If Project 2's discounted payback period is two years, then: a. Project 1 definitely also has a discounted payback perio...
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When a strategy of vertical integration is used, the firm may or may not _____. A) produce all of its own components B) manufacture its own capital equipment C) manufacture its own products D) sub-contract some component elements of its final product
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Bacterial resistance to Beta-lactams may be mediated by all of the following except: A. Prevention of phagolysosomes formation B. Altered antibiotic target proteins C. Decreased intracellular uptake of the drug D. Active elimination of efflux pump E. Enzymatic destruction of the antibiotics
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What is the pH of a solution whose [H3O+] is 3.5 x 10-4 M? A) - 3.46 pH B) 3.46 pH C) 3.29 pH D) - 3.29 pH
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If the Fed changes its policy interest rate during the period when a bank has made a loan, which of the following items on the bank's balance sheet is affected? A. Required reserves B. Excess reserves C. Net Worth D. None of the above
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Which method uses an aging of Accounts Receivable to calculate the Bad-Debts Expense? A) Income statement approach B) Balance sheet approach C) Aging the Accounts Receivable D) Direct write-off
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Ming Company makes and sells two types of pens. Information about these two products for the most recent year appears below: Gross Margin$120,000 Total Fixed Cost$180,000 Average per unit product: Product O72 $24 $42 Product M67 $20 $50 The total contribution margin for the entire 25,000 units (both products)...
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I am looking for a minimal working example of a Bernoulli random variable in R where I do not see the benefit of using rbinom.
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Use implicit differentiation to find the equation of the tangent line to the curve 4(x^2 + y^2)^2 = 9x^2y^2 at the point (1, 2).
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If demand for Henritos potato chips is perfectly elastic, then a $10 tax on Henritos will a. result in no change in the price paid by consumers. b. lower the price paid by consumers by exactly $10. c. result in no deadweight loss. d. lower the deadweight loss.
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What are the equivalent units of production for a process-costing system under the following circumstances? Units in beginning inventory 4,000 Units started during the month 16,000 Units completed during the month 13,000 Units in ending inventory that were 60...
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Suppose {eq}\overrightarrow{F} (x, y) = 2y\overrightarrow{i} + 4xy\overrightarrow{j}{/eq} Use Green's Theorem to calculate the line Integral of {eq}\overrightarrow{F}{/eq} around the perimeter of a circle {eq}C{/eq} of radius {eq}2{/eq} centered at the origin and oriented counter-clockwise.
-8\pi
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Which of the following is a valid interpretation of Say's law? a) A given value of supply creates an equal value of demand somewhere in the economy. b) Each time goods are produced, it represents income for someone. c) In the long run, supply and demand grow at the same rate. d) Demand creates its own supply. e) F...
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Tax revenues divided by the value of goods and services sold within the country is an example of: A. an exchange rate-based measure of the size of the domestic market B. a price-based measure of the size of the domestic market C. a wage-based measure of the size of the domestic market D. none of the above
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Find the limit of {eq}F(x) = \frac {x - \tan(x)}{x^2} {/eq} as x approaches 0.
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Use the Log Rule to evaluate the integral. (Use C for the constant of integration.) {eq}\displaystyle\int \frac{e^x}{\sqrt {9-e^{2x}}} \: dx{/eq}
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Given the following information, which segments are reportable under the 10 percent rule? Intercompany Sales: North Division $4,000 South Division $5,000 Total Company $20,000 External Sales: North Division $1,000 South Division $4,000 Total Company $16,000 Segment Income (Loss): North Division ($300) South ...
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Based on your reading of the Coca Cola/Pepsi case (in your Harvard Course Pack), there are two kinds of "buyers". These are: a. syrup concentrate providers and advertisers. b. Bottlers and consumers c. Millenials and gen x d. Syrup concentrate providers and bottlers.
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Compute the Euler totient function $\phi(1721)$.
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Sulzberger Co. stock has a beta of 2.65. If the expected return on the market is 12.75% and the risk-free rate is 3.80%, then what is the expected return on the stock?
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According to the Phillips Curve, if the unemployment rate is below the natural unemployment rate, there will be: A. an inflationary gap. B. a deflationary gap. C. a full-employment equilibrium. D. a demand shock.
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I need to find the derivative of an equation with respect to the value {eq}\beta{/eq}. Here the equation is as follows: {eq}\int_{0}^{t} e^{-y/L}\times(1 - \beta e^{-y/L})^{\beta -1} \times \beta\ dy{/eq} where {eq}t > 0, \; \beta > 0{/eq}.
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This question translates a supply and demand schedule for an output to demand for pollution. Suppose the output is kwh of electricity, and each kwh of electricity generates 0.5 tons of CO2. The supply and demand schedules for electricity are as follows: Quantity of Electricity (kwh)Demand for Electricity (WTP)Supply ...
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The development of subcultures within an organization occurs when _____. a. the organization has many locations b. there is high leader trustworthiness c. there are many departments in an organization d. there is low leader trustworthiness
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What is the future value of $3,000 in 15 years at an interest rate of 8%, compounded annually? a. $6,846.71 b. $6,827.04 c. $6,805.41 d. $6,870.05 e. $6,812.73
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Two equal positive point charges, each of charge q, are separated by distance L. There are no other charges anywhere. The potential at the midpoint of the line joining the charges is defined to be zero. The electrostatic potential at an infinite distance from the two charges is therefore: A) 0 B) {eq}q/4\pi\epsilon_0...
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What is the probability that a quality control inspector selected at random will find 15 or fewer defective compact disc drives in a sample of 50, given that 3% of all compact disc drives are defective?
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Consider a price ceiling imposed at a price below the equilibrium price. Which of the following statements is true? (a) Producer economic profits will increase. (b) Consumer surplus will increase. (c) Deadweight loss will increase. (d) None of the above.
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Evaluate {eq}\displaystyle \iint_{R} e^{-x^{2}} \ dA, {/eq} where {eq}R = [0, 3] \times [0, 2].{/eq}
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Which idea stresses finding the proper balance between logos and pathos? harmony of the worlds catharsis doctrine of ethos music of the spheres
C
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A company manufactures a single product, sells it for $30 per unit, and incurs variable costs per unit of $22. The fixed manufacturing overhead totals $10,000, and the fixed administrative expense totals $9,000. If each unit of finished goods contains three pounds of direct materials, and each pound of direct material ...
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Consider a perfectly competitive labor market, the equilibrium wage will decrease if: A) labor supply shifts right. B) labor supply shifts left. C) labor demand shifts right. D) labor demand shifts left.
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How do you calculate expected return and what factors affect it? The expected return for a share of common stock is the? Select one: a. Risk-free interest rate b. Total of the after-tax cost of debt and the cost of equity c. Weighted average cost of capital d. Sum of the risk-free interest rate and the market risk...
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Explain the interest rate parity with an example. Make sure to distinguish between the forward and futures rate. Assume an investor can borrow at 3% in the domestic market. A U.S investor is expecting 20 million euros to be received in one year. The current one-year interest rate is 3% in the U.S. and 4% in euros. Th...
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Which of the following is most likely to have the most favorable long-term income tax treatment? a. Long-term capital loss carryback. b. Short-term capital loss carryforward. c. Long-term capital loss carryforward. d. Short-term capital gain.
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Which of the following is true of the demand curve faced by a monopolist? a. A monopolist's demand curve is infinitely elastic. b. A monopolist's demand curve is more elastic than a competitive firm's demand curve. c. A monopolist faces a relatively inelastic demand curve. d. A monopolist's demand curve coincides w...
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Delazaga Corporation found the following errors in their year-end financial statements: Year Ended December 31, 2013Year Ended December 31, 2014 Ending inventory$25,000 understated$36,000 overstated Depreciation expense$14,000 understated On December 31, 2014, a fully depreciated machine was sold for $32,000 but the ...
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On April 1, Ivy Corp began operating a service company with an initial cash investment by shareholders of {eq}\$1,000,000 {/eq}. The company provided {eq}\$3,200,000 {/eq} of services in April and received full payment in May. Ivy also incurred expenses of {eq}\$1,500,000 {/eq} in April that was paid in June. During...
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In an exchange economy with two goods (1 and 2) and two people (A and B), each person's utility function is $U=X_1X_2$, where $X_i$ is the amount of good i. Person A is endowed with 100 units of good 1 and no units of good 2. Person B is endowed with 100 units of good 2 and no units of good 1. Then the competitive equi...
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Suppose the mean income of firms in an industry for a year is $39 million with a standard deviation of $8 million. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than $47 million? (Round your answer to four decimal places.)
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Which of the following statements is incorrect? A. If a firm decreases the price of its product, its total revenue will decrease. B. The own price elasticity of demand is constant at all points along a linear demand curve. C. As the price of X falls and we move down an individual's demand curve for X, the money inco...
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Suppose than an oil well is expected to produce 100,000 barrels of oil during its first year in production. However, its subsequent production (yield) is expected to decrease by 10% over the previous year's production. The price of oil is expected to be $60/barrel for the next several years. What would be the present w...
b
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Which of the following statements is true about the mass moment of inertia? (a) It measures how an area is distributed about particular axes. (b) It depends on the geometry of an area (size and shape). (c) It depends on the selected axes. (d) It depends on the density of the material.
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It is possible that when the money supply rises, interest rates may _____ if the _____ effect is more than offset by changes in income, the price level, and expected inflation. A) fall; liquidity. B) fall; risk. C) rise; liquidity. D) rise; risk.
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Let $p,q \in \mathbb{R}$. Consider the function $f: \mathbb{R^2} \rightarrow \mathbb{R}$ defined as: $$ f(x,y) = \frac{xy(p^2+q^2)}{(x^2+y^2)^\frac{3}{2}} $$$$ f(0,0) = 0 $$ To find the partial derivatives of $f$ I used the definition of partial derivative: $$ \frac{\partial f}{\partial x}(x,y) = \lim_{t \rightarrow 0}...
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If X is N(0, 1), find P(−1.2 < X < 0).
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Which of the following is not a source of equity capital? A. Common stock. B. Dividends. C. Retained earnings. D. Additional shares of common stock issued.
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For the companies that are able to engage in price discrimination, the practice: a. is profitable. b. increases the welfare of consumers. c. is sometimes inefficient for the market. d. is difficult to maintain over the long run. e. decreases the welfare of producers.
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Consider the following endowment economy with two individuals and two goods. The utility function for the two individuals are $U_{1}= x_{1}y_{1}$ and $U_{2}= x_{2}y_{2}$. The initial endowment is (5,20) for (x,y) for individual 1 and (15,20) for individual 2. Find all Pareto optimal allocations.
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The long run average cost curve connects A) the minimum points of all the short run average variable cost curves. B) the maximum points of all the short run average cost curves. C) the minimum points of all the short run total cost curves. D) the maximum points of all the short run total cost curves. E) the minimu...
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In a sample of 200 students, 30% own a computer. How many students own a computer?
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Why might the Laffer curve have a negative slope? A. When tax rates increase, tax revenue might actually decrease, thus causing the Laffer curve to slope downward. B. The Laffer curve's downward slope is due to the fact that as tax rates increase, tax evasion and other tax-motivated forms of economic distortion incre...
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Calculate the limit by using the definition: $$ \lim_{x\to 4} (3x^2 + 2x - 5) $$
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Futuristic coiffures (FC) needs to raise $85,000 to purchase a new machine. FC knows its component costs of capital are rd = 5%, rps = 7%, rs = 11% and re = 13%. FC maintains a capital structure that consists of 60 percent debt, 10 percent preferred stock, and 30 percent common equity. The firm's marginal tax rate is 3...
6.7%
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A university gifts all its international students with a free one-year subscription to USA Today. Each international student has a choice whether to use the newspaper during the year or not. Since all international students have this choice, the university's subscription is an opportunity cost of: a. having an interna...
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An increase in expected future interest would cause a(n) _____ in the _____ of bonds. a. increase . . . demand b. decrease . . . demand c. increase . . . supply d. decrease . . . supply
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For a given labor demand curve, which of the following is not held constant? A. the production function B. the price of the input C. the productivity of labor D. the price of labor
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What mass of solid potassium hydroxide (KOH) is needed to prepare 1.1 L of a 0.10 M KOH solution?
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Benton Inc. has sales of $4,439,580, total assets of $3,221,910, and a debt-equity ratio of 1.10. If its return on equity is 13 percent, what is its net income?
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Norio Manufacturing uses powdered plastics (PPS) to manufacture a high-pressure board used in a digital equipment product, Flex 10. Information concerning its operation in June is as follows: Budgeted units of Flex 10 for June6,700 Budgeted usage of PPS60,300 pounds Actual number of units of Flex 10 manufactured5,700...
C
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Unit two of a chain of restaurants has 160 seats (tables). For each additional unit in the chain, the number of seats in the new unit is 20 less than twice the number of seats in the previous unit. What is the number of seats in the seventh unit of this chain of restaurants?
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Suppose that the average annual amount spent for daily meals by medical interns is $3,000. A sample of 36 medical interns is studied. The sample standard deviation of the sample is $300. What is the probability that the average annual amount spent was between $2,850 and $3,150?
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Aggressive Corporation sold some machinery to Travis Company on January 1, 2013. The cash selling price would have been $822,670. Travis entered into an installment sales contract that required annual payments of $200,000, including interest at 12%, over four years. The first payment was due on December 31, 2013. What ...
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Homer purchased a call option on 100 shares of XYZ Corporation, with a strike price of $25 per share, and a premium of $2 per share. At the expiration of the option, the price of a share of XYZ Corporation was $30. What is Homer's gain or loss on his call option? A. $300 B. $500 C. $0 D. $200
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What is the integral of ∫1/x^2cos(1/x)dx?
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Hook Industries capital structure consists solely of debt and common equity. It can issue debt at 10% and its common stock currently pays a $3.25 per share. The stock's price is currently $35.00, its dividend is expected to grow at a constant rate of 8% per year, its tax rate is 40%, and its WACC is 13.70%. What percen...
36.00%
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Given the plane equation {eq}2x - 3y + z = 4 {/eq}, find the shortest distance from the point {eq}(1, 3, 2) {/eq} to this plane.
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