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$$\lim _{n \rightarrow \infty} \prod_{i=1}^{n+1} \cos \frac{\sqrt{2 i-1}}{n} a^{2}=\mathrm{e}^{-\frac{a^{4}}{2}}$$ Prove this limit using the "fitting method" as described in the provided example and notes. The example demonstrates proving $\lim _{n \rightarrow \infty} x_{n}=a$ given $x \rightarrow 0$, $f(x) \sim x$, a...
e^{-a^4/2}
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Compute the line integral {eq}\int_{C} F \cdot dr{/eq} for the vector field {eq}F(x, y, z) = \left \langle P, Q, R \right \rangle = \left \langle x^2y, y^2z, z^2x \right \rangle{/eq} and curve {eq}r(t) = \left \langle \cos t, \sin t, t \right \rangle, \ \ 0 \leq t \leq \pi{/eq}.
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The cumulative distribution function of a random variable X is given by $$F(x) = \begin{cases} 0 &\text{ if } x\leq -1, \\\ \dfrac 12 x+ 1&\text{ if } -1< x\leq 1, \\\ 1 &\text{ if } x >1. \end{cases}$$ What is $\mathrm{Var}(2 - 3X)$?
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For a population with a standard deviation of {eq}\sigma = 20 {/eq}, what is the z-score for a score that is 5 points above the mean? (Round your answer to two decimal places.) Z-score: _____
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The pH of a solution is 4.74. The solution can be made more basic by: A) decreasing the temperature of the solution B) adding more of the solution to itself C) adding a strong acid to the solution D) adding a strong base to the solution E) removing some water from the solution
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A cash sale would most likely be made by a business under which of the following circumstances? a. When the merchandise is sold on the installment basis. b. When the buyer has a history of returning merchandise. c. When the buyer has a history of paying for the merchandise before receiving it. d. When the buyer has...
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Assume that on January 1, 2013, Weber Company issues bonds with a face value of $300,000 with a coupon interest rate of 10%. The bonds pay interest semiannually and mature in 10 years. Assume that the market interest rate at the date of issuance is 8%. The journal entry for the bond issuance would include a: A) Credit...
B
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A firm is currently selling 42,000 units of a product at $240 per unit. Fixed costs are $840,000, and variable costs are $180 per unit. What is the firm's profit before taxes? A. $260,000. B. $360,000. C. $4,200,000. D. $4,560,000.
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Peanut butter and jelly are complements in consumption. Assuming that the supply curve of peanut butter is upward sloping, if there is a decrease in the price of jelly, producer surplus in the peanut butter market: a. will decrease. b. will increase. c. will not change. d. may change, but it is impossible to tell w...
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A random sample of 4000 observations has a mean of 63 and a standard deviation of 8. Construct a 95% confidence interval for the population mean. A) 63.240 and 63.260 B) 62.516 and 63.484 C) 62.795 and 63.205 D) 63.025 and 62.975
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The volume of a solid is given by the following integral. Find the volume generated. {eq}\int_0^4\pi(\frac{25}{16}x^2+25)dx{/eq}
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At {eq}16:35 {/eq} hours, a {eq}15 \textrm{ kg} {/eq} object moving along the x-axis with an initial velocity of {eq}15 \frac{\textrm{m}}{\textrm{s}} {/eq} was {eq}8 \textrm{ m} {/eq} from the origin and at rest. From {eq}16:35 \textrm{ hours} {/eq} to {eq}16:39 \textrm{ hours} {/eq}, the object's velocity was given by...
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Which of the following series of commands will restrict Telnet access to the router? Options are: answer A Lab_A(config)#access-list 10 permit 172.16.1.1 Lab_A(config)#line con 0 Lab_A(config-line)#ip access-group 10 in; answer B Lab_A(config)#access-list 10 permit 172.16.1.1 Lab_A(config)#line vty 0 4 Lab_A(config-lin...
C
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An investor can design a risky portfolio based on two stocks, X and Y. X has an expected return of {eq}21\% {/eq} and a standard deviation of {eq}24\% {/eq}. Y has an expected return of {eq}14\% {/eq} and a standard deviation of {eq}18\% {/eq}. The correlation coefficient between the returns of X and Y is {eq}-1 {...
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Which of the following is included as a subdiscipline by the Association for Psychological Science but not the American Psychological Association? a. rehabilitation b. behavioral genetics c. suicide d. measurement
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Fidelity Mutual (an insurance company) has a defined-benefit pension plan that has been assigned an unexpected credit loss. Fidelity Mutual's accountants are unable to reach a consensus about whether or not the following entry to record the loss should be made: Cash$50,000 Project Credited$50,000 Instructions (a) E...
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In financial statements, income is often defined as a. cash inflows plus non-cash inflows. b. cash inflows minus non-cash outflows. c. cash inflows plus non-cash outflows. d. cash inflows minus non-cash inflows.
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Which of the following would not be an economic transaction? A) A stock split. B) Reissuing previously held treasury stock. C) Selling treasury stock at a profit. D) Converting bonds payable into common stock.
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In order to be relevant, accounting information must: a. provide a basis for forecasts. b. be verifiable. c. be neutral. d. be a faithful representation.
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Find the area of the surface cut from the plane 4x + 3y + z = 4 by the cylinder whose walls are {eq}\displaystyle x = y^2 {/eq} and {eq}\displaystyle x = 2 - y^2 {/eq}.
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Service department costs can be allocated to the producing department using the: a) Direct method only. b) Step-down method only. c) Reciprocal method only. d) Direct, step-down or reciprocal method.
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Suppose people expect a 5% reduction in the money supply, and as a result they increase their holdings of cash from 15% to 25% of their overall wealth. According to monetarists, this will cause _____. A. real GDP to decline B. employment to rise C. prices to decline D. All of the answers are correct.
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Let \(\mathbf{v}\) and \(\mathbf{w}\) be orthogonal vectors such that \(\|\mathbf{v}\|=1\), \(\|\mathbf{w}\|=2\). Find the projection of \(3\mathbf{v}+\mathbf{w}\) onto \(\mathbf{v}\).
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The workers at the Axme Corporation have divided into several cliques. Employees in each clique tend to stick together, sharing lunch and coffee breaks. The employees in one clique very seldom interact with workers in another clique. This type of situation may create _____ barriers that prevent effective communication....
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What is the most immediate (or direct) cause of growth in real GDP per capita? A. Factors of production B. Incentives C. Institutions D. The political system in the economy
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Period costs, such as selling and administrative expenses, a. are deducted as incurred. b. are not included in the cost of inventory. c. are included in the cost of inventory. d. are included in the cost of the product under variable costing. e. are ignored in the income statement under absorption costing.
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A company had net income of $460,000. Depreciation expense is $80,000. During the year, accounts receivable and inventory increased $40,000 and $140,000, respectively. Prepaid expenses and accounts payable decreased by $2,000 and $14,000, respectively. How much cash was provided by operating activities? a. $260,000 b...
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A 50.00 mL aliquot of 0.1000 M benzoic acid, {eq}C_6H_5COOH{/eq}, is titrated with 0.1000 M NaOH. What is the pH at the equivalence point?
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Suppose the M1 money multiplier is 3. If the Fed purchases $100,000 worth of government bonds when the required reserve ratio is 8%, what will be the total increase in the money supply? a. $300,000 b. $1,300,000 c. $1,500,000 d. $2,600,000
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After a large balloon burst loudly and suddenly at her birthday party, Cindy showed fear of balloons. In terms of the acquisition phase of classical conditioning, the balloon is the _____, and her fear is the _____. a. CS; US b. US; UR c. CS; CR d. CR; CS
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Todrick Company is a merchandiser that reported the following information based on 1,000 units sold. Calculate the contribution margin per unit. Sales $420,000 Beginning merchandise inventory $28,000 Purchases $280,000 Ending merchandise inventory $14,000 Fixed selling expense $ ? Fixed administrative expe...
$84
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Given the following account balances at year end, compute the total intangible assets on the balance sheet of Janssen Enterprises. Cash $1,500,000 Accounts Receivable 4,000,000 Trademarks 1,000,000 Goodwill 2,500,000 Research & Development Costs 2,000,000
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A catenary is the curve formed by a hanging flexible chain, or cable, like the one showing in the figure. Its equation is y = (1/2)(a + x)(a - x), where a is a constant and x is the horizontal coordinate. What is the length of the catenary for 0 < x < 3 given a = 2?
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During the initiation stage of carcinogenesis, the mutation occurs in a. cells of the DNA sequence. b. DNA in every cell of the body. c. the genes of the DNA sequence. d. DNA in a subset of cells.
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If $3x^4+2x^3+x^2y=4$ and $\frac{dx}{dt}=-2,$ find $\frac{dy}{dt}$ when $x=-1$ and $y=-1$.
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Integrate e^x ln x by parts.
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The kinked oligopoly demand curve is a result of the assumption by an oligopolist that: a. price increases will be matched, but price reductions will not. b. price increases will not be matched, but price reductions will. c. both price increases and price reductions will be matched. d. neither price increases nor p...
b
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Why does a firm that produces in the long run never have a fixed cost or sunk cost? a. because of the flexibility it enjoys in the long run b. because it can change all of its inputs in the long run c. because it can make or break even in the long run d. because all resources can be changed in the long run e. beca...
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Homer Telecommunications has a target capital structure that consists of 70 percent debt and 30 percent equity. The company anticipates that its capital budget for the upcoming year will be $2,000,000. If Homer reports net income of $1,000,000 and it follows a residual dividend payout policy, what will be its dividend...
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How large a sample should be taken to be within $200 of the actual average with 99% confidence, given a standard deviation of $1,000?
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Which of the following items is not included in the calculation of free cash flow? a. Cash paid for income taxes b. Interest paid c. Purchases of long-term assets d. Cash paid for new plant and equipment e. Proceeds from the issuance of new debt
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At a special event held in the year 20XX, three boxes of gold were given out as prizes. A total of 68 participants were present at the event. If three people were found to be ineligible, how many different ways could the gold boxes have been awarded? The number of different ways to award the gold boxes is?
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Use Green's theorem in the vector form to calculate the outward flux {eq}\phi = \oint_c \vec{F}\cdot \vec{n} ds for {eq}\vec{F} = (y^2 - x^2) \vec{i} + 2xy \vec{j} and C the triangle with vertices (0, 0), (3,0) and (0,6).
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A firm had $100 of revenue, $60 of cost (including $30 of fixed cost), and $40 of profit. Its marginal cost is $4. If it charges a higher price, then a. it will decrease its fixed cost. b. it will decrease its variable cost. c. it will increase its profit. d. it will produce more units. e. None of the above
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Based on the following estimates of the marginal utility of the last unit of each of the products purchased, which of the following statements is true? Product Quantity Price Marginal Utility A 4 $12 60 B 3 $16 64 C 2 ...
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Suppose the current spot rate for the Swiss Franc (CHF) is $0.92/CHF. The one-year forward rate for the CHF is $0.95/CHF. Assume a bank can borrow at 1.5% for one year. The interest rate for a one year deposit in U.S. dollars is 1% per year. What must be the interest rate in Switzerland for this one-year deposit?
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Dividend yield of 2.7%; price of stock is $43 per share; net income is $7,853,600, and there are 2,800,000 shares outstanding. What is the ROE?
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How many of the following are validly concluded from the statements? I. All phages are parthenogenetic. II. Some phages are not vegetarians. III. No phages are vegetarians. IV. Some carnivores are not phages. All vegetarians are parthenogenetic. Some parthenogenetics are not phages. No carnivores are parthenogenetic.
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Harris Inc.'s preferred stock was issued five years ago to yield 9%. Investors buying those shares on the secondary market today are getting a 14% return. Harris generally pays flotation costs of 12% on new securities issues. What is Harris's cost of preferred financing?
15.91%
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Given that the standard error of the mean is 4.6 and the sample size is 20, what is the margin of error at the 95% confidence level?
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What is the average value of f(x) = 5x + 3 on the interval [0, 2]?
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When the home interest rate is greater than the foreign interest rate, the quantity of domestic currency supplied in the foreign exchange market _____ at any given exchange rate. A) increases B) decreases C) is not affected
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A company has 3 projects, A, B, and C, that have the following free cash flows. Each project has a WACC of 13.5%. Project CASH FLOW A:Year 0 -$1,000 Year 1 $450 Year 2 $450 Year 3 $450 Year 4 $450 B:Year 0 -$1,000 Year 1 $250 Year 2 $380 Year 3 $380 Year 4 $380 C:Year 0 -$1,000 Year 1 $100 Year 2 $295 Year 3 $590 Y...
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At the current price level, the elasticity of demand for good X is -0.6. Based on this information, we know that a decrease in price will: a) decrease total revenues. b) have no effect on total revenues. c) increase total revenues. d) Possibly increase or decrease total revenues, but more information is needed. e)...
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Your manager notes that you calculated the multifactor productivity for April as 4.81. She asks you what that means. You reply: a. "For every $4.81 in revenue, we cover all labor, overhead and material costs." b. "For every $1 in revenue, we produce 4.81 units." c. "For every $1 spent in operations, we produce 4.81...
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A mean temperature reading for a month was 28 degrees Celsius and the standard deviation was 4.32 degrees Celsius. Assuming data is normally distributed and at least 75% of the data is within X standard deviations from the mean, what are the maximum and minimum temperatures of the month?
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Use the differential dy to approximate $\Delta y$ when $x$ changes as indicated. $y = 9 - x^{2/3}$; from $x=27$ to $x=27.14$.
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Which of the following statements does not apply to intrastatement tax allocation? A) It is also referred to as intraperiod tax allocation. B) It includes showing prior period adjustments net of tax effect. C) It includes showing extraordinary items, changes in accounting principle, and operations of discontinued se...
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Using the limit definition of a derivative, how do you find the derivative of f(x) = x/(x-7)?
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An increase in the interest rate sensitivity of investment will cause the aggregate demand curve to A. become steeper B. become flatter C. shift leftward D. become steeper and shift leftward E. become flatter and shift leftward
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The long-run aggregate supply curve (LRAS) is Y = Yf, which depends on the amount of resources and the level of technology innovation. If a country has more resources and better technology, which of the following is true? A. The LRAS curve will shift to the right. B. The SRAS will shift to the right. C. The SRAS wil...
D
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To finance its activities, the First National Bank of Springfield must maintain a ratio of its average daily liabilities to its average daily assets equal to at least 12 percent. If its average daily liabilities during a period of time are $10 million and its average daily assets are $9 million, then it must reduce its...
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Let $f(z)$ be analytic in the annulus $1<|z|<2$. Prove that $\int_{|z|=r} \frac{f'(z)}{f(z)} \ dz = 2 \pi i k $ for some integer $k$ and for all $r$ satisfying $1<r<2$. Here $z$ is a complex variable and the integral is counterclockwise.
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Garden Source began January with 30 units of inventory on hand that had a unit cost of $40. During January, the following purchases of inventory were made: On January 12, 70 units were purchased at $45. On January 26, 30 units were purchased at $50. The company also had a sale for 40 units on January 10 and 50 units o...
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$300 invested at 10% interest compounded annually (FV = P(1 + i)^n) for 6 years will grow to how much?
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Rasman Co. owned 60% of Shuvelle Corp. and 40% of Taylor Corp. and Shuvelle owned 35% of Taylor. When Rasman prepared consolidated financial statements, it should include: a. Shuvelle, but not Taylor. b. Taylor, but not Shuvelle. c. either Shuvelle or Taylor. d. Shuvelle and Taylor. e. Neither Shuvelle nor Taylor.
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A beaker with 2.00 x10^2 mL of an acetic acid buffer with a pH of 5.000 is sitting on a benchtop. The total molarity of acid and conjugate base in this buffer is 0.100 M. A student adds 7.20 mL of a 0.450 M HCl solution to the beaker. How much will the pH change? The pKa of acetic acid is 4.740. Express your answer num...
-0.29
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What is the slope of the labor demand curve, and how is it related to the marginal revenue product of labor and the marginal product of labor curves? What factor(s) determine the slope of the labor demand curve?
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The Glass Box has a 60/40 debt/equity ratio and a cost of equity of 11 percent. The pre-tax cost of debt is 5 percent and the tax rate is 30 percent. What is the firm's weighted average cost of capital? a. 6.2 percent b. 6.4 percent c. 8.3 percent d. 9.8 percent e. 12.2 percent
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Explain why a good company might choose to ignore the "marketing concept".
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My statement: On average, firm's cost less income tax is equal to zero because income tax is based on profits that are zero. My question: Why can we make such a statement?
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Find the length of the curve \(y = \frac{1}{6}x^3 + \frac{1}{2x}\) from \(x = 2\) to \(x = 3\).
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The objective of the physical and document review phase is a. to build an appropriately sized case file. b. to become as familiar as possible with the relevant business processes and individuals involved. c. to assist in the preparation of the engagement letter. d. All of the above e. None of the above
b
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Ocado plc owns and operates an online grocery shop where it sells food and drink to members in the United Kingdom. The company reports its results in millions sterling with 2016 as its most recent fiscal year (note: one U.K. pound is approximately equal to one U.S. dollar). In its 2017 annual report, the company includ...
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Which one of the following statements is correct about a corporation in the 35% tax bracket that can invest either in a bond paying 8% interest or in the preferred stock of another corporation that pays a 6% dividend? A. The preferred stock should be selected because its after-tax yield is 0.17% higher. B. The prefer...
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Buildwell Builders Inc. has a debt-to-equity ratio of 0.90. If it had no debt, its cost equity would be 9%. Its cost of debt is 7%. What is its cost of equity if the corporate tax rate is 35%? A. 10.72% B. 9.85% C. 8.85% D. 7.72%
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HouseWorks, Inc. made the decision to purchase a building because of its location and for the purpose of providing a work environment that was attractive to its employees. The price was $65 million. Based on this information, we know the company has made an _____. a) opportunity cost of $65 million b) economic profit...
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Suppose the Fed purchases government bonds with $2 million of reserves and a currency drain of 2. What is the maximum amount by which the money supply can increase? A. $10 million B. $5 million C. $2 million D. $1 million
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Two mutually exclusive alternatives are being considered. Alternative A has an initial cost of $100 and uniform annual benefit of $19.93. The useful life is 10 years, and the IRR is 15%. Alternative B has an initial cost of $50 and uniform annual benefit of $11.93. The useful life is 10 years, and the IRR is 20%. Th...
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Find the divergence of the vector field {eq}F = \langle z^2e^{xy},x\sin y,z\rangle{/eq}.
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A firm owns a resource that gives it a cost advantage over rival firms. This cost advantage is likely to be largest and longest lasting if the resource is: a. something that cannot be easily imitated. b. something that other firms can easily acquire. c. something that other firms could acquire if they spent enough m...
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Your broker calls to tell you that you are now eligible to sell shares of your car company's stock since the firm has been delisted from another exchange. Your broker wants you to sell it at the current market price of $6.00. You sold the stock on the other exchange last week for $6.75, and you consider this a long-ter...
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________ reports the relationship between each item in the financial statements and an appropriate base figure. a. Analytical statements b. Trend statements c. Common size statements d. Pro forma statements
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Show that $e^x$ can be differentiated using the definition $f'(x)=\lim_{y\to x} \frac{e^y - e^x}{y-x}$, and find its derivative.
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Refer to the following table and income statement data: MARNI COMPANY Balance Sheet As of December 31 ASSETS: Cash $50,000 Accounts receivable 100,000 Inventory 200,000 Net plant and equipment 650,000 Total assets $1,00...
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Find the $$\lim_{x \to 0}\frac{e^x-\sqrt{1+x^3}}{\cos\sqrt{\sin x}-1}$$
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NASA collected data on the mean weight of NASA astronauts in 1987 and in 2005. The data revealed that the mean weight of the population of astronauts was about the same in both years, but the standard deviation was much greater in 2005. What was the likely cause of this change? a. NASA selected a different sample in ...
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Blessing Corporation uses a job-order costing system with a single plantwide predetermined overhead rate based on direct labor hours. The company based its predetermined overhead rate for the current year on 19,000 direct labor hours, a total fixed manufacturing overhead cost of $250,800, and a variable manufacturing o...
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Under which of the following market classifications does a commercial bank belong? a. pure competition b. pure monopoly c. monopolistic competition d. oligopoly
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Benson Co. purchases an asset for $5,000. This asset qualifies as a three-year recovery asset under MACRS. Benson has a tax rate of 30%. The three-year expense percentages for years 1, 2, 3, and 4 are 33.33%, 44.45%, 14.81%, and 7.41%, respectively. If the asset is sold at the end of four years for $2,000, what is the ...
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Suppose that the time between calls from your aunt Debbie has an exponential distribution with a mean time of 3 days. You realize that you have not received a call in at least 2 days. What is the probability that she will not call you within the next two days?
0.5134
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How would you classify the following as either a demand shock or a supply shock? A successful advertising campaign for a new product. a) Supply shock b) Demand shock
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The Franklin Corporation has a stock price of $50 per share. It expects to pay a $15 per share dividend in one year and expects to pay $10,000,000 in dividends in the coming year. If Franklin's investors expect the $15 dividend to be the last dividend paid then the implied growth rate for Franklin is: A) 0% B) -20% ...
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In financial accounting, a change in accounting principle refers to a change: A. from the FIFO inventory method to the LIFO inventory method. B. to a new accounting method within a consistent principle. C. from the cash basis of accounting to the accrual basis of accounting. D. from one method of amortizing a premi...
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In this section, we are asked to determine the return on stockholders' equity for the given data. Net Income: $3,801,700 Stockholders' Equity: Common Stock: $6,100,000 Preferred Stock: $250,000 Additional-Paid-in-Capital: $750,000 Retained Earnings: $10,200,000 Total Stockholders' Equity: $17,300,000
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The cross-price elasticity of butter and margarine would probably be: A. close to zero B. less than -1.0 C. between -1.0 and 0 D. greater than 1.0
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Tray Co. reported current earnings of $560,000 while paying $56,000 in cash dividends. Sparrish Co. earned $140,000 in net income and distributed $14,000 in dividends. Tray held a 70% interest in Sparrish for several years, an investment that it originally acquired by transferring consideration equal to the book valu...
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Which of the following is a common stock account? A. Common stock and paid-in capital in excess of par B. Common stock only C. Preferred stock and common stock D. Preferred stock and paid-in capital in excess of par
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West Shore Power is considering issuing a 5,000 bond with 10 years maturity and a 9% coupon paid semiannually. If the market interest rate goes down to 7% and the issuer has to pay 4% flotation costs per bond, what will be the approximate total cost of the bond issue if the company must also pay $15,000 in flotation co...
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Calculate. {eq}\bigtriangledown f (x, y, z) \;\text{where}\; f(x, y, z) = e^{-x\cos yz} {/eq}
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