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Find the index $[G:H]$ of $H=\langle3\rangle$ where $G= \mathbb{Z}/20\mathbb{Z}$. How can I find the order of $\mathbb{Z}/20\mathbb{Z}$ in order to find the index?
1
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How can I show that the integral $\int_{0}^{\infty} \frac{1}{(x^2+1)^{n+1}} \, dx \leq \int_{0}^{\infty} \frac{1}{(x^2+1)^n} \, dx$ when $n > 0$, given that I haven't had much luck applying the Comparison Test or the Limit Comparison Test?
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A test of linear regression is being conducted with a critical value of 2.045. The regression equation is found to be Y = 44.121 + 11.702 X and the standard error of estimate 6.129. Which of the following statements is correct? a. The slope is not statistically significant. b. The slope is statistically significant. ...
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Xytex Products just paid a dividend of $2.54 per share, and the stock currently sells for $36. If the discount rate is 11 percent, what is the dividend growth rate?
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The following data have been provided by the Heidenescher Corporation: Actual machine hours 8,500 Standard machine hours per unit of output 1.8 machine hours per unit Raw materials standard 13 pounds per unit Raw materials standard 5.10 pounds per pound Raw materials used 15,000 pounds Raw materials efficiency varian...
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Which of the following items are exclusions from gross income? Select all that apply. a. Alimony payments received. b. Damages award received by the taxpayer for personal physical injury - none were punitive damages. c. A new golf cart won in a church raffle. d. Amount collected on a loan previously made to a colle...
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Consider a solution containing 0.100 M fluoride ions and 0.126 M hydrogen fluoride. Calculate the concentration of fluoride ions after the addition of 5.00 mL of 0.100 M HCl to 25.0 mL of this solution. Use the Henderson-Hasslebalch equation.
0.0667 M
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A coupon bond that pays interest of 4% annually has a par value of $1,000, matures in 5 years, and is selling today at $785. The actual yield to maturity on this bond is a) 0.2% b) 8.8% c) 9.1% d) 9.6%
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What are some examples of functions where $F(b)-F(a) \neq \int_{a}^{b} f(x) \, dx$, and why does this happen?
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Evaluate the triple integral over the box {eq}D=\{(x,y,z)| -2<x<2, 0<y<3, 1<z<4\} $$\int \int_D \int (xy+3xz^2+y)dV
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A long-term employment contract is: a. always desirable when there is a perfect labor market. b. sometimes desirable when there are no unions in the labor market. c. sometimes desirable when there is a monopsony in the labor market. d. always desirable when there is a monopsony in the labor market.
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Let R be the region defined by the inequalities x^2 + y^2 ≤ 1 and 1 ≤ x ≤ 1. The integral ∫∫_R (6xy) dxdy is equal to __.
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If there is an excess demand for money, then _____. (a) there is also an excess supply of bonds (b) the interest rate is lower than the equilibrium value (c) the interest rate will rise (d) All of the above (e) None of the above.
c
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The following information applies to All-Match Golf Corp. for 2012: Total assets $600,000 Total shareholders' equity $400,000 Total debt $200,000 Interest paid $10,000 Current assets $100,000 Current liabilities $50,000 Net income $200,000 All match has a tax rate of 35%. What is All-Match's times inter...
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Roberto Corporation uses the FIFO method in its process costing system. Data concerning the first processing department for the most recent month are listed below: Beginning work in process inventory: Units in the beginning work in process inventory 200 Units started into production during the month 2,500 Units tran...
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A person just graduated and planned to work for 10 years and then retire. As soon as the person retired, they would need $100,000/year for 20 years to travel and have a good retirement. How much must be invested each year if the investments earn 8% compounded annually? a. 3509 b. 4869 c. 2896 d. 4079
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Given the Fourier series: $$\frac{4}{\pi}\sum_{k=1}^{\infty}\frac{\sin(kx)}{k}$$ find the sum of this series for $x = \frac{\pi}{2}$. You may use the fact that $\sum_{k=1}^{\infty}\frac{1}{k^2} = \frac{\pi^2}{6}$ and don't directly substitute $x = \frac{\pi}{2}$ into the original series, as it leads to an indeterminate...
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You have $59,681.90 in a brokerage account, and you plan to deposit an additional $7,500 at the end of every future year until your account totals $400,000. You expect to earn 13 percent annually on the account. How many years will it take to reach your goal?
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Worldwide Travel Service has made an investment in certain equipment that cost the company $307,100. The equipment is expected to generate cash inflows of $50,000 each year. How many years will the equipment have to be used in order to provide the company with a 14% return on its investment?
15
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Calculate the iterated integral. {eq}\int\int_D \ln(x^2 + 1) \, dA {/eq} where {eq}D{/eq} is the region in the first quadrant bounded by the parabolas {eq}x^2 + y^2 = 25{/eq} and {eq}x^2 + y^2 = 16{/eq}, and the lines {eq}y = 0, \; y = x{/eq} (the region {eq}D{/eq} is the area in the first quadrant between the two par...
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For the following, find the area in the appropriate tail of the t distribution. a. t = 3.387 and n = 20 b. t = 3.012 and n = 6 c. t = -2.567 and n = 28 d. t = -1.892 and n = 43 e. t = 3.232 and n = 12
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Which of the following is true of the cash flow approach? a. It involves adding depreciation expense to net income in order to find the operating cash flow. b. It subtracts all non-cash charges (interest, and especially, depreciation expense) from net income to determine cash flow. c. It involves multiplying the cha...
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Carruthers Co. sold for {eq}\$117,600 {/eq} a machine with a net book value of {eq}\$121,500 {/eq}. There is no evidence that the fair market value will recover in the future. At the time of the sale, Carruthers should recognize a loss of: A. {eq}\$3,900 {/eq}. B. {eq}\$0 {/eq}. C. {eq}\$121,500 {/eq}. D. {eq}...
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Thiret Inc. uses the indirect method to prepare its statement of cash flows. Refer to the following sections of the comparative balance sheet: Dec. 31, 2009 Dec. 31, 2008 Accounts receivable $240,000 $175,000 Inventory $390,000 $350,000 Prepaid expenses $30,000 $25,000 Accounts payable $180,000 $130,000 Wages payab...
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Which of the following can be used to make recombinant DNA? A. protoplast fusion B. tungsten "bullets" C. microinjection D. transformation E. all of the above
E
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The degree to which an organization rewards its employees based on individual and team performance is known as: A) individualist behavior. B) group behavior. C) task behavior. D) reward behavior.
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How many juggling states are there for three balls?
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Baker Corporation has provided the following information concerning a capital budgeting project: Year 1Year 2Year 3Year 4 Investment required in equipment$(120,000) Salvage value of equipment$30,000 Working capital requirement$30,000 Annual sales$500,000$500,000$500,000$500,000 Annual cash operating expenses$400,00...
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Evaluate $\frac{3}{x+1}$ when $x = \frac{4}{3}$.
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Assume the current is a competitive constant cost industry with 1000 firms. Each firm has the following cost structure: Quantity Marginal Cost Average Variable Cost Average Total Cost 0 $0 $0 $30 1 $5 $5 $35 2 $10 $7.5 $40 3 $15 $10 $45 4 $20 $12.5 $50 5 $25 $15 $55 6 $30 $17.5 $60 7 $35 $20 $65 8 $40 $22.5 $70 9 $45 ...
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We have to find $\det(A^{2}+A^{T})$. It is given that eigenvalues of $A$ are $1,2,3$. Prove it for general $A$.
144
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Shown below is a condensed income statement for Prather Corporation for the past year. Actual Budgeted Sales $435,000 $400,000 Variable expenses 163,000 140,000 Contribution margin 272,000 260,000 Fixed expenses 222,000 ...
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A stationary observer on Earth observes spaceships A and B moving in the same direction toward the Earth. Spaceship A has speed 0.50c and spaceship B has speed 0.80c. What is the velocity of spaceship A as measured by an observer at rest in spaceship B?
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P Corporation owns 80% of the outstanding common stock of S Corporation. In Year 1, P sold merchandise to S for $450,000 that cost P only $300,000. At the end of Year 1, 20% of the merchandise remained in S's inventory. What is the consolidated adjustment for the intercompany transfer of merchandise to be recorded in ...
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I know that $${2n \choose n} \sim \frac{4^n}{\sqrt{n\pi}}$$ but I don't know how to use that information to find the limit $$\lim_{n\rightarrow \infty} \frac{{2n \choose n}^{1/n}}{2}$$
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On which axis is the aggregate demand curve downward sloping? a. it is downward sloping along the vertical axis, b. it is downward sloping along the horizontal axis, c. it is upward sloping along the horizontal axis, d. it is upward sloping along the vertical axis.
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The Ace Company is considering investing in a piece of property that costs $105,000. The property will return a constant cash flow forever. If the firm s cost of capital is 9% and the corporate tax rate is over 40%, what is the minimum after-tax cash flow that would make the investment acceptable to Ace?
$9,450
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A single firm in an industry is able to produce compact discs at a lower opportunity cost than other firms in the industry. This firm has __________ and, in the long run, it will earn __________. a) economies of scale; above-normal profit b) economies of scale; only normal profit c) economies of scope; above-normal ...
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If the index of refraction of a medium is 2, then the angle of refraction will always be {eq}\frac {1}{2} {/eq} the angle of incidence. True or False?
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Superior, Inc. expects sales for next year to be $3.1 million. Construct a pro forma income statement assuming the following. The current income statement (found on the Internet) for The Superiors Corporation (www.superior-inc.com) for the year ended 12/31/15 for reference. a. There will be no change in fixed costs. ...
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Compared to a plant with a P/E ratio of 15, a plant with a P/E ratio of 30 a. is expected to earn 30 percent more in the future. b. is expected to decline in value over the next year. c. is expected to pay out a larger proportion of earnings as dividends. d. should have an expected higher return on equity. e. none...
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You have been asked by the president of your company to evaluate the proposed acquisition of a new special-purpose truck for $240,000. The truck falls into the MACRS 7-year class, and it will be sold after 7 years for $24,000. Use of the truck will require an increase in NWC (spare parts inventory) of $5,400. The truck...
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Find the area of the region cut from the plane {eq}6x + 2y + 3z = 8{/eq} by the cylinder whose walls are {eq}x = y^2{/eq} and {eq}x = 18 - y^2{/eq}.
168
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The amount of loss absorption for a company with $100,000 in before-tax income, 10,000 in depreciation expense, and a tax rate of 30% is: A. $20,000 B. $10,000 C. $30,000 D. $15,000
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Which of the following statements is correct with respect to the market share rule (MRR)? a. If the top 60 percent of customers account for 80 percent of the revenue, then the law will force the company to stop selling to the lowest 40 percent of customers. b. If a company does not wish to cut off sales to the lowest...
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Use Stokes' Theorem to evaluate $\int_C F \cdot dr$ where $F(x, y, z) = -5x^2y\mathbf{i} + 3y^2 \mathbf{j} +5xz^2 \mathbf{k}$ and C is the triangle with vertices $(0, 0, 0)$, $(7, 7, 0)$ and $(0, 0, 4)$ oriented counterclockwise as viewed from above.
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The estimate of the population proportion should be within plus or minus 0.06, with a 95% level of confidence. The best estimate of the population proportion is 0.17. How large a sample is required?
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A country's economic strategy that focuses on creative destruction is a strategy that: a) reduces the cost of moving goods across borders. b) promotes free trade. c) promotes the advance of technology. d) reduces government regulation of business.
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Which of the following $4,000 face-value securities would you prefer to be selling? Assume n = 20 for all instruments. a. a 6% coupon bond selling for $6,500 b. a 10% coupon bond selling for $4,500 c. a 12% coupon bond selling for $4,500 d. a 6% coupon bond selling for $3,000 e. a 10% coupon bond selling for $5,00...
c
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Which of the following fiscal policies would the Fed most likely use to reduce inflation? Select one. a. The Fed would open a window of fiscal restraint. b. The Fed would fully accommodate a contractionary fiscal policy. c. The Fed would keep the money supply constant to ensure that any changes in the interest rate ...
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A sample of size 15 taken from a normally distributed population has a sample variance of 30. What is the probability that the population variance is less than 10? a. 0.0129 b. 0.0200 c. 0.1075 d. 0.0800
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Find the integral of: ∫(1 / sqrt(1+x) + 1 / sqrt(1-x)) dx
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Differentiate $f(x)=(x^2+1)\sin(1/x)$ w.r.t $x$ for $x \neq 0$. Why does Mathematica return $2x\sin(1/x)-(x^2+1)\cos(1/x)$ for the derivative, while this function is not differentiable at $x=0$ and not even continuous there?
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How would I integrate around $\left|z\right|=\frac{1}{2}$ $$\frac{1}{2 \pi i}\int_{\lvert z \rvert = \frac{1}{2}} \frac{\sin z}{z^2}dz$$
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If $$x + \mathcal{N}(0,\,1) = 6$$ $$y + \mathcal{N}(0,\,1) = 7.5$$ $$\left|{y-x}\right| < 1$$ then what is the median of $y$?
7.5
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Dising Systems uses two measures of activity, machine-hours and number of orders processed, in the cost formulas in its two cost categories. The cost formulas for its manufacturing overhead and labor wages are given below: Manufacturing overhead: Variable cost per machine-hour$5.68 Variable cost per order processed$...
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What is the present value of $1,000 per year for 10 years at a discount rate of 15 percent?
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Omega Services, Inc., is considering the purchase of a machine that would cost $280,000 and would have a useful life of 8 years. The machine would have no salvage value. The machine would reduce labor and other operating costs by $45,500 per year. The internal rate of return on the investment in the new machine is clos...
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In the perfectly competitive case, the firm's average revenue curve, A. becomes smaller as output increases. B. is a positively sloped curve that begins from the origin and has the same slope as the firm's supply curve. C. has the same slope as the demand curve facing the firm and is horizontal. D. intersects the a...
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Suppose the government purchases increase and consumption decreases by the same amount. Assume the MPC is 0.80 and there are no income taxes. After the multiplier effect is complete, aggregate demand will have _____. A) increased by 5 times the amount of the government expenditure increase B) decreased by 4 times the...
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Compute the area of the surface with parametric equations x = u^2, y = uv, z = \frac{1}{2}v^2, 0 \leq u \leq 3, 0 \leq v \leq 3.
81
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On January 2, 2010, Donner Company paid $784,800 for all of the outstanding common shares of Staley Company. Staley reported a balance in its common stock account of $18,400 and retained earnings of $38,900 on January 2, 2010. During 2010 Staley reported net income of $35,800 and paid cash dividends of $12,000. At Dec...
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Identify the related transaction assertion to the following question: Are shipping documents authorized and prepared for goods returned to vendors? A. occurrence B. completeness C. accuracy D. classification E. cutoff
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Watkins Corporation purchased a machine on December 31, 2012, for $165,660. The machine is expected to have a five-year useful life, with no residual value. Due to technological advances, the estimated useful life was reduced to four years on January 1, 2017. The company uses the straight-line method to calculate depre...
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Suppose a manufacturing company makes a product that the selling price is $350 per unit, and the variable cost is $270 per unit. Fixed costs total $108,000. What is the breakeven point for this company? (Solve for the quantity, Q.)
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The December 31, 2008, adjusted trial balance of Hawkeye Supply Company showed the following balances: merchandise inventory $60,000, and inventory held on consignment $110,000. These balances have not been adjusted for any of the following: a. Merchandise costing $6,500 was returned to the supplier before any of the ...
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What range would you expect to see 95 percent of the time if long-term government bonds have a mean return of 6.3 percent and a standard deviation of 9 percent and the returns are normally distributed?
-11.7% to 24.3%
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Jorge is the project manager for a large construction project for a luxury resort. The project manager has decided that his company should internationalize the project. The project manager wants to assign a level of autonomy to the project managers in the other countries involved with the project. The project manager w...
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In the theory of the firm, firms choose to produce at that level of output where price equals: A) marginal revenue B) marginal revenue minus marginal cost C) total revenue D) marginal cost
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A company wants to have $53,195 in their account at the end of 5 years. They plan to accumulate that amount by making annual deposits of $12,000 at the beginning of each year. If the account pays interest at 8% compounded annually, how much will be in the account at the end of 5 years?
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Interest rate swaps and options, in common, have what characteristic? A) They are both financial derivative instruments. B) They both derive their value from the performance of one or more underlying assets. C) They are both a form of insurance. D) A, B and C.
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Determine the longest interval in which the given initial value problem is certain to have a unique solution. t(t - 4)y' + y = 3t, y(2) = 1 A) 0 < t < 4 B) -2 < t < 2 C) t > 4 D) t < 0 E) All real t
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?in _____, different memory images may become combined or confused with one another. a. ?unconscious retrieval b. ?subconscious retrieval c. ?unconscious transference d. ?transference confusion
c
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A random sample of size 12 from a normal distribution has a mean of 45 and a standard deviation of 7. A random sample of size 16 from a second normal distribution has a mean of 52 and a standard deviation of 9. Assume the two variances are equal. What is the 90% confidence interval for the difference between the two po...
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The cross-price elasticity coefficient is negative for: a. substitute goods b. complementary goods c. normal goods d. inferior goods
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Find the probability that a financial manager earns at least $45 per hour, given that the mean hourly pay rate for financial managers in the East North Central region is $48.93 with a standard deviation of $2.76 and pay rates are normally distributed.
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The common stock is preferred over bonds because: a. it represents ownership in the firm. b. it has a higher claim on assets in the case of liquidation. c. it receives tax benefits. d. it has no default risk.
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A portfolio is composed of two stocks A and B. Stock A has a standard deviation of return of 24 percent while stock B has a standard deviation of return of 18 percent. Stock A comprises 60 percent of the portfolio while stock B comprises 40 percent. If the variance of return on the portfolio is .0380, what is the corre...
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Show that y = x^3+3x+1 satisfies the differential equation y''' +xy'' -2y' = 0
0
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On January 1 of Year 1, Congo Express Airways issued $3,750,000 of 7% bonds that pay interest semiannually on January 1 and July 1. The bond issue price is $3,480,990, and the market rate of interest for similar bonds is 8%. The bond premium or discount is being amortized using the straight-line method at a rate of $7,...
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A popular budget forecasting approach that makes a series of zero-coupon bond forecasts is known as: a. expert surveys b. the cash flow approach c. buy and hold analysis d. CAFE analysis
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You recently purchased a stock that is expected to pay $1.30 per share in dividends for the next three years. The stock currently has a market value of $45 a share. What is your expected return on this stock? a) 4.6% b) 9.2% c) 10.7% d) 15.4% e) 22.1%
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A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 10%. Assume that the liquidity premium on the corporate bond is 0.5%, and the maturity risk premium on the 10-year corporate bond is 1%. What is the default risk premium on the corporate bond? Round your answer to two d...
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Divestment may take the form of either: A. divesting a non-core asset. B. selling off an unprofitable asset. C. creating a new division. D. splitting off a new operating unit. E. both a and d.
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Grill Company had the following data available for 2015 (before making any adjustments): Accounts receivable, 12/31/15 $343,000 (Dr.) Allowance for doubtful accounts, 12/31/15 3,800 (Cr.) Net credit sales, 2015 829,000 (Cr.) Accounts written off during 2015 21,000 Grill expects that it will not be able to col...
$23,640
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Find the maximum and minimum values of the function {eq}f(x,y) = 4x^2 - 2y{/eq}, where x and y are the coordinates of points in the region between the parabolas {eq}y = 4 - x^2{/eq} and {eq}y = x^2 + 1{/eq}.
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Consider the market for a standard-sized cardboard box. The demand function is q = 1,200 - 200p, where q measures the number of boxes demanded, in thousands of boxes, and p measures the price of a box in dollars. The supply function is q = 200 + 300p. Suppose a tax is imposed on these items. Let the tax be $1.4 per ite...
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Calculate the probability that the mean number of business bankruptcies per month is less than 2400, given that the mean number of business bankruptcies per month in the United States is 5900 and the standard deviation is 400, and the distribution is positively skewed.
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Leisure Lodge Corporation has a 10 percent coupon bond outstanding with a current market price of $915.42. The yield to maturity is 11.22 percent and the face value is $1,000. Interest is paid semiannually. The bond matures in: A. 3 years. B. 4 years. C. 6 years. D. 8 years. E. 10 years.
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A company declared a cash dividend on its common stock on December 15, year 1, payable on January 12, year 2. How would this dividend affect stockholders' equity on the following dates? December 15, Year 1 December 31, Year 1 January 12, Year 2 a. Decrease, No effect, Decrease b. Decrease, No effect, No effect c. N...
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The Needy Corporation borrowed $10,000 from Bank Ease. According to the terms of the loan, Needy must pay the bank $400 in interest every three months for the three-year life of the loan, with the principal to be repaid at the maturity of the loan. What effective annual rate is Needy paying?
16.99%
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The buyer: a. pays the full invoice price and increases the stock. b. pays less than the invoice price and increases the stock. c. pays more than the invoice price and increases the stock. d. receives a price discount and increases the stock. e. pays the invoice price and increases the stock.
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Using the single-factor APT model, an investment with a beta of 0.2 has an expected return of 8%. If the risk-free rate is 3%, what is the expected return on the market portfolio? A. 25% B. 11% C. 13% D. 10%
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Compute {eq}\lim_{x\rightarrow 1} \frac {1-\cot (\pi x)}{x-1} {/eq} or show it does not exist.
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Sales volume variance for operating income equals $_____. Sales price, 9.00 per unit Actual results Sales volume 2,200 units Variable costs 5.00 per unit Actual results Sales volume 2,200 units Fixed costs $15,700 per month Operating income $17,600
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When the Bank of Canada sells government securities to a bank, how are the assets of the Bank of Canada affected? A) The amount of the Bank of Canada's government securities increases. B) The bank's reserves held at the Bank of Canada decrease. C) Bank of Canada notes increase. D) The bank's reserves held at the Ba...
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The mean per capita income is $24,863 per annum with a standard deviation of $743 per annum. What is the probability that the sample mean would be less than $24,910 if a sample of 422 persons is randomly selected?
0.9032
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Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5%? Use {eq}\alpha{/eq} = 0.1. Find the sample mean dividend yield.
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Will an increase in the required reserve ratio raise the money multiplier, lower the money multiplier, have no effect on the money multiplier, or cause the money supply to decrease?
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A firm has total current assets of $1,200,000 and total current liabilities of $900,000. The firm has no accumulated depreciation and $100,000 of working capital. If the firm's tax rate is 30% and its required return is 12%, what is the most the firm can spend on depreciation without using any external financing?
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