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Use Lagrange multipliers to determine the point on the plane x-2y+3z=6 that is closest to the point (0,5,4).
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Trudeau Company has two product lines: Butter Scissors and Cheesecakes. Budgeted data for next month follows: Butter Cheesecake Sales $145,000$675,000 Variable expenses $60,000$560,000 Contribution margin$85,000$115,000 Fixed expenses Butter $30,000 Fixed expenses Cheesecake $48,000 Segment margin $55,000 $67,000 T...
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Lucky Co. had earnings per share of $150 for 2013 before taking any dilutive securities into consideration. No conversion or exercise of dilutive securities took place in 2013. However, the possible conversion of convertible preference share would have reduced earnings per share to $130. The effect of possible exercise...
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A tax cut of a given amount that is more favorable to lower-income people will: a. increase AD more than a similar tax cut that is less favorable to the poor. b. decrease AD more than a similar tax cut that is less favorable to the poor. c. affect AD in the same way as a similar tax cut that is less favorable to the...
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Moxie Corporation is considering purchasing Regan Company. Projected incremental cash flows will result in a PV of $79.3 million. The appropriate discount rate is 12%. Regan has 10 million shares outstanding and no debt. Regan's current stock price is $18.75. What is the maximum price per share that Moxie should offer?
$7.93
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Calculate the bond equivalent yield on a $100,000 Treasury bill that is trading at $98,500 and matures in 151 days. a. 0.15% b. 1.02% c. 1.45% d. 3.04%
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A company is considering a new dividend policy which will set dividend payments at 70 percent of earnings. This policy would then: i. ensure the company will never run out of earnings. ii. leave the company's P/E ratio unchanged. iii. give shareholders the highest possible return on their investment. iv. will resul...
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Given that $m$ is a positive integer, and the arithmetic sequence $\{a_n\}$ satisfies $$a_{m-1}+a_{m+1}-a_m^2-1=0,$$ then when $m=6$, the radius of the circumcircle of $\triangle OAB$ is
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Let X1 and X2 be two independent and uniformly distributed random variables on {eq}(-1,1) {/eq}. Define {eq}Y=X1+X2 {/eq} and {eq}Z=X1X2 {/eq}. Find the joint density of {eq}(Y,Z) {/eq}. Hint: Consider the transformation {eq}(x1,x2)\rightarrow(y,z) {/eq} where {eq}y=x1+x2 {/eq} and {eq}z=x1x2 {/eq}.
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Which of the following market structures is likely to have the least number of sellers? a) Monopolistic competition. b) Oligopoly. c) Duopoly. d) Monopoly.
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Let {eq}\Phi{/eq} (u,v)=(7u+6v,7u+6v) be a map from the uv-plane to the xy-plane. Describe the image of the line v=4u under {eq}\Phi{/eq} in slope-intercept form. y=
y=x
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Using the following information, calculate the value of the hypergeometric random variable x. N=1000 n=40 k=20 x=4 a. 0.0065 b. 0.0555 c. 0.0105 d. 0.0331 e. 0.0034
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Which of the following is not a function of marketing? A. obtaining inputs B. getting information to customers C. acquiring customers D. communication E. converting customers into consumers
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The table below reports the unemployment rates for the United States from 1990 to 2012. Year Unemployment Rate (Percent) 1990 7.5 1991 8.9 1992 7.5 1993 6.9 1994 6.1 1995 5.6 1996 5.4 ...
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Use the information provided to calculate the direct materials cost variance (round the answer to the nearest dollar). Actual cost of direct materials purchased $38,000 Actual units of finished goods sold 5,000 units Standard cost of finished product $95 per unit Standard units of direct materials 2.00 lbs per unit...
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The members of Delmar, Inc. were complaining about the accuracy of the predetermined overhead rate for the firm's specialty jam joint (the jam is produced in batches). A review of the company's accounting records revealed the following information: Total 100 batches Manufacturing...
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Find the equation (in terms of x and y) of the tangent line to the curve r = 4 sin(4θ) at θ = π/4.
y=x
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Compute the third derivative of {eq}F(x) = \frac{3x}{x + 4} {/eq}.
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What is the probability that an IQ test, which has a mean of 100 and a standard deviation of 16, will contain an IQ of at least 130?
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Suppose $X$ is a random variable with the following mass function: $$P(X=x) = \begin{cases} 1/2, & \text{if $x=-1$} \\ 1/4, & \text{if $x=0$} \\ 1/4, & \text{if $x=1$} \end{cases}$$ What is $E(X^3)$?
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Vander Company had the following results for the year: Sales revenue $1,200,000 Beginning merchandise inventory $108,000 Purchases (at cost) $630,000 Freight-in on purchases $27,000 Ending merchandise inventory $144,000 Calculate the gross profit percentage (assume FIFO for inventory costing). Choose the closest...
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An individual may, by a gift (inter vivos or by will), make the share of another a (0.25, 0.50, or 1.00) interest. A gift of an entire partnership is always a _____ interest. a) 0.25; 0.50 b) 0.25; 1.00 c) 0.50; 0.50 d) 0.50; 1.00 e) 1.00; 1.00
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Hank Corp.'s common stock currently sells for $29 per share. The most recent dividend (Do) was $2.36, and the expected growth rate in dividends per year is 7%. The cost of common equity, Re, is __________%.
15.71%
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ABC Company determines its selling price for the product by adding a markup of $8.25 to its cost. It then takes this full cost and adds a further markup of 20% to arrive at the selling price. If its unit cost is $24, what is its gross profit?
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The exercise involves the analysis of a point source below an idealized plane surface of water 1000 ft wide, 200 ft long, and 10 ft deep. If the source is at a location on the plane surface where x = 100 ft, y = 10 ft, and z = -5 ft and has a flow rate of 2000 gpm, calculate the total concentration flux at the bottom o...
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As disposable income increases, average propensity to consume A. increases. B. decreases. C. rises first and then falls. D. falls first and then rises. E. does not change.
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Which of the following is true? a. A constant returns to scale case will occur if there are economies of scale in all input factors. b. In a decreasing returns to scale case, there will be economies of scale in all input factors. c. An increasing returns to scale case will occur if there are economies of scale in al...
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Find the antiderivative of f(t) = 8t^3 - 3t^2 + 5t - 7
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In 2017, Trout Corporation constructed assets which cost $1,000,000. The weighted-average accumulated expenditures on these assets during 2017 was $600,000. To help pay for construction, Trout Corporation borrowed $440,000 at 10% on January 1, 2017. Funds not necessary for construction were invested in short-term secur...
c
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Two firms with identical asset structures are considering issuing debt with the proceeds to be used to repurchase stock. Firm U is unlevered while firm L is levered (i.e., Firm L has debt outstanding). In comparing the effects of the repurchases, which of the following statements is correct? Assume there are no tax eff...
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Compute the integral by changing to polar coordinates. {eq}\int \int_D 4xy^2 dA, where D is the region that lies inside the cylinder x^2 + y^2 = 4 and outside the cylinder x^2 + y^2 = 1.
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Davies Company uses the LIFO inventory method. At the beginning of the year, the inventory was $580,000 and at the end of the year, the inventory was $555,000. What effect does this change in inventory have on the company's net income? A. decreases net income B. increases net income C. no effect on net income
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Suppose there are two stocks in the market, and Stock A has expected return of 20%, volatility of 25% and a correlation of 50% with the market. If the market's expected return is 15%, and its volatility is 20% and the risk-free rate is 5.25%, then, according to the CAPM, the expected return of stock A should be? (show ...
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$32,000 was deposited in cash in a bank. The currency is then withdrawn and $140,000 worth of deposits are made to the bank accounts of private individuals. Which of the following would be true? a. M1 decreased by $140,000. b. M2 decreased by $140,000. c. M2 increased by $108,000. d. M3 increased by $108,000.
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If the correlation between two stocks is +1, then a portfolio combining these two stocks will have a variance that is: A. is less than the weighted average of the two individual variances. B. is greater than the weighted average of the two individual variances. C. equal to the weighted average of the two individual ...
C
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XYZ Corp., a manufacturer has two divisions that had the following operating results for last year: Division A Division B Total contribution margin $800,000 $700,000 Contribution margin ratio 30% 45% Sales $1,900,000 $1,600,000 Con...
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High inventory turnover indicates that a company: a. has little in the way of excess inventory. b. places an emphasis on customer service. c. does not keep up with fashion trends. d. makes its products with high precision.
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A foreign currency is expected to have a fixed price in domestic currency over the next three months. Suppose the domestic risk-free rate is 2%, the foreign risk-free rate is 1%, and the current exchange rate is 1.00. What is the expected exchange rate at maturity in three months, assuming the interest rate parity hol...
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Clover Sweet Company uses the weighted-average method in its process costing system. Information for the month of February concerning Department A, the first stage of the company's production process, follows: Materials Conversion costs Work in process, beginning $ 5,600 $ 3,600 ...
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Evaluate the double integral {eq}\displaystyle \ \int\int_R \frac {1}{(2x+3y)^2} \ dA {/eq} over the rectangle {eq}\displaystyle \ R = \{(x,y)| \ \ 0 \leq x \leq 2, 0 \leq y \leq 1\} {/eq}.
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The term "modernism" has come to be used synonymously with the term: a. perspectivism b. enlightenment c. postmodernism d. romanticism
b
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Last year, your firm's dividend payments were $4 per share and its earnings were $7 per share. You expect next year's dividend to be $4.1 per share. What is your estimate of next year's earnings if the company's return on equity is 17%?
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As interest rates increase, the _____. a. market price of bonds with a fixed coupon rate decreases b. number of bonds outstanding for a given bond issue decreases c. present value of coupons paid on a bond decreases d. present value of a bond's face value decreases
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The sales volume variance for variable costs is: a. 4,000 U b. 6,400 U c. 1,800 F d. 5,600 U Actual variable overhead: $26,400 Standard variable overhead: $25,600 Actual units produced: 1,600 Standard units produced: 1,550 Variable overhead efficiency variance: $2,400 U
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Galaxy United, Inc. 2009 Income Statement ($ in millions) Net Sales $8,500 Less: Cost of goods sold 7,190 Less: Depreciation 410 Earnings before interest and taxes 900 Less: Interest paid 82 Taxable Income 818 Le...
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What is the present value of a series of $1150 payments made every year forever, if the discount rate is 13%?
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Compute the Euler totient function $\phi(3661)$.
3132
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The future value factor for an annuity is calculated using which formula? a. (FV i%, n) x (PV i%, n) b. (PV i%, n) x (FV i%, n) c. [(1 + i) - 1] / i d. [(1 + i) n - 1] / i e. (1 + i) - (PV i%, n)
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Kelln Inc. buys and sells investments for cash. Management of Kelln classifies its investments as available for sale. On January 1, 2016, Kelln owns 6,000 shares of the common stock of Sainz, Inc., which it purchased on January 1, 2014, at a cost of $65 per share. On June 15, 2016, Kelln sold 3,000 shares of Sainz comm...
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Which of the following will always occur in a monopolistic market in long-run equilibrium? a. P>MC b. P>AC c. MR>MC d. MR>AC
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Given the following data, what is the residual income? Income $154,000 Average operating assets $700,000 Hurdle rate 15% A. $33,600 B. $77,000 C. $154,000 D. $112,000
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A company has 15,000 shares of $1 par value common stock issued and outstanding. The stock has a market value of $50 per share. The company also has $100,000 of 6% bonds payable. If the market rate of interest is 8%, what is the total dollar amount of the debt component of the diluted earnings per share? A. $73,463 B...
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I am trying to prove that the global maxima of $f(x_1,x_2,...,x_n)=(x_1x_2···x_n)^2$, subject to $\lVert(x_1,x_2,...,x_n)\rVert_2=r$ is $(r^2/n)^n$ I know I have to find the critical points of the Lagrange function, that is $$F(x_1,x_2,...,x_n,\lambda)=(x_1x_2···x_n)^2+\lambda(\sqrt{\sum_{i=1}^nx_i^2}-r)$$ In order to ...
(r^2/n)^n
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Jackson Company purchased a computer for $20,000. The estimated useful life of the computer is five years and it has no residual value. Assume straight-line depreciation is being used. If the computer was sold at the end of the fourth year for $5,000, the gain or loss on disposal is: a. $6,000 loss b. $5,000 gain c....
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A company is deciding between a debt or equity financing. Their current capital structure has a debt ratio of 0.3. Their current cost of equity is 15%. Their current pretax cost of debt is 9%. The corporate tax rate is 35%. Unlevered cost of capital is 14.38%. If they change their capital structure to have a debt ratio...
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Solve for x using PV formula: Present Value = 14,285.71, Periodic Interest Rate = 3.5%, Number of Periods = 8, Payment Amount = 0
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Which of the following statements about psychographics is most true? a. Psychographics is another name for the analysis of consumer lifestyles. b. It is useful in segmenting and targeting consumers for new products. c. SRI Consulting Business Intelligence provides a psychographic system. d. Psychographics combines ...
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ABC Company sold a delivery van for $10,000 cash. The company had owned the delivery vehicle for two complete years when it was sold. The estimated useful life of the vehicle was four years and the residual value was $Nil. Accumulated depreciation at the time of the sale was $20,000. Which of the following correctly re...
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The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people uses the new toothpaste for 6 months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a 6-month checkup is 1.73 (σ = 1....
-1.59
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$$\lim_{(x,y)\to(0,0)}\frac{(\sin x)^2}{\sqrt{x^2+y^2}}$$ How can I prove that this limit is equal to 0 using the epsilon-delta definition?
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Food costs make up the largest portion of the expenses of operating a banquet center. An increase in the price of food will: A. cause the marginal cost and the average variable cost curves to shift upward. B. have no effect on the marginal cost and the average variable cost curves. C. cause the marginal cost curve t...
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Two firms, Alpha Corp. and Beta Corp., both selling the same product and both having service department cost of $2,000,000, have provided the following information: Alpha Corp. Beta Corp. Sales (total) $800,000 $100,000 Service department cost allocated 100,000 2...
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Parker Inc. uses the perpetual inventory method. On March 1, Parker had an inventory of 116 units with a unit cost of $40. On March 4, they purchased 194 units of inventory with a unit cost of $52. On March 10, they sold 160 units. Using the weighted average method, what is the amount of Cost of Goods Sold (COGS) on Ma...
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A U.S. investor buys shares of a Japanese company. The stock price goes up, but the dollar declines over the period. The investor's return in dollars will be: a. higher than if stock prices and the dollar had both risen. b. lower than if the stock price and the dollar had both fallen. c. the same as if the stock pri...
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Manley operates a law practice on the accrual method and calendar year. At the beginning of the year, Manely's firm had an allowance for doubtful accounts with a balance of $15,000. At the end of the year, Manley recorded bad debt expense of $23,000 on his income statement and the balance of the allowance for doubtful ...
E
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Which of the following are examples of long-run fixed costs? a. mortgage payments b. hourly wage costs c. payments for production inputs d. none of the above
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Maximize f(x,y) = x^2 + y^2 subject to the constraints x+y=36 and x-y=4.
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Axel Corporation is expected to maintain a constant 3.5 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 5.2 percent, what is the required return on the company's stock?
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In a Poisson process with rate $\lambda$, how many total random times $S_1, ..., S_N$ are there before time $t$? Specifically, is it correct to think of this as $N$, the number of arrivals by time $t$, which is a binomial random variable with parameters $(\lambda t, p)$, where $p$ is the probability that an arrival occ...
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How many prophase I cells result from one primary oocyte? a. One b. Two c. Three d. None of the above Please explain why.
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In which of the following steps of the classical model do managers access sources and reasons for potential resistance to the decision? A) monitoring and evaluation results B) implementing the decision C) selecting alternatives D) generating alternatives
B
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Use L'Hopital's rule to find {eq}\lim_{t \rightarrow 0^+} \frac{\ln t}{e^{\ln t} -1} {/eq}
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What is the appropriate solution for the price-elasticity of demand when $x \to 0$ in the function $Q= a \log(b x)$, given that mathematically the elasticity $e = b x$ tends to zero but intuitively it should be -1?
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Which of the following statements regarding option B is false? a) It is a European option. b) Its payoff depends on the performance of the underlying asset. c) The amount of the premium paid for this option increases with an increase in the volatility of the underlying asset. d) Its payoff is determined only on the...
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Use the margin of error, confidence level, and standard deviation to find the minimum sample size required to estimate an unknown population mean, assuming a sample standard deviation of {eq}s = 22{/eq} for the given confidence level and margin of error. Margin of error: {eq}E = 4{/eq}; confidence level: 90%.
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How do you find the integral of #(e^x+e^(-x))/2 dx#?
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An order size increases, total A. inventory costs will increase, reach a maximum and then quickly decrease B. inventory costs will decrease, reach a minimum and then increase C. ordering costs will initially increase while total carrying costs will continue to decrease D. carrying costs decreases while the total o...
B
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Consider a competitive constant-cost industry with many identical firms (i.e. firms with identical U-shaped cost curves). The demand curve in this market is downward sloping, and the market is currently in long-run equilibrium. Assume that there is an increase in demand, ceteris paribus. Compared to the initial long-ru...
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A private good is that: a) Private firms produce the goods. b) Can be provided efficiently by a non-profit organization. c) Can be provided efficiently by either private or public firms. d) Has private cost as well as private benefits.
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Suppose that Apple and the investors buying the firm's bonds both expect a 4% inflation rate for the year. Further, suppose the nominal interest rate on bonds is 8% and the expected real interest rate is 4%. Now suppose that a year after the investors purchase the bonds, the inflation rate turns out to be 3%, rather th...
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The average variable cost curve is U-shaped because of: A. the law of demand. B. output-related fixed costs. C. economies of scale. D. the law of diminishing returns. E. minimum efficient scale.
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What is the likelihood of a sample mean between $3.08 and $3.16, given that the mean price per gallon of regular gas is $3.10 with a population standard deviation of $0.20 and a random sample of 16 gasoline stations is selected?
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One section of a conducting rod of radius {eq}R_{1} {/eq} = 1.46 mm & length L = 11.20 m is inside a thin-walled coaxial conducting cylindrical shell of radius {eq}R_{2} {/eq} = 12.3 mm and the same length L. The net charge on the rod is {eq}Q_{1} {/eq} = +3.73 x 10{eq}^{-12} {/eq} C; that on the shell is {eq}Q_{2}...
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A company currently has 100,000 shares of $6 par value common stock outstanding. The stock has been authorized for the issuance of an additional 50,000 shares. In its recent financial statements, the company reported a deficit accumulated during the current year in excess of par of $160,000. The market value per share...
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A spherical shell of radius 2cm has a thin hole drilled through its center. The hole has a radius 2mm. A total charge of -6 nC is distributed uniformly throughout the material contained in the shell. What is the charge density, charge per unit volume, inside the shell, in nC/m$^3$? Use ϵ0 = 8.85419*10$^{-12}$ C$^2$/N/m...
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Nancy's Sweet Acacia Corporation had a beginning inventory of 15,000 shares of common stock with a total par value of $150,000. During the year, 5,000 shares of common stock were sold for $5 per share and 7,500 shares of common stock were reacquired for $4 per share. The company also declared and paid cash dividends of...
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In order to produce a public good a. only the government can produce it. b. it must be produced at a minimum cost. c. it must be supplied to all those who demand it. d. It is not possible to exclude those who do not pay for it from using it.
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Company X has a beta of 1.6, while Company Ys beta is 0.7. The risk-free rate is 7 percent, and the required rate of return on an average stock is 12 percent. Now the expected rate of inflation built into rRF rises by 1 percentage point, the real risk-free rate remains constant, the required return on the market rises ...
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The accounts receivable of a large department store are normally distributed with a mean of $250 and a standard deviation of $80. If a random sample of 225 accounts is chosen, what is the probability that the mean of the sample is between $232 and $268?
0.9992
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Find $\lim_{n \rightarrow +\infty} n\left(\dfrac{1}{(n + 1)^2} + \dfrac{1}{(n + 2)^2} + \dfrac{1}{(n + 3)^2} + \cdots + \dfrac{1}{(n + n)^2}\right)$. Is it correct to calculate the limit of the function $\dfrac{1}{(n + k)^2} $ when $n \rightarrow +\infty$ as $\dfrac{1}{n^2}$, and then say that the limit of the sum is $...
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The following data are extracted from the equity section of the balance sheet of Ebbs Corporation: Dec. 31, Yr 6 Dec. 31, Yr 7 Common stock ($2 par value) $100,000 $102,000 Paid-in capital in excess of par 50,000 58,000 Retained earnings100,000 104,600 During Yr 7, the corporation declared and paid cash dividends of...
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Given the integral $\int_0^{2\pi r} \frac{1}{r + a \cos(x)}dx = \frac{2\pi}{\sqrt{4a^2+1}} $, prove that $\int_0^{2\pi r} \frac{1}{(r + a \cos(x))^n}dx = \frac{2\pi}{\sqrt{4a^2+1}}\frac{1}{(r + a)^n}P_{n-1}\left(\frac{r}{\sqrt{4a^2+1}}\right)$ for $n \geq 1$, where $P_n(x)$ is the $n$th Legendre polynomial, and $a, r >...
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What is the present value of an annuity of $2,600 per year for five years at an interest rate of 8%?
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The Market Portfolio a) consists of all publicly traded stocks b) is rare because it is impossible to know all the possible trades in existence c) consists of all trading possibilities d) both A and C are correct e) none of the above
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Which of the following statements is true? A. A primary advantage of using the dividend growth model approach to estimating the cost of equity is its simplicity. A disadvantage of using the dividend growth model approach is that it does not explicitly consider risk. B. A firm that uses its WACC as a cutoff will tend...
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Which of the following is not one of the reasons monetarists believe discretionary fiscal or monetary policy interventions are ineffective? a. Discretionary monetary policy can destabilize the economy. b. Short-run economic conditions have no impact on macroeconomic fluctuations. c. Effective monetary policy causes ...
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If a firm is expected to pay a $10 dividend at the end of this year, a $15 dividend in two years, and a $20 dividend in three years, and its stock has a constant required return of 10%, what is the value of the stock today?
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Which of the following statements are correct? a. Risk-taking may yield a positive result. b. Risk is a future event. c. Risk is avoidable. d. Risk can never be eliminated.
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Evaluate {eq}\int_C F. dr where {eq}F = (zy, xz, xy) and the curve {eq}C is given by the vector function {eq}r(t) = (t^2,t^2,t), 0 \leq t \leq 1
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Stone Shoe Co. has concluded that additional equity financing will be needed to expand operations and that the needed funds will be best obtained through a rights offering. It has correctly determined that as a result of the rights offering, the share price will fall from $51 to $47.80 ($51 is the "rights-on" price; $...
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