- Q: Betsy, a recent retiree, requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year? The amount of money invested at 13% = The amount of money invested at 3% =
- Q: For discrete time signal convolution pairs x[n] over N elements and h[n] over length M elements, prove that
- Q: The ordinary differential equation is given X 1 (v 1)dx + (xy 2x + |dy = 0, y = y(x). y Find the integral factor so that the given differential equation to become exact (complete) and then to calculate its general solution.
- Q: If A={x: x is an even integer and x <10} and B=(x: x is the integer and x <10}. Find the cardinality (order) of A and B.
- Q: Firm D is considering investing $674,000 cash in a three-year project with the following cash flows. Year 1 $0 100,800 (40,440) $ 60,360 Year 2 $ 674,000 60,800 (18,240) $ 716,560 Investment/return of investment Revenues Expenses Before-tax net cash flow Year 0 $ (674,000) 134,800 (40,440) $ (579,640) Required: a1. The revenue is taxable, the expenses are deductible, and the marginal tax rate is 15 percent. Use a 10 percent discount rate to compute NPV. a2. Should firm D make the investment? b1. The revenue is taxable, the expenses are deductible, and the marginal tax rate is 40 percent. Use a 10 percent discount rate to compute NPV. b2. Should firm D make the investment? c1. The revenue is taxable, only one-half of the expenses are deductible, and the marginal tax rate is 15 percent. Use a 10 percent discount rate to compute NPV. c2. Should firm D make the investment? d1. Firm D can deduct the expenses in the year paid (against other sources of income) but can defer recognizing the $296,400 total income until year 2. (It will collect the revenues as indicated in years 0, 1, and 2 so that before-tax cash flows don't change.) The marginal tax rate is 40 percent. Use a 10 percent discount rate to compute NPV. d2. Should firm D make the investment?
- Q: Find the LT of the function f(t) given by f(t) H -2 0 for 0t 1, for t > 1.
- Q: Your company is in the business of manufacturing cowboy boots. You sell the boots directly to customers online, and sales have been increasing steadily over the past five years. While doing some standard financial ratio analysis, you see that your gross profit margin (gross profit* / sales) has been steadily declining over that same five-year period. Upon further investigation, you find that the industry average for gross profit margin among cowboy boot manufacturers has been holding relatively equal for the past five years. What does this set of facts tell you about your company's operations during that period? What are some possible explanations for your firm's performance, given that the industry averages differ from yours? *gross profit = sales - cost of goods sold?
- Q: Consider a hypothetical unstable particle of mass M which decays into two identical particles of mass m. Work out the dynamics of this interaction by answering below questions. When you plug in the numbers, use the hypothetical masses M = 1000 MeV/c and m= 100 MeV/c. (a) Consider the interaction in the "center-of-momentum" frame, where the total momentum of all particles in the system is zero. What are the kinetic energies of the two particles of mass m? Work out an algebraic expression for kinetic energies in terms of known parameters (M, m, and c) first, and give numerical value of the kinetic energy in electron-volt units. 1 (b) In this "center-of-momentum" frame, what are the speeds of the two identical particles of mass m? Give their speeds as a fraction of speed of light (c) and use enough significant figures to distinguish the speeds of these masses from the speed of light in this highly relativistic situation. (c) The hypothetical particle of mass M is actually moving at speed v=0.8c in the lab frame. If the particles of mass m are emitted along the direction of motion of mass M (one moving in the same direction, and the other moving in the exact opposite direction), what are the total energies (kinetic plus rest) of the two particles of mass m in the lab frame? 1.1. IEDA 1 A (d) What are the speeds of the two particles of mass m. in the lab frame? (e) In the lab frame, the hypothetical unstable particle M is observed to live for 10-6 us. What is the lifetime of the particle M, measured in its own reference frame (proper lifetime)?
- Q: Define that b ^= (ad). A What is tr(A1) (0)? (Hint: This can be computed quickly by using the cyclic property of the trace and the outer product representation of A. Do master this trick; it will be used repeatedly in the course and save you much time.) (10) + 1)). Use the same trick above, along with the fact that the trace is linear, to Let +) = quickly evaluate tr(A-|+)(+)).
- Q: -Write out the 4-dimensional vector for (a (0) +31)) (70) +81))? Let B(1), 2)}, B= {01), 0)} be two orthonormal bases for C. Construct an orthonormal basis for C4?
- Q: In May 2017, Apple (NASDAQ: AAPL) filed a prospectus with the SEC, indicating that it would be issuing another $7 billion in bonds during 2017. (Apple issued $10 billion in bonds in February 2017 in the US and $1 billion in Taiwan.) With the bond proceeds, Apple will be buying back its own stock. Apple has also indicated that there will be a 10.5 percent dividend increase for its shareholders. Questions What journal entry would Apple make when it issues $7 billion in bonds? How are assets, liabilities, and equity impacted by the bond issuance? Name the account(s) impacted and whether an increase of decrease. On what financial statement is the balance of bonds payable shown? Where is it shown on that financial statement? What journal entry would be made for the payment of interest (ignore the dollar amount - just account title(s) and debit/credit). How does Apple's issuance of bonds and buyback of its own stock impact its accounting equation?
- Q: Mountessa sells soft drinks to Bev Averages, a pub, on 10 September 2010 for $3,600 (GST inclusive) and issues a tax invoice on the same day. Bev Averages pays Mountessa on 10 October 2010. Discuss how Mountessa and Bev Averages will account for GST to the IRD under the different alternatives: (a) Mountessa uses the invoice basis whereas Bev Averages uses the payments basis. (b) Mountessa uses the payments basis and Bev Averages uses the hybrid basis.
- Q: The oscillations of a mass-spring-damper system is governed by a single 2nd order ODE with constant coefficients for a(t): At Bi+ Cr= 0, where dx(t) dt = x. = ax + by, (a) Express the system of coupled first order ODES dx dt ...(1) dt = cx + dy (2) in the form of equation (1) for a(t). Confirm that you get the same ODE for y(t). (b) Consider the system i i. Find the corresponding second order ODE in the form (1) and solve it using the method you learned in Calculus 2. ii. Classify the oscillation into one of the following types: underdamped, critically damped, overdamped. iii. Use MATLAB to plot the oscillatory displacement (t) versus t from part i.
- Q: A summary of cash receipts and payments for a GST period is provided below: $360 Stationery Expenses Advertising $720 $450 - Bank charges & interest Salaries Sales Purchase of goods for resale Loan from bank Lease on shop Purchase of computer for business use Power & Gas Phone $4,500 $18,000 $9,000 $4,500 $1,800 $3,600 $360 $360 Required: (a) If the appropriate receipt and payment amounts were indicated GST inclusive, what is the amount of GST Receivable from or Payable to the IRD? (b) If the appropriate receipt and payment amounts were indicated GST exclusive, what is the amount of GST Receivable from or Payable to the IRD?
- Q: The data below are for HKUST Company. Sales Rent, depreciation, and other operating expenses Prepaid Rent Expense Long-term debt Inventory Interest expense Income tax expense Net income Equipment Cost of goods sold Cash Account receivable Accounts payable 13,000 1,100 4,500 30,000 3,500 1,700 ? 5,258 6,000 4,000 120 1,600 750 Prepare HKUST's Income statement. What is HKUST's income tax rate?
- Q: On January 1, 2007, Nichols Company's inventory of Item X consisted of 2,000 units that cost $8 each. During 2007 the company purchased 5,000 units of Item X at $10, each, and it sold 4,500 units. Periodic inventory procedure is used. Calculate the Cost of ending inventory using FIFO.
- Q: A particle of mass M decays at rest into two particles that move off in opposite directions. One of the decay particles has a mass m and total energy E and the second decay particle has a mass of m2 and total energy E2. (a) In terms of M, m and m show that the total energies of the two decay particles are given by the expressions E = E = = (M+ m - m) c 2M (M+ m-m) c 2M Hint: First show that E - E2 = (m - m) c (b) The initial particle was a pion (rest energy 140 MeV). One of the decay particles is a muon (rest energy 106 MeV) and the other is a neutrino (assumed to have negligible mass here). What is the total energy of the muon? (c) What is the kinetic energy of the muon? (d) What is the momentum of the muon (you may choose to leave your answer in units of MeV/c)? (e) What is the energy of the neutrino that was produced?
- Q: Determine whether the following statements are true or not. Give a brief ex- planation. (e.g. proof, provide counter-examples etc.) In the following problems, let fn (r) be a sequence of functions on E 1. If fn(x) converges uniformly to f(x) on E, then f(x) converges pointwise to f(x) on E. 2. If f(x) converges pointwise to f(x) on E, then fn(r) converges uniformly on E. 3. Given a series of functions 1 fn(x), then its domain of convergence MUST be an interval. 4. The domain of convergence of power series is always an interval WITH BOTH ENDPOINTS. 5. Given a sequence of continuous functions f(x) on E, then f(x) limn ofn (r) is also continuous on E.
- Q: Oak Creek Furniture Factory (OCFF), a custom furniture manufacturer, uses job order costing to track the cost of each customer ordet On March 1, OCFF had two jobs in process with the following costs Work in Process Job 33 Job 34 Balance on 3/1 $ 4,500 3,300 $7,000 Source documents revealed the following during March Materials Requisitions Forms $ 2,700 2,700 4,000 800 $ 11,000 Job 33 Job 34 Job 35 Indirect Labor Tine Tickets $ 5,900 3,300 2,600 2,400 $ 14,200 Status of Job at Month-End Completed and sold Completed, but not sold In process The company applies overhead to products at a rate of 55 percent of direct labor cost Required: Prepare journal entries to record the materials requisitions, labor costs, and applied overhead Note: If no entry is required for a transaction/event, select "No Journal Entry Required in the first account fiel
- Q: For each theory, describe a STEM-related scenario of the theory's application in an early childhood classroom setting (e.g., a lesson, activity, or experience). Your scenarios can be based on your own experience as a teacher or an early childhood classroom scenario that you imagine. In each of your scenarios, discuss whether it aligns more with a naturalistic, informal, or structured lesson plan, and why? Also, discuss the role that the teacher's disposition has on student achievement in your scenarios. What would be an example?
- Q: A system is initially in the State =1/7[2 +3 +1 +1 ] where are eigenstates of the system's Hamiltonian Such that H = n^2 epsilon (a) If Energy is measured, what values will be with what probabilities? obtained and (b) Consider an operator A whose action. is defined by A 142 = (51) 9. If A is measured, what Values will be obtained and with what probabilities?
- Q: Compute the orthogonal projection of [1] onto the line through [-2] and the origin.
- Q: The company's Accounting Department has determined the break-even point to be 14,000 units per month, computed as follows: Fixed cost per month Unit contribution margin $420,000 = 14,000 units $30 per unit On receiving this figure, the president commented, "There's something peculiar here. The comptroller says that the break-even point is 14,000 units per month. Yet we sold only 13,000 units in May, and the income statement we received showed a $2,000 profit. Which figure do we believe?" Prepare a brief explanation of what happened on the May income statement.
- Q: BiGGym produces two types of exercise treadmills: Regular and Deluxe. The exercise craze is such that BiGGym could use all of its available machine hours producing either model. The two models are processed through the same Production Department. What product mix will maximize operating income? Sales price.......... Costs:.......... Direct materials.......... Direct labour......... Per Unit Deluxe Regular $990 $290 86 $560 $100 188
- Q: Fibre Systems manufactures an optical switch that it uses in its final product. Fibre Systems incurred the following manufacturing costs when it produced 75,000 units last year: Fibre Systems does not yet know how many switches it will need this year; however, another company has offered to sell Fibre Systems the switch for $14 per unit. If Fibre Systems buys the switch from the outside supplier, the manufacturing facilities that become idle cannot be used for any other purpose, yet none of the fixed costs are avoidable. Requirements 1. Given the same cost structure, should Fibre Systems make or buy the switch? Show your analysis. 2. Now, assume that Fibre Systems can avoid $80,000 of fixed costs a year by outsourcing production. In addition, because sales are increasing, Fibre Systems needs 80,000 switches a year rather than 75,000. What should Fibre Systems do now? 3. Given the last scenario, what is the most Fibre Systems would be willing to pay to outsource the switches? Direct materials............ Direct labour.......... Variable overhead......... $ 600,000 105,000 180,000
- Q: Show that the following sequence of functions sin nx nx+1 fn(x) = converges uniformly on [1, +). Prove that the following series xe-nz n=1 converges uniformly on (0, +).
- Q: Bennett Builders builds townhomes in a new subdivision just outside of Calgary. Land and labour are cheap, and competition among developers is fierce. The homes in the subdivision are identical to one another, but buyers can upgrade features by paying the difference. Bennett Builders costs per developed sublot are as follows: Bennett Builders would like to earn a profit of 15% of the variable cost of each home sale. Similar homes offered by competing builders sell for $200,000 each. Requirements 1. Which approach to pricing should Bennett Builders emphasize? Why? 2. Will Bennett Builders be able to achieve its target profit levels? Show your computations. 3. Bathrooms and kitchens are typically the most important selling features of a home. Bennett Builders could differentiate the homes by upgrading bathrooms and kitchens. The upgrades would cost $18,000 per home but would enable Bennett Builders to increase the selling prices by $35,000 per home. (In general, kitchen and bathroom upgrades typically add at least 150% of their cost to the value of any home.) If Bennett Builders upgrades, what will the new cost-plus price per home be? Should the company differentiate its product in this manner? Show your analysis. Land......... $ 55,000
- Q: A function f E R is called Lipschitz (or more precisely M-Lipschitz) if there exists an M >0 such that for all x, y E, f(x)-f(y)| Mx - y. 1. Show that any Lipschitz function is uniformly continuous. 2. Show that if f: (a, b) R is a differentiable function such that f'(t)| M for all t (a, b), then f is M-Lipschitz.
- Q: Give and explain your opinion regarding the following statement balance is definitely true! 2. Identify the following accounts, which accounts require adjusting entries (AE) and closing entries (CE)? which financial statements will be in? and where is the normal balance of the account? AE/CE Financial Statement Normal Balance No Account 1 Prepaid insurance 2 Capital Prive 3 4 5 Account payable Cash 6 Uneamed revenue Supplies 7 S Land 9 Account receivable 10 Salaries expense 11 Insurance expense Gain on sale of equipment Sales revenue 12 13 14 Supplies expense 15 Accrued expense CASE This information is available for Nestle in 2016 and 2017. 2016 Beginning inventory Ending inventory Cost of goods sold Sales $200,000 300,000 1,200,000 1,600,000 2017 $300,000 380,000 1,368,000 1,900,000 Requested: 3. Calculate the inventory tumover, days in inventory, and gross profit rate for Nestl for 2016 and 2017? and give your opinion on the trend or the results of ratio analysis?
- Q: Suppose the Hockey Hall of Fame in Toronto has approached Sports-Cardz with a special order. The Hall of Fame wants to purchase 60,000 hockey card packs for a special promotional campaign and offers $0.40 per pack, a total of $24,000. SportsCardzs total production cost is $0.60 per pack, as follows: Sports-Cardz has enough excess capacity to handle the special order. Requirements 1. Prepare an incremental analysis to determine whether Sports-Cardz should accept the special sales order assuming fixed costs would not be affected by the special order. 2. Now assume that the Hall of Fame wants special hologram hockey cards. Sports-Cardz must spend $2,000 to develop this hologram, which will be useless after the special order is completed. Should SportsCardz accept the special order under these circumstances? Show your analysis. Variable costs:......... Direct materials.......... $0.15
- Q: If you can spare $1,572 at most as monthly payment, how much mortgage can you afford (30 year at 3% annual interest)?
- Q: Assume that you were working as Enron's outside auditor, Arthur Anderson. Would you have done anything differently? You had legal counsel that OK'd documents being shredded after the SEC began to investigate. Is that enough?
- Q: The following data are taken from the books of Maria Makling, a resident Filipino citizen, for year 2020 Sales 3,200,000.00 Cost of Sales 1920,000.00 80,000.00 128,000.00 1020,000.00 Gambling winnings Gambling lossess Compensation income, net of tax withheld P20,000.00 13th month pay, and other bonuses Proceeds from fe insurance of her mother Business expenses, including robbery loss of P50,000.00, contribution to Deped's priority projects, P100,000.00, and interest expense, P300,000.00 Bad debts recovery Lotto winnings Personal expenses tuition fees of children Interest income personal lending Compensation income, net of withholding tax of 20%-bracket Interest income, net of withholding tax of 20% Commission income, net of withholding tac of 5% Compute the income tax still due and payable per ITR, if the taxpayer is an individual Filipino resident Show your solution Lotto winnings Dividend income 96,000.00 800,000,00 2 A taxpayer named Balangaw S. Rimbo had the following incomes and expenses during the taxable year 2020: 800,000.00 96,000.00 Nonresident citizens and Resident alen 480,000.00 160,000.00 240,000.00 32,000.00 Loss on unrealized earnings Casusity losses Abandoned equiemnt due to technological problem Accumulated depreciation of abandoned equipment Compensatory liquidated damages Embezzled funds by the cashier Book value of the damaged equipment Replacement cost of the damaged portion of machine Philippines 360,000.00 $2.250.00 50,000.00 57,000.00 100,000.00 9,000.00 3. Mr. Saboy incurred the following losses related to his construction business USA One U.S. dollar is equal to P49.00 All income without derived from USA Assume that withholding taxes were applied to income within the Philippines. Required Determine the income taxes due and payable of the taxpayer assuming that he is a Resident citizen b 500,000.00 250,000.00 150,000.00 120,000.00 100,000.00 70,000.00 50,000.00 40,000.00 1,200.00 950.00 1,800.00 The casualty losses was reported to the BIR within 45 days and compensated by insurance amounting to P300,000,00 Compute the total amount of deductible loss
- Q: What is the main common interest of Iceberg and Keep-it-Cold in this dispute? (8 marks) How far should Iceberg push for compensation? (8 marks) Should Keep-it- Cold resist or pay compensation? (8 marks)
- Q: Do sunk costs affect a sell or process-further decision? Why or why not?
- Q: A non-fiction picture book that you will read to a peer or a member of your family. You will design a lesson plan that will introduce the book using pre-reading strategies. For the rest of the book, your activities will focus on three of the six languages arts: reading, writing, speaking, listening, viewing, and visually representing. A lesson plan where the introduction or initiation is the prereading activity and three follow up activities will be something children will read, write, speak (this can be teaching them a song or poem about the topic of the book), listen to, view, or visually represent. What would be your example?
- Q: Solve this : Solve this : 25x^2 - 20x + K.
- Q: Nombre Company management predicts $720,000 of variable costs, $866,000 of fixed costs, and a pretax income of $214,000 in the next period. Management also predicts that the contribution margin per unit will be $15. (1) Compute the total expected dollar sales for next period. Sales Variable costs Contribution margin Fixed costs Pretax income (2) Compute the number of units expected to be sold next period. Choose Numerator: 1 Fixed costs plus pretax income Choose Denominator: Contribution margin per unit = # Units Units 0
- Q: Simplify 16x^2 -4/4x^2 +2x -2 divide by 2x-2/x+1
- Q: At the end of 2019, the world was shocked by the spread of the COVID-19 epidemic. Malaysia is also not exempt from the COVID-19 outbreak which has a negative impact on public health. In order to curb the spread of the COVID-19 epidemic, the Malaysian Government has announced a Movement Control Order throughout Malaysia. This Movement Control Order has affected the country's economy and has had a huge negative impact on Malaysians. People's lives are severely affected and the government needs to intervene so that the situation does not worsen. The government has announced an economic stimulus package with various initiatives to re-stimulate the Malaysian economy. The announcement of this initiative needs to be accompanied by financial allocation so that the initiatives concerned can be implemented effectively and efficiently. Therefore, the government has allocated part of the government's finances for that purpose and the financial allocation is included in the COVID-19 Trust Fund for that purpose. Required: a) Explain the accounting for the trust fund and the procedure for establishing the COVID-19 Trust Fund as a special fund created by the Government during the pandemic period. b) Explain the difference between a Trust Account (Section 10, Act 61) and a Trust Account (Section 9, Act 61) c) Discuss how the COVID-19 pandemic affects the Government's financial.
- Q: a. Compute cost of goods sold under the AVERAGE COST inventory costing method for the month of March for Coldman Enterprises. b. Compute the value of ending inventory under the AVERAGE COST inventory costing method for the month of March for Coldman Enterprises. c. Compute gross profit under the AVERAGE COST inventory costing method for the month of March for Coldman Enterprises. Coldman Enterprises uses a periodic inventory system. Its records show the following for the month of March, in which 280 units were sold for a total of $2,800 cash: Number of units Cost per unit Date March 1 March 15 March 25 Total Inventory, beginning Purchase Purchase 200 100 100 400 $5.00 $5.30 $5.50 Total cost $1,000 $530 $550 $2,080 Coldman uses an average cost inventory costing method to compute cost of goods sold and value ending inventory
- Q: Evans Inc. manufactures only two products, Medium (42-inch) and Large (63-inch) plasma screen TVs. To generate adequate profit and cover its expenses throughout the value chain, Evans prices its TVs at 300% of manufacturing cost. The company is concerned because the Large model is facing severe pricing competition, whereas the Medium model is the low-price leader in the market. The CEO questions whether the cost numbers generated by the accounting system are correct. He has just learned about ABC and wants to reanalyze this past years product costs using an ABC system. Information about the companys products this past year are as follows: Currently, the company applies manufacturing overhead based on direct labour hours. The company incurred $800,000 of MOH this year and 25,000 direct labour hours (9,000 direct labour hours making Medium TVs and 16,000 making Large TVs). The ABC team identified three primary production activities that generate MOH costs: The companys only two products required the following activity levels during the year: Requirements 1. Use the companys current costing system to find the total cost of producing all Medium TVs and the total cost of producing all Large TVs. What was the average cost of making each unit of each model? Round your answers to the nearest cent. 2. Use ABC to find the total cost of producing all Medium TVs and the total cost of producing all Large TVs. What was the average cost of making each unit of each model? Round your answers to the nearest cent. 3. How much cost distortion was occurring between Evans two products? Calculate the cost distortion in total and on a per-unit basis. Could the cost distortion explain the CEOs confusion about pricing competition? Explain. Medium (42-inch) Plasma TVs Total direct materials cost: $660,000 Total direct labour cost: $216,000 Production volume: 3,000 units Large (63-inch) Plasma TVs
- Q: Solve this: Solve this: 23/x - 1/x^2 -120 =0.
- Q: Required 1. Calculate and enter the adjusted account balances in the Adjusted Trial Balance columns. 2. Describe each adjusting entry. For example, a. Prepaid rent expires, $1,500.
- Q: Find the complete solution to Ax=b, for [30-9-3 07 2 A 6 0 -21 0 00 0 0 0 3 X= 21 12 13 14 Is b=
- Q: Pharoah Limited sponsors a defined benefit pension plan, and follows ASPE. The corporation's actuary provides the following information about the plan (in thousands of dollars): Vested benefit obligation Defined benefit obligation, accounting basis Plan assets (fair value) Interest/discount rate Net defined benefit liability/asset Past service cost, plan amendment, effective December 30, 2020 Service cost for the year 2020 Contributions (funding) 2020 Benefits paid in 2020 (Enter answers in thousands of dollars.) Calculate the actual return on the plan assets in 2020. Actual return on the plan assets in 2020 $ Calculate the amount of the net defined benefit liability/asset as at January 1, 2020. Net defined benefit January 1, 2020 January 1, 2020 $1,400 2,260 1,400 10% ? $ December 31, 2020 $1,480 2,976 2,205 10% ? 340 280 700 130
- Q: Victors Sporting Goods is a retailer of sporting equipment. Last year, Victors Sporting Goods sales revenues totalled $8,000,000. Total expenses were $2,100,000. Of this amount, approximately $1,500,000 were variable, while the remainder were fixed. Since Victors Sporting Goods offers thousands of different products, its managers prefer to calculate the breakeven point in terms of sales dollars rather than units. Assume that Victors Sporting Goods gathers information on the sales of its products based on two departments: Winter Sports and Summer Sports. Winter Sports revenues are $4,000,000 of the total $8,000,000 and the department has an average contribution margin of 70%, while Summer Sports brings in the remaining revenues. Of the fixed costs, $250,000 can be directly traced to Winter Sports and $300,000 can be traced to Summer Sports. Prepare a segmented contribution margin income statement for Victors Sporting Goods. Check sum: Common costs are $50,000
- Q: Refer to Asokans Golden Brown Pancake Restaurant in E3- 33A. Data in E3- 33A. Asokans Golden Brown Pancake Restaurant features sourdough pancakes made from a strain of sourdough dating back to the Yukon gold rush. To plan for the future, Asokan needs to figure out his cost behaviour patterns. He has the following information about his operating costs and the number of pancakes served: Requirements 1. Use the high-low method to determine Asokans operating cost equation. 2. Use your answer from Requirement 1 to predict total monthly operating costs if Asokan serves 5,000 pancakes in one month. 3. Can you predict total monthly operating costs if Asokan serves 10,000 pancakes a month? Explain. Month July August September October November December ........... Number of Pancakes 3,600 3,900 3,200 3,300 3,850 3,620 Total Operating Costs $2,340 $2,390 $2,320 $2,270 $2,560 $2,530
- Q: Refer to Cliffs Fresh Stacks Pancake Restaurant in E3-57B. Data in E3-57B. Cliffs Fresh Stacks Pancake Restaurant features sourdough pancakes made from a strain of sourdough dating back to Confederation. To plan for the future, Cliff needs to figure out his cost behaviour patterns. He has the following information about his operating costs and the number of pancakes served: Requirements 1. Use the high-low method to determine Cliffs operating cost equation. 2. Use your answer from Requirement 1 to predict total monthly operating costs if Cliff serves 4,500 pancakes a month. 3. Can you predict total monthly operating costs if Cliff serves 15,000 pancakes a month? Explain. Month July August Number of Pancakes 3,900 4,200 Total Operating Costs $2,340 $2,530
- Q: Use the information from the Royal Hellenic Cruiseline data set. If Royal Hellenic Cruiseline sells 10,000 dinner cruises, compute the margin of safety a. In units (dinner cruise tickets). b. In sales dollars. c. As a percentage of sales. Check sum: (a) 4,750 passengers
- Q: Conduct your hypothesis test at a level of significance 5%, a = 0.05 A. What is your test statistic B. What is your p-value? C. What is your conclusion about the null hypothesis? D. In 1-2 sentences, write the conclusion of your hypothesis test in context of the application, using correct units.
- Q: Use the information from the Royal Hellenic Cruiseline data set. a. Compute the operating leverage factor when Royal Hellenic Cruiseline sells 12,000 dinner cruises. b. If volume increases by 10%, by what percentage will operating income increase? c. If volume decreases by 5%, by what percentage will operating income decrease? Check sum: (a) Operating leverage is 1.78.
- Q: Use three repetitions of the NewtonRaphson algorithm to approximate the following: 5
- Q: Use the integral test to determine whether the infinite series is convergent or divergent. (You may assume that the hypotheses of the integral test are satisfied.) 00 3 k=1Vk
- Q: Define the nth Taylor polynomial of f (x) at x = a.
- Q: Suppose Kay sells 1,000 posters. Use the data from S4-13 to compute her operating leverage factor. If sales volume increases 10%, by what percentage will her operating income change? Prove your answer. Data in S4-13 Kay has an e-tail poster business. Suppose Kay expects to sell 1,000 posters. Her average sales price per poster is $30 and her average cost per poster is $24. Her fixed expenses total $3,600. Compute her margin of safety . Check sum: Operating leverage is 2.5.
- Q: Find the Taylor series at x = 0 of the given function by computing three or four derivatives and using the definition of the Taylor series. 1 2x + 3
- Q: Little Piggie produces sports socks. The company has fixed expenses of $80,000 and variable expenses of $1.20 per package. Each package sells for $2.50. Requirements 1. Compute the contribution margin per package and the contribution margin ratio. 2. Find the break-even point in units and in dollars using the contribution margin shortcut approaches. 3. Find the number of packages Little Piggie needs to sell to earn a $25,000 operating income. Check sum: (1) Contribution margin per unit is $1.30.
- Q: Vairs Steel Parts produces parts for the automobile industry. The company has monthly fixed expenses of $500,000 and a contribution margin of 80% of revenues. Requirements 1. Compute Vairs Steel Parts monthly break-even sales in dollars. Use the contribution margin ratio shortcut approach. 2. Use the contribution margin ratio to project operating income (or loss) if revenues are $700,000 and if they are $1,000,000. 3. Do the results in Requirement 2 make sense given the break-even sales you computed in Requirement 1? Explain. Check sum: (1) Break-even sales in dollars is $625,000.
- Q: Determine the sums of the following geometric series when they are convergent. 1 + 1 6 + 1 + 6 1 1 64 63 +
- Q: Warren Oil Company owns a refinery in Louisiana. The refinery needs to place a special order for platinum on December 1, 2020 for use in operating the refinery. Because platinum is expensive and the market price for platinum has proven to be erratic, management decides to hedge the price of the platinum. It enters into a hedging contract with Counterparty Investment Company. The contract provides that if Warren pays more than $2,000 per ounce for platinum, Counterparty will pay Warren in cash the amount it pays in excess of $2,000 per ounce. The Contract is for 10,000 ounces. The contract is signed on October 1, 2020 and Warren pays Counterparty $2,000 on that date. Warren's accountant must prepare adjusting entries on October 31, 2020 - the end of the accounting period. The market price of the platinum is $2,200 per ounce on that date. On December 1, 2020, Warren purchases 10,000 ounces of platinum from Zero Resources for $2,200 per ounce. On that date it also settles the hedging agreement with Counterparty and is paid by Counterparty. What are the necessary accounting entries for October 1, October 31, and December 1.
- Q: Pistone Industries is planning to purchase a new piece of equipment that will increase the quality of its production. It hopes the increased quality will generate more sales. The companys contribution margin ratio is 30%, and its current break-even point is $500,000 in sales revenue. If Pistone Industries fixed expenses increase by $50,000 due to the equipment, what will its new break-even point be (in sales revenue)? Check sum: Break-even in dollars is $666,667.
- Q: Kick-As Sporting Goods is a retailer of sporting equipment. Last year, Kick-As sales revenues totalled $5,000,000. Total expenses were $2,100,000. Of this amount, approximately $1,500,000 were variable, while the remainder were fixed. Since Kick-As Sporting Goods offers thousands of different products, its managers prefer to calculate the break-even point in terms of sales dollars rather than units. Requirements 1. What is Kick-As Sporting Goods current operating income? (Prepare a contribution margin format income statement.) 2. What is Kick-As contribution margin ratio? 3. What is Kick-As break-even point in sales dollars? 4. Top management is deciding whether to embark on a $200,000 advertising campaign. The marketing firm has projected annual sales volume to increase by 15% as a result of this campaign. Assuming that the projections are correct, what effect would this advertising campaign have on Kick-As Sporting Goods annual operating income? Check sum: (2) Contribution margin ratio is 70%.
- Q: Refer to the differential equation in Exercise 39. (a) Obviously, if you start with zero fish, f(t) = 0 for all t. Confirm this on the slope field. Are there any other constant solutions? (b) Describe the population of fish if the initial population is greater than 5000; less than 5000. On the slope field in Fig. 9 or a copy of it, draw solution curves to illustrate your description. Exercise 39 Let f (t) denote the number (in thousands) of fish in a lake after t years, and suppose that f (t) satisfies the differential equation y = 0.1y (5 - y). The slope field for this equation is shown in Fig. 9. 6 5 4 3 y (in thousands) 2- 1 1 1 \\\\\\\\\\\\\ 0 1 Figure 9 // 2 / 3 1 17 1 4 5 6 / t
- Q: Mathieu Manufacturing had a 1.2 operating leverage factor when sales were $50,000. Mathieu Manufacturings contribution margin ratio was 20%. What were Mathieu Manufacturings fixed expenses? Check sum: Operating income is $8,333.
- Q: Let f (t) denote the number (in thousands) of fish in a lake after t years, and suppose that f (t) satisfies the differential equation y = 0.1y (5 - y). The slope field for this equation is shown in Fig. 9. (a) With the help of the slope field, discuss what happens to an initial population of 6000 fish. Does it increase or decrease? (b) How about an initial population of 1000 fish? Does it increase or decrease? (c) On the slope field in Fig. 9 or a copy of it, draw the solution of the initial-value problem y = 0.1y (5 - y), y (0) = 1. What does this solution represent? 6 5 4 3 y (in thousands) 2- 1 1 1 \\\\\\\\\\\\\ 0 1 Figure 9 // 2 / 3 1 17 1 4 5 6 / t
- Q: Antigonish Steel Parts produces parts for the automobile industry. The company has monthly fixed expenses of $620,000 and a contribution margin of 75% of revenues. Requirements 1. Compute Antigonish Steel Parts monthly break-even sales in dollars. Use the contribution margin ratio shortcut approach. 2. Use the contribution margin ratio to project operating income (or loss) if revenues are $500,000 and if they are $1,030,000. 3. Do the results in Requirement 2 make sense given the break-even sales you computed in Requirement 1? Explain. Check sum: (1) Break-even sales is $826,667.
- Q: Draw the graph of g(x) = e x - 100x 2 - 1, and use the graph to sketch the solution of the differential equation y = e y - 100y 2 - 1 with initial condition y(0) = 4 on a ty-coordinate system.
- Q: The Gompertz growth equation is where a and b are positive constants. This equation is used in biology to describe the growth of certain populations. Find the general form of solutions to this differential equation. (Figure 8 shows several solutions corresponding to a = .04 and b = 90.) dy dt = -ay In b'
- Q: The function is the solution of the differential equation y = .0002y(5000 - y) from Example 8. (a) Graph the function in the window [0, 10] by [-750, 5750]. (b) In the home screen, compute .0002 f(3)(5000 - f (3)), and compare this value with f(3). f(t) = 5000 1+ 49e t
- Q: A parachutist has a terminal velocity of -176 feet per second. That is, no matter how long a person falls, his or her speed will not exceed 176 feet per second, but it will get arbitrarily close to that value. The velocity in feet per second, y(t), after t seconds satisfies the differential equation y(t) = 32 - k y(t). What is the value of k?
- Q: When a certain liquid substance A is heated in a flask, it decomposes into a substance B at such a rate (measured in units of A per hour) that at any time t is proportional to the square of the amount of substance A present. Let y = f (t) be the amount of substance A present at time t. Construct and solve a differential equation that is satisfied by f (t).
- Q: Draw the graph of g(x) = (x - 2) 2 (x - 6) 2 , and use the graph to sketch the solutions of the differential equation y = (y - 2) 2 (y - 6)2 with initial conditions y(0) = 1, y(0) = 3, y(0) = 5, and y(0) = 7 on a ty-coordinate system.
- Q: Use Eulers method with n = 5 on the interval 0 t 1 to approximate the solution f (t) to y' 2 (-10), y(0) = 9.
- Q: A model that describes the relationship between the price and the weekly sales of a product might have a form such as where y is the volume of sales and p is the price per unit. That is, at any time, the rate of decrease of sales with respect to price is directly proportional to the sales level and inversely proportional to the sales price plus a constant. Solve this differential equation. (Figure 6 shows several typical solutions.) dy dp y 2\p+3,
- Q: One problem in psychology is to determine the relation between some physical stimulus and the corresponding sensation or reaction produced in a subject. Suppose that, measured in appropriate units, the strength of a stimulus is s and the intensity of the corresponding sensation is some function of s, say, f (s). Some experimental data suggest that the rate of change of intensity of the sensation with respect to the stimulus is directly proportional to the intensity of the sensation and inversely proportional to the strength of the stimulus; that is, f (s) satisfies the differential equation for some positive constant k. Solve this differential equation. dy ds =k- S
- Q: In certain learning situations a maximum amount, M, of information can be learned, and at any time, the rate of learning is proportional to the amount yet to be learned. Let y = f (t) be the amount of information learned up to time t. Construct and solve a differential equation that is satisfied by f (t).
- Q: Mothballs tend to evaporate at a rate proportional to their surface area. If V is the volume of a mothball, then its surface area is roughly a constant times V 2/3 . So the mothballs volume decreases at a rate proportional to V 2/3 . Suppose that initially a mothball has a volume of 27 cubic centimeters and 4 weeks later has a volume of 15.625 cubic centimeters. Construct and solve a differential equation satisfied by the volume at time t. Then, determine if and when the mothball will vanish (V = 0).
- Q: Some homeowners insurance policies include automatic inflation coverage based on the U.S. Commerce Departments construction cost index (CCI). Each year, the property insurance coverage is increased by an amount based on the change in the CCI. Let f (t) be the CCI at time t years since January 1, 1990, and let f (0) = 100. Suppose that the construction cost index is rising at a rate proportional to the CCI and the index was 115 on January 1, 1992. Construct and solve a differential equation satisfied by f(t). Then, determine when the CCI will reach 200.
- Q: Solve the following differential equations with the given initial conditions. dy dt t + 1 ty , t > 0, y(1) = 3
- Q: Suppose that, once a sunflower plant has started growing, the rate of growth at any time is proportional to the product of its height and the difference between its height at maturity and its current height. Give a differential equation that is satisfied by f (t), the height at time t, and sketch the solution.
- Q: Solve the following differential equations with the given initial conditions. dy dt t = (1 + 7) y y(0) = 2
- Q: In the study of the effect of natural selection on a population, we encounter the differential equation where q is the frequency of a gene a and the selection pressure is against the recessive genotype aa. Sketch a solution of this equation when q(0) is close to but slightly less than 1. dq dt || -.0001q(1-9),
- Q: Nates Repair Shop has a monthly target operating income of $13,500. Variable expenses are 80% of sales, and monthly fixed expenses are $10,000. Requirements 1. Compute the monthly margin of safety in dollars if the shop achieves its income goal. 2. Express Nates margin of safety as a percentage of target sales. 3. What is Nates operating leverage factor at the target level of operating income? 4. Assume that Nate reaches his target. By what percentage will his operating income fall if sales volume declines by 9%? Check sum: (1) Contribution margin ratio is 20%.
- Q: Let t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p(t) represent the probability that the driver will have at least one accident during these t hours. Then, 0 p(t) 1, and 1 - p(t) represents the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of t) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.
- Q: Let f (t) be the solution to y = (t + 1)/y, y(0) = 1. Use Eulers method with n = 3 on 0 t 1 to estimate f (1). Then, show that Eulers method gives the exact value of f (1) by solving the differential equation.
- Q: Consider the differential equation y = .2(10 - y) from Example 6. If the initial temperature of the steel rod is 510, the function f (t) = 10 + 500e -0.2t is the solution of the differential equation. (a) Graph the function in the window [0, 30] by [-75, 550]. (b) In the home screen, compute .2(10 - f (5)) and compare this value with f(5).
- Q: The health officials that studied the flu epidemic in Example 8 made an error in counting the initial number of infected people. They are now claiming that f (t) (the number of infected people after t days) is a solution of the initial-value problem y = .0002y (5000 - y), y(0) = 1500. Under this new assumption, can f (t) exceed 5000?
- Q: Morphine is a drug that is widely used for pain management. However, morphine can cause fatal respiratory arrest. Since pain perception and drug tolerance vary with patients, morphine is gradually administered with small increments until pain is controlled or side effects begin to appear. In one intravenous infusion, morphine was injected continuously at an increasing rate of t milligrams per hour. Suppose that the body removes the drug at a rate proportional to the amount of the drug present in the body, with constant of proportionality k = .35. Let f (t) denote the amount of morphine in the body, t hours from the beginning of the infusion. (a) Find a differential equation satisfied by f (t). (b) Assuming that the infusion lasted 8 hours, determine the amount of morphine in the body during the infusion if at the beginning of the infusion the body was free of morphine.
- Q: Hillsboro Recycling recycles newsprint, cardboard, and so on into recycled packaging materials. For the coming year, Hillsboro Recycling estimates total manufacturing overhead to be $360,000. The companys managers are not sure if direct labour hours (estimated to be 10,000) or machine hours (estimated to be 15,000 hours) is the best allocation base to use for allocating manufacturing overhead. Hillsboro Recycling bids for jobs using a 30% markup over total manufacturing cost. After the new fiscal year began, B.C. Paper Supply asked Hillsboro Recycling to bid for a job that would take 3,000 machine hours and 1,600 direct labour hours to produce. The direct labour cost for this job would be $12 per hour, and the direct materials would total $25,000. Requirements 1. Compute the total job cost and bid price if Hillsboro Recycling decides to use direct labour hours as the manufacturing overhead allocation base for the year. 2. Compute the total job cost and bid price if Hillsboro Recycling decides to use machine hours as the manufacturing overhead allocation base for the year. 3. In addition to the bid from Hillsboro Recycling, B.C. Paper Supply received a bid of $125,000 for this job from Sun Prairie Recycling. What are the ramifications for Hillsboro Recycling? Check sum: Direct labour costs are $19,200.
- Q: Suppose that in a chemical reaction, each gram of substance A combines with 3 grams of substance B to form 4 grams of substance C. The reaction begins with 10 grams of A, 15 grams of B, and 0 grams of C present. Let y = f (t) be the amount of C present at time t. The rate at which substance C is formed is proportional to the product of the unreacted amounts of A and B present. That is, f (t) satisfies the differential equation. where k is a constant. (a) What do the quantities 10 - 1/4 f (t) and 15 - 3/4 f (t) represent? (b) Should the constant k be positive or negative? (c) Make a qualitative sketch of the solution of the preceding differential equation. y' =k(10-y) (15 - 3y), y(0) = 0,
- Q: The birth rate in a certain city is 3.5% per year, and the death rate is 2% per year. Also, there is a net movement of population out of the city at a steady rate of 3000 people per year. Let N = f (t) be the citys population at time t. (a) Write a differential equation satisfied by N. (b) Use a qualitative analysis of the equation to determine if there is a size at which the population would remain constant. Is it likely that a city would have such a constant population?
- Q: Solve the following differential equations with the given initial conditions. y' = y , y(0) = -5
- Q: Solve the initial-value problem. y + y = e 2t , y(0) = -1
- Q: A certain drug is administered intravenously to a patient at the continuous rate of r milligrams per hour. The patients body removes the drug from the bloodstream at a rate proportional to the amount of the drug in the blood, with constant of proportionality k = .5. (a) Write a differential equation that is satisfied by the amount f(t) of the drug in the blood at time t (in hours). (b) Find f (t) assuming that f (0) = 0. (Give your answer in terms of r.) (c) In a therapeutic 2-hour infusion, the amount of drug in the body should reach 1 milligram within 1 hour of administration and stay above this level for another hour. However, to avoid toxicity, the amount of drug in the body should not exceed 2 milligrams at any time. Plot the graph of f (t) on the interval 1 t 2, as r varies between 1 and 2 by increments of .1. That is, plot f (t) for r = 1, 1.1, 1.2, 1.3,c, 2. By looking at the graphs, pick the values of r that yield a therapeutic and nontoxic 2-hour infusion.
- Q: A bank account has $20,000 earning 5% interest compounded continuously. A pensioner uses the account to pay himself an annuity, drawing continuously at a $2000 annual rate. How long will it take for the balance in the account to drop to zero?
- Q: Figure 8 shows a portion of the solution curve of the differential equation y = 2y (1 - y) through the point (0, 2). On Fig. 8 or a copy of it, draw an approximation of the solution curve of the differential equation y = 2y (1 - y) through the point (0, 3). Use the slope field to guide your graph. y 3 2 1 0 -1 22 1 1111 11 t 0 2 3 4 Figure 8 Slope field of y'= 2y (1 - y).
- Q: Solve the following differential equations with the given initial conditions. y = 5ty - 2t, y(0) = 1
- Q: Solve the following differential equations with the given initial conditions. dy dx In x Vxy y(1) = 4
- Q: Solve the initial-value problem. ty - y = -1, y(1) = 1, t > 0

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