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Verify the identity {eq}\displaystyle X^2+Z^2+Y^2=\frac{1}{4}(x+z-y)^2+\frac{1}{4}(x-z+y)^2+y^2{/eq} by expanding the squares and collecting like terms. Assume that all variables represent positive numbers.
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Let ABC be a triangle, $\omega$ - its incircle, $r$ - inradius, $p$ - semiperimeter. In the questions, $a,b,c$ are sides of the triangle, $A,B,C$ are angles of the triangle, $a^2+b^2+c^2=p^2+16Rr$. Find the maximal value of $\frac{1}{sin(A/2)}+\frac{1}{sin(B/2)}+\frac{1}{sin(C/2)}$. Note, if the maximal value is expres...
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Simplify using definition of modulus function: {eq}\left| {\left| {x - 3} \right| - \left| {x + 3} \right|} \right| {/eq} if {eq}-3 \leq x \leq 3{/eq}.
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In June 2017, New Corporation purchased a 5-year, 7% bond issued by Arrow Corporation on June 1, 2015, for {eq}\$530,000 {/eq}. The bond has a face value of {eq}\$500,000 {/eq} and pays interest semiannually. The market interest rate is 6%. New uses the straight-line method of amortization. What is the carrying value...
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Lorien Corporation has the following inventory data: 1/1/18 Beginning inventory 20 units at $5.00 1/10/18 Purchases 100 units at $5.40 1/28/18 Purchases 20 units at $5.80 2/14/18 Sales 60 units The weighted average method is used. Assume that a sale occurred on February 14 for 60 units sold at $7.00. What is the a...
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Find the value of $$ \int_0^{\pi} e^{a\cos{t}}\cos{(a\sin{t})}dt $$
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The overhead volume variance will be favorable if the: a. actual overhead is less than the standard overhead b. overhead spending variance is favorable c. standard overhead allocated to production is greater than the budgeted overhead d. standard overhead allocated to production is less than the budgeted overhead
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What is the present value of a $1,000 discount bond with five years to maturity if the yield to maturity is 6%?
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Calculate the derivative with respect to $x$ of the integral $$\int_{0}^{x} \! \sin(\ln(t)) \, \mathrm{d}t.$$
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Drez Company had the following current-year information: Beginning balance of Allowance for Doubtful Accounts$2,500 Write-offs during current year$2,800 Collection of accounts previously written off $200 Bad debt expense$3,200 Ending balance of Accounts Receivable$114,000 Assuming the ending balance of Accounts Recei...
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The accounts payable ledger of Gannon Corp. contains the following information: Date Item Account No. Explanation Debit Credit Balance March 1 Balance 3,800 8 Purchase 14 Book purchases 1,640 5,440 2...
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The {eq}PV {/eq} of a {eq}20 {/eq}-year stream of {eq}\$2,000 {/eq} annual payments (beginning today) that will not be received until the end of year {eq}5 {/eq} is ({eq}R = 7\% {/eq}): a. {eq}\$18,591 {/eq}. b. {eq}\$18,191 {/eq}. c. {eq}\$17,633 {/eq}. d. {eq}\$14,591 {/eq}.
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Forsyth Corporation reported net income of $198,140 for 2014. Forsyth also reported depreciation expense of $45,860 and a gain of $4,580 on the disposal of equipment. The comparative balance sheet shows an increase in accounts receivable of $12,410 for the year, a $16,590 increase in accounts payable, and a $3,380 inc...
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A mother buys a $1000, 15-year maturity bond at its face value of $1000 on January 1, 2012. The bond pays an annual coupon of $100 on January 1 of each year. If the mother plans to sell the bond on May 1, 2016, when the conversion factor for the bond is 0.9228, and the quoted price of a $100 face value T-bond with the ...
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Flexible production systems, just-in-time production, and corporate alliances are all associated with a(n) _____ strategy. A. cost leadership B. customer intimacy C. differentiation D. operational excellence E. product leadership
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Elliott Corporation's net income was $619,000. Elliott Corporation's income tax expense was $175,000. Elliott Corporation issued 2,200 shares of $20 par value common stock for $42 per share during the year ended December 31, 2016. Beginning and ending balances of stockholders' equity were as follows: 2016 2015 Common...
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Galindo Corporation produces large commercial doors for warehouses and other facilities. In the most recent month, the company budgeted production of 5,800 doors. Actual production was 5,700 doors. According to standards, each door requires 5.3 machine-hours. The actual machine-hours for the month were 31,400 machine-h...
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On January 1, 2014, Hess, Inc. acquired all of the outstanding common shares of Acme Inc. for $2,400,000. In 2014, prior to the acquisition, Acme reported net income of $450,000 and declared dividends of $180,000. On January 1, 2014, Acme reported common stock of $2,000,000 and retained earnings of $250,000. Equipment ...
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Davide Inc. reported net income of $135,400 for the year ended December 31, 2016. January 1 balances in accounts receivable and accounts payable were $28,200 and $26,500, respectively. Year-end balances in these accounts were $32,000 and $22,400, respectively. Assuming that all relevant information has been presented, ...
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The demand for a product is more elastic the: A. more broadly defined the product. B. higher the price of the product is. C. less substitutes available for that product. D. smaller the share of a consumer's income the item represents. E. none of the above.
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Let P be a polynomial in the variable X with degree n. At what rate (wrt n) does the number of operations in the following algorithm grow? for k = 0 to n { X : = X; Y : = P; for i = 0 to k - 1 { Y: = Multiply(X,Y) } } output Y
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A project produces a return of 5% in year 1, -10% in year 2, 40% in year 3, and 20% in year 4. What is the average accounting return for this four-year project?
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A multiple-step income statement for May 2014 for Joanna's Specialty Equipment Corporation reveals the following: $ Sales 500,000 Cost of goods sold 200,000 Gross margin 300,000 Salaries expenses 150,000 Depreciation expense ...
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A study found that there is a weak positive correlation between the number of years an employee has been with a company and the number of insurance claims the employee filed in the past year. From this, you can conclude that: a) firing long-term employees will lower the number of claims filed in the future b) long-te...
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The total market value of the common stock of the Albert Company is $6 million, the total value of the debt is $4 million, and that of the preferred stock is $2 million. What is the percentage of the total value of the firm that is equity capital?
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Consider the following cash flow table below. 0 1 2 3 4 5 A $30,000 $10,000 $10,000 $10,000 $10,000 $5,000 B $15,000 $10,000 $25,000 $20,000 $20,000 $25,000 C $5,000 $7,000 $9,000 ...
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Brock Company had the following inventory balances at the beginning and end of November: November 1November 30 Raw Materials$58,000$41,000 Work in Process$59,000$45,000 Finished Goods$123,000$137,000 During November, $416,000 of raw materials (all direct materials) were drawn from inventory and used in production. Th...
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Let {eq}F= \left \langle z,\;x^2,\;y^2 \right \rangle. {/eq} Use the Divergence Theorem to calculate {eq}\int \int_SF\cdot n\,dS, {/eq} where S is the boundary of the region between the cylinder {eq}x^2+y^2=1 {/eq} and the planes {eq}z=-2 {/eq} and {eq}z=4. {/eq}
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In an annuity, there are 20 annual payments of $4,432.10. The first payment is made immediately, and the interest rate is 11%. What is the present value of this annuity? What is the future value of this annuity?
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Sketch the region bounded by the lines y = x, y = x/3, and y = 2. Then express the region's area as an iterated double integral and evaluate the integral.
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When a firm uses the residual income approach to evaluate projects, projects should be accepted if their net present value is _____. A. greater than zero B. less than zero C. equal to zero D. greater than the company's cost of capital
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Bill plans to repay a $25,000 debt with quarterly payments of $1,200 for 23 quarters and a final payment of X at the end of 24th quarter. If the interest rate is 12% per year, compounded quarterly, then find X. Select the correct answer. a. $10,173 b. $14,223 c. $13,070 d. $13,918
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The senior partners at Finson & Company, a boutique investment bank, believe there will be a significant jump in the common stock price of ABC Inc. if a rights offering is held. The current market price of ABC's stock is $58 a share, and there are 100,000 shares outstanding. The company plans to sell 10,000 shares. The...
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Below is productivity data for firm Nearly Done Inc. which purchases resources in a perfectly competitive labor market. Quantity of TP MP_L Unit Price of Product $ 1 4 4 2.00 2 10 6 2.00 3 18 8 2.00 4 ...
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Following is a set of identical transactions. Assuming all counterparties have the same credit rating, which transaction should preferably be executed? A. Buying gas from a trading firm B. Buying gas from a gas producer C. Buying gas from a distributor D. Indifferent between a., b., and c.
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Determine the radius of convergence and the sum of the following power series: $$\sum_{n=1}^\infty 4^n x^n n!$$
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Department A had 4,000 units in work-in-process that were 60% completed at the beginning of the period at a cost of $12,000. 14,000 units of direct materials were added during the period at a cost of $28,700. 13,000 units were completed during the period, and 500 units were 40% completed at the end of the period. All m...
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A major equipment purchase is being considered by the MBA department at IU East. The initial cost is determined to be $400,000. It is estimated that this new equipment will save $75,000 the first year and increase by 5% each year. MARR is 6%. The equipment will have no salvage value over its expected life of 10 years. ...
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Five light bulbs are selected from a batch of ten light bulbs. If the batch contains three defective light bulbs, how many different selections contain exactly two defective light bulbs?
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Use the definition to find {eq}\frac{d}{dx}\ln(3x - 2){/eq}.
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Suppose that in a certain country, the average IQ score of high school students is 110 with a standard deviation of 15. If the scores are normally distributed, about how many people in a class of 60 would you expect to have an IQ score between 85 and 110?
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The cost of constructing a building is $400,000 and its estimated useful life is 5 years. What is its book value after 1 year using the straight-line method of depreciation? a. $320,000 b. $300,000 c. $280,000 d. $160,000
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An electron with energy equal to K1 = 4.19 x 10{eq}^2 {/eq} eV and an electron with energy equal to K2 = 8.31 x 10{eq}^1 {/eq} eV are trapped in a uniform magnetic field and move in circular paths in a plane perpendicular to the magnetic field. What is the ratio (r1/r2) of the radii of their orbits?
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The quantity that a firm can produce and sell at a particular price is called: a. marginal revenue b. revenue c. elasticity of demand d. demand
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A manufacturing company completed and sold 45,000 units of a product. Beginning inventory consisted of 18,000 units, 60% complete. The company started 144,000 units during the period, and ending inventory consisted of 12,000 units, 30% complete. Compute the equivalent units of production using the average cost method.
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Beasley Company acquired 70% of Donovan Company for $600,000 on January 1, 2014. Donovan reported common stock of $400,000 and retained earning of $310,000 on that date. Equipment was undervalued by $40,000 and buildings were undervalued by $50,000. Each having a 10-year remaining life. Any excess consideration transfe...
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On July 1, 2011, Alton Corporation sells ten-year, 12%, bonds with a face value of $300,000 for {eq}\$345,000 {/eq}, yielding an effective interest rate of 10%. Alton uses the straight-line method of amortization. The fiscal year ends on December 31. What is the total interest expense for 2011? a. {eq}\$40,500 {/eq...
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In its first month of operation, Natalie purchased 250 units of inventory for $8, then 350 units for $9, and finally 300 units for $10. At the end of the month, 320 units remained. Compute the amount of phantom profit that would result if the company used FIFO rather than LIFO. Phantom profit $ _ _ _ _ _ .
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A firm's fixed costs total $100, its average variable cost is $2, and its total costs are $400 at 150 units of output. Its average fixed cost is: a. $1. b. $2. c. $3. d. $4.
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What is the flaw in my reasoning when trying to find the error in the usage of the series expansion for the expression $(1+x)^{3/2}$, given that it should be valid for $|x|\lt1$ but the series expansion gives a finite result for $x=2$, while substituting $x=2$ directly into the expression gives an infinite result?
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A cost accounting system that fully reveals the costs of the departments or activities within an organization and the responsible managers for those costs is: A) operations costing B) job-order costing C) direct costing D) normal costing E) activity-based costing
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Intercontinental company purchased $20,000 of stock in iowa company, its principal supplier, on September 15. The investment represented 10% of the voting stock of iowa company, which is included in the company's stock investments in the financial statements. The company reported a balance in its allowance for doubtful...
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A monopolist faces the following demand: {eq}p=100-Q {/eq}. It has total cost {eq}C=16+5Q+Q^2 {/eq}. Find its Lerner index at its profit-maximizing quantity. A) 0.167. B) 0.25. C) 0.5. D) 0.667. E) 1.0.
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Let {eq}f(R) = \int_{-R}^R e^{-x^2}dx{/eq}. Find {eq}\lim_{R \to \infty} f(R){/eq}. Use the fact that {eq}f^2(R) = \int_{-R}^R e^{-x^2} dx \int_{-R}^R e^{-y^2} dy{/eq} and represent {eq}f^2(R){/eq} as a two dimensional integral over the square {eq}S = \{(x, y) \in \mathbb{R}^2 : |x| \leq R, |y| \leq R\}{/eq}. Then show...
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The _______ is the first element to be sold in the liquidation process. a. Appraisal Value b. Retained Earnings c. Capital Stock d. Discount on Bonds
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When is driver tracing used? a. When the resource is shared by more than one activity. b. When the resource is exclusive to the activity. c. When the resource is a labor resource. d. All of these choices are correct.
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If C is the z-axis from the origin to the point (0, 0, 12), then the integral over C of (-5j-5k) \* dr = .
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Which of the following would cause the price of a share of stock to decline? A) The growth rate of dividends increases. B) The required rate of return is reduced. C) The dividend yield is increased. D) The beta is increased. E) A and D
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A stock has a beta of 1.10, the expected return on the market is 12 percent, and the risk-free rate is 2.2 percent. What must the expected return on this stock be?
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Mitchell Co. had 5,000 shares of 6%, $100 par value preferred stock and 10,000 shares of $10 par value common stock outstanding during 2014. In 2015, Mitchell decided to declare a total dividend of $100,000 to the preferred and common stockholders. If the preferred stock is cumulative and partially participating, up t...
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The mean height of women in a country (ages 20 - 29) is 64 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample will be greater than 65 inches? Assume the standard deviation is 2.78. Please show the answers step by step.
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Morales Corporation produces microwave units. The following per unit cost information is available: Direct materials $38 Direct labor $23 Variable manufacturing overhead $12 Fixed manufacturing overhead $39 Variable selling and administrative expenses $10 Fixed selling and administrative expenses $23 Its desired...
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Given the data below, compute the inventory turnover ratio. 2006 2005 Inventory 85 92 Cost of goods sold 1,150 1,250 a. 11.2 b. 14.1 c. 12.5 d. 7.5
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In 2013, Yolanda, a single individual, had earnings from self-employment of $75,000. During 2013, Yolanda made her residence available to a sister on a month-to-month basis for $2,400 per month (payments received on a monthly basis). Her brother was a full-time student at a local university and she felt that this arran...
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Ace Products has projected the following sales for the first seven months of 2018: January $ 34,000 February $ 52,000 March $ 58,000 April $ 42,000 May $ 46,000 June $ 40,000 July $ 45,000 Sales are typically collected as follows: Month of sale 60% Month following sale 35% Other 5% Operating expenses include:...
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Stilton Industries has total assets of $1,494,000 and total liabilities of $1,200,000. Sales for 2011 totaled $2,400,000 and the profit margin was 6%. The firm paid a total dividend of $40,000. What is its ROE? A. 4.8% B. 3.0% C. 6% D. 7.2% E. 8.4%
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What is the probability that in a random sample of 20 such customers, at least 10 of them order a non-alcoholic beverage, given that 80% of the customers in a coffee shop order a cup of coffee and 20% order a non-alcoholic beverage?
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Bill and Tom are the only buyers of Good X. Each has a different demand function. When the market price is $8, Bill's quantity demanded is 4, and Tom's is 2. If the market price increases to $10, Bill's quantity demanded will fall to 2, while Tom's will fall to 0. Based on this information, at a price of $10, the total...
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Select the three most acidic hydrogen atoms in lactic acid, {eq}CH_{3}CH(OH)CO_{2} H {/eq}, and rank them in order of decreasing acidity. Explain your reasoning. A. alcohol OHB. {eq}\rm CH_{3} {/eq}C. a-CHD. COOH
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Calculate $$\lim_{n\to\infty} \left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\cdots+\frac{n}{n^2+n}\right).$$ The provided hint is: $$\lim_{x\to\infty} \frac{\ln(1+x)-\ln x}{1/x}=\lim_{x\to\infty} \frac{1/(1+x)-1/x}{-1/x^2}.$$
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Eddy's Enterprises Inc. leases equipment to Aaron Corporation for a period of 10 years. The lease contains the following terms: The term of the lease is equal to 80 percent of the estimated economic life of the leased property. Eddy's purchases the property from an unaffiliated party at a price equal to the fair value...
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Evaluate the integral by changing to spherical coordinates. {eq}\displaystyle\int_{0}^{5}\int_{0}^{\sqrt {25-y^{2}}}\int_{0}^{\sqrt{25-x^{2}-y^{2}}}\sqrt {x^{2}+y^{2}+z^{2}}\ dz\ dx\ dy {/eq}
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An efficiency wage that leads to a higher turnover rate is said to be _____. A. suboptimal B. market clearing C. optimal D. surplus maximizing
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A certain industrial agency is buying a piece of equipment which costs $50,000.00 and will last them for 10 years. They need to choose between financing the equipment through a nonbanking financial institution which will charge them 8% interest compounded quarterly, or financing through a bank charging 8.5% interest co...
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M & M Proposition I with tax supports which of the following statements? a) A firm's cost of equity increases as the debt-equity ratio of the firm increases. b) A firm's weighted average cost of capital decreases as the firm's debt-equity ratio increases. c) A firm's cost of debt increases as the debt-equity ratio o...
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Which of the following statements is true? a) Absorption costing promotes cost control because it holds managers accountable for the variable overhead costs they incur. b) Both absorption costing and variable costing can be used to prepare financial statements in compliance with Generally Accepted Accounting Principl...
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The Knoell 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 inventory600 Materials costs$7,800 Conversion costs$6,500 Percent complete...
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The following data are available for a period of 3 years: Units Unit Cost Total Cost 20xx 20xx 20xx 20xx 20xx 20xx Beginning inventory 20,000 $1.00 $20,000 Purchases 120,000 $2.00 $240,000 Available ...
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Economic profit is found by subtracting _____ expenses from total revenues. A. all B. implicit C. explicit D. fixed E. sunk
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The variance of a random variable X is defined as {eq}Var[X] = E[(X-\mu)^2] {/eq} where {eq}\mu {/eq} is the mean of X. Evaluate the following statement: {eq}Var[aX + b] {/eq} is a normal random variable and therefore we can apply Chebychev's inequality.
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Suppose four alternatives are being considered for a particular project, each with a three-year life. The cash flows associated with each alternative are shown below. If the MARR is 15% per year, which alternative should be selected? Year Alt A Alt B Alt C Alt D 0 -$10,000 ...
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Verify that the conclusion of Clairaut's Theorem holds (that is, uxy = uyf = -e-yf(x) = uyx) for the function u(x, y) = -e-yf(x) + yf(x)g(y).
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Three different projects have been proposed by a computer manufacturer. These projects are described in the table below, along with their initial costs and net present value figures. Which of the three projects should be chosen? Project AProject BProject C Initial Cost$15,000$27,000$12,000 Net Present Value $3,000 ...
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The Fed reduces the money supply growth rate. The classical theory predicts that the A. natural rate of unemployment will increase. B. natural rate of unemployment will decrease. C. price level will increase. D. price level will remain constant. E. interest rate will fall.
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How much is going to be the corporate tax after raising 1 billion dollars of debt with an interest rate of 8%, and paying 15% of the interest as tax? Is it 8% x 1 billion x 15%, or is it 15% x (8% x 1 billion) x (15%)?
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Hershey's financing policy, which will probably result in a lower current ratio compared to last year, is a: A) conservative policy that will also decrease the return on sales B) liberal policy that will also decrease the return on sales C) conservative policy that will also increase the return on sales D) liberal ...
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A standard addition was performed to determine the amount of lead in an analytical sample. The sample was placed in a 50-mL graduated cylinder and the following volumes of a 1.000 mg/mL lead solution were added to the graduated cylinder. V sample (mL) - V added (mL) - Absorption 50 - 0.0 - 0.348 50 - 1.0 - 0.406 50 -...
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The Smith Company's inventory balance on December 31, 2020, was $300,000 (based on a 12/31/2020 physical count) before considering the following transactions: 1. Goods shipped to Smith f.o.b. destination on December 20, 2020, was received on January 4, 2021. The invoice cost was $45,000. 2. Goods shipped to Smith f.o...
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Purchasing an asset with cash: a. Results in an increase in cash and a decrease in an asset. b. Results in an increase in an asset and a decrease in cash. c. Results in an increase in an asset and an increase in a liability. d. Results in an increase in assets and stockholders' equity.
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A project has an initial cost of $36,000.00, expected net cash inflows of $9,900.00 per year for 11 years, and a cost of capital of 9.00%. What is the project's PI?
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How do you find the determinant of a 3x3 matrix?
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Examine the following cash flow problem. Determine the interest rate using a Financial calculator. Year Cash Flow 0 -$1,000 1 200 2 300 3 400 4 300 5 200 7.51% 7.01% 6.51% 7.91% 8.31%
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Consider three electric charges in a straight line. The middle one (charge = +3 nC) is 10 cm to the right of the left one (charge = -4 nC), and is held in place by the left charge. How far away can the rightmost (charge = +3 nC) be placed if the middle charge is to remain at rest?
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If the government attempted to establish a price floor above the equilibrium price, then: a) a surplus would occur. b) supply would increase. c) there would be no effect on the market. d) a shortage would occur.
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The Blackhawk Co. just paid a dividend of $2.48 per share on its common stock. The stock is selling for $32 a share and has a growth rate of 3 percent. What is the dividend yield, using the constant growth model? A) 7.75% B) 7.33% C) 1.63% D) 6.91% E) 4.86%
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Calculate the expected earnings per share from the following information for ABC Company. Expected Net Profit = $500,000 Cash Flow from Operations = $1,000,000 Total Assets = $6,000,000 Interest Expense = $300,000 Tax Rate = 30% Accounts Payable = $400,000 Number of Shares of Stock = 4,000,000
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An asset has a four-year service life with annual cash flow of -$6,000, $5,000, $4,000, and $3,000 for the first four years, respectively. What is the payback period of this asset? a. 3 years. b. 2 years. c. 4 years. d. 1 year.
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Leaky Pipe Company paid out $3,812.00 in interest, and the company had interest expense of $3,500.00 and tax expenses of $1,642.00. What are their interest coverage ratio and their times interest earned ratio?
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What is the stock price if the next dividend is $5.60, growth rate is expected to be 2%, and the appropriate discount rate is 9%?
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Rosnan Industries' 2013 and 2012 balance sheets and income statements are shown below. Balance Sheets: 20132012 Cash and equivalents$60 $45 Accounts receivable275 300 Inventories375 350 Total current assets$710 $695 Net plant and equipment2,000 1,490 Total assets$2,710 $2,185 Accounts payable$150 $85 Accruals75 50 ...
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