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...HAU STORIUM
Parasitic Plants Newsletter Official Organ of the International Paras .c Seed Plant Research Group
~ ~ ~
November 1995
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Number 31
SIXTH INTERNATIONAL PARASITIC WEED SYMPOSIUM CORDOBA, SPAIN 16-18 APRIL 1996 t FINAL ANNOUNCEMENT t
Th...
...No. 5
J u n e 1980
LI'SPRG N e w s
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S t e e r i n g Committee Formed
A t t h e 1979 R a l e i g h Symposium a S t e e r i n g Conunittee was nominated. Some nominees were u n a b l e t o s e r v e c a u s i n g c o n s i d e r a b l e d e l a y...
...HAUSTORIUM 46 December 2004
1
HAUSTORIUM
Parasitic Plants Newsletter
Official Organ of the International Parasitic Plant Society
December 2004
IPPS TO ELECT NEW OFFICERS The time has come to elect a new set of officers for the International Parasi...
...HAUSTORIUM 50 January 2007
1
HAUSTORIUM
Parasitic Plants Newsletter
Official Organ of the International Parasitic Plant Society
50 ISSUE!
January 2007 MESSAGE FROM THE IPPS PRESIDENT Dear IPPS Members, The IPPS wishes you a happy festive season a...
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Practice SOLUTIONS questions for final exam PLEASE NOTE: The purpose of this document is to help you review the material and PRACTICE. Some questions might be harder than the real exam while some might be easier. There is NO guarantee that the real exam will be similar to this one. This document also does NOT necessarily cover all the material. Section A. Accounts Receivable B. Inventory C. Property, Plant and Equipment D. Financial Statement Analysis E. Bonds 1 Section A: Accounts Receivables Part I: multiple choice questions, choose the single best answer 1. ___A____ Angela Corporation writes off an uncollectible account of a bankrupt customer. How would this transaction affect net income and net account receivable? Net income No effect No effect Increase Decrease Increase Net account receivable No effect Increase No effect No effect Increase a. b. c. d. e. Part II: calculation question To address this part of the problem please refer to the information provided in the Financial Statements of Bull's Eye Company that are included at the end of the practice question. REQUIRED: Assuming that all sales are on credit, compute the total amount of cash collected from sales during 2003. You must label and circle your answer for full credit Allowance for Doubtful Accounts 36 40 Write-offs (plug) 56 20 Ending Balance Beginning Balance Bad Debt Expense Accounts Receivable Beginning Balance Sales 261= (225+36) 56 465 475 Cash Collected Write-offs Ending Balance 195= (175+20) 2 Section B: Inventory Part I: multiple choice questions, choose the single best answer 1. ________ In periods of rising prices, which of the following statements is most likely to be true? a. FIFO may result in a lower ending inventory than LIFO. b. FIFO may result in a lower cost of goods sold than LIFO. c. FIFO may result in a lower profit margin than LIFO. d. FIFO may result in a lower net income than LIFO. e. In periods of rising prices, none of the above statements is likely to be true. (Rising prices FIFO method results in lower cost, higher net income) 2. ________ Which of the following statements about the selection of a cost flow assumption is correct? a. Management may use LIFO for income tax purposes only if it also uses LIFO in its financial statement. b. Management needs to match the cost flow assumption to the physical flow of the goods. c. Management must select the method that consistently provides the most net income. d. Management must use the method that is standard in its industry. Part II: Calculation question Peeke Company has the following inventory information: Beginning Inventory 100 units @ $30.00 per unit Purchase #1 60 units @ $35.00 per unit Purchase #2 40 units @ $40.00 per unit Units sold 170 units Required: Use the above information to fill in the following table for this year. Cost of goods sold, $ Ending inventory, $ FIFO 100*$30+60*$35+10*$40=5,500 30*$40=1200 LIFO 40*$40+60*$35+70*$30= 5800 30*$30=900 3 Section C: Property, plant and equipment Part I: multiple choice questions, choose the single best answer 1. ________ Depreciation expense is recorded in order to a. ensure that the firm has adequate cash to replace the asset. b. present assets at fair market value. c. prevent the recognition of large losses at disposition. d. allocate the cost of noncurrent, nonmonetary assets to periods benefited. e. All of the above. 2. ________ A firm acquires a car for company business. The car costs $12,000, has a useful life of 5 years, and a salvage value of $2,000. The straight-line method of depreciation is used. What is the gain or loss on retirement if the car is sold for $5,000 after three years of use? a. b. c. d. a gain of $200 a loss of $1,000 a gain of $1,000 a loss of $200 (Accumulative deprecation =(12,000-2,000)/5*3years=6,000 AT THE TIME OF SALE. Thus, the journal entry is (Cash 5,000 ACC. Dep 6,000 Loss 1,000 PP&E 12,000) Part II: Calculation question The following information is related to equipment purchased by White Inc.: Equipment purchase date January 1, 2001 Acquisition cost $40,000 Estimated residual value $4,000 Estimated useful life 5 years Compute the annual depreciation expense related to the equipment for the next two years, using the following method: 1. Straight-line Dep expense =(40,000-4000)/5=7,200 in both 2001 and 2002 2. Double-declining-balance (DDB), where depreciation expense=(cost-accumulated depreciation)*(2/estimated useful life) Dep expense in 2001 =(40,000)*2/5=16,000 in 2001 Dep Expense in 2002 =(40,000-16,000)*2/5=9,600 4 Part III: Financial Statement Impact Suppose White Inc. sells a machine at the end of the sixth year for $3,000. The machine has a historical cost of 290,600 and accumulated depreciation of 288,000 at the time of sale. Show the effects the entry would have on the balance sheet, income statement and the statement of cash flow (indirect). Be specific about the amount, direction and line item. For the Balance Sheet impact, you must indicate whether the entry affects an Asset, Liability or Owners' Equity account; for the Income Statement you must indicate whether the item affects Revenues or Expenses and its effect on Net Income. For the statement of cash flows, if operating cash flow is not affected but there are adjustments needed, specify the adjustments. If operating cash flow is affected but there is no adjustment needed, then write "No adjustment." Post your answers in the table below. Balance Sheet Income Cash Flow Statement Statement Cash (Asset) 3000 Gain 400 Operating PPE(Assets) -290600 NI 400 NI 400 -AccDep(XAssets) (288000) -gain -400 Op. Cash 0 RE (OE) 400 Investing Sale of PPE 3000 The journal entry is Cash 3000 ACC Dep 288000 PPE 290600 Gain 400 5 Section D: Financial Statement Analysis Assume the following financial ratio definitions. Answer the following questions: - ROA equals net income divided by average total assets. - ROCE equals net income divided by average total stockholders' equity. - The Leverage Ratio equals average total assets divided by average total stockholders' equity. - The Current Ratio current equals assets divided by current liabilities. - The Asset Turnover Ratio equals Sales divided by average total assets. - The Profit Margin ratio equals Net Income divided by Sales. - The Gross Profit Margin ratio equals Sales minus Costs of Goods Sold, divided by Sales. Find attached the Balance Sheet (BS) and Income Statement (IS) for Bull's Eye Company. Answer the following questions: Part I: multiple choice questions, choose the single best answer 1. ________ Bull's Eye company issues additional $5,000 of long-term debt. This transaction would: a. Increase its current ratio b. Decrease its current ratio c. Increase its profit margin d. Decrease its profit margin Part II. Search/calculation questions 1. What is the Balance Sheet equation? Prove that this equation holds for Bull's Eye on December 31, 2003. A=L+OE 40,000= 320,000+80,000 2. What is Bull's Eye's historical acquisition cost (i.e., purchase cost) for Property, Plant and Equipment (PP&E) at the end of 2003? On which statement (BS or IS) do you find the numbers? BS 65,000 (41,000+24,000) 3. How much is Bull's Eye's profit margin in 2003? Show your calculation and indicate on which statement (BS or IS) do you find the numbers? IS, profit margin=13,000/465,000=2.8% 6 Section E: Bonds Part I: multiple choice questions, choose the single best answer 1. ________ Ramblin Rose Company plans to issue $100,000 bonds with a stated interest rate of 8 percent. Similar bonds currently yield 10 percent. Ramblin Rose can expect to receive a. b. c. d. $100,000. more than $100,000. less than $100,000. Cannot be determined with the above information. Market rate greater than coupon rate => bonds issued at discount 2. ______ The bond issuer will receive the full face value of the bond if the a. b. c. d. stated interest rate equals the market rate of interest. bonds have been rated by a nationally known rating agency. bonds are issued by a nationally known company. bonds are secured by collateral equaling the face value of the bonds. 7 Part II: Calculation question The Wretched Heart Company is a manufacturer of Witch Hazel and prepares accrual basis financial statements on January 1 and July 1. On January 1, 1995 Wretched Heart issued Bonds to the public. The bonds are due at the end of 15 years. The face value of the bonds is $1,000,000 and the coupon rate is 6%. The bonds were issued to yield 8%. Note: please refer to the present values tables attached to the end of this document for relevant numbers. Required: (1) Assume Interest payments are made to the bondholders annually every December 1. Make the journal entry to record the first interest payment to the bondholders on December 1, 1995. annul payments to bondholders = (1,000,000*6%) = 60,000 Book value of bonds payable at 1/1/95 = (1,000,000*.31524[table 2, 15 periods, 8%]) + (60,000* 8.55948[table 4]) = 315,240 + 513,569 = 828,809 Interest expense (828,809*.08) Cash Bonds payable 66,304 60,000 6,304 (2) Assume Interest payments are made to the bondholders semi-annually every January 1 and July 1. Make the journal entry to record the first interest payment to the bondholders on July 1, 1995. Semi-annul payments to bondholders = (1,000,000*6%*6/12) = 30,000 Book value of bonds payable at 1/1/95 = (1,000,000*.30832[table 2, 30 periods /4%]) + (30,000* 17.29203[table 4]) = 308,320 + 518,761 = 827,081 Interest expense (827,081*.08*6/12) Cash Bonds payable 33,083 30,000 3,083 8 Part III: Financial Statement Impact Specify the net impact of the following two journal entries on the items listed in the table below. If the transaction does not affect a particular item, write `No Effect.' Journal entry #1. Bond issuance Cash 3000 Bond payable 3000 Journal entry #2. Interest payment Interest expense 200 Cash Bonds payable 180 20 Item Current assets Journal entry #1 Net impact (direction and amount) 3000 Journal entry #2 Net impact (direction and amount) -180 Total Liabilities 3000 20 Retained earnings No effect -200 Cash flows from operating activities Cash flows from investing activities Cash flows from financing activities Net income No effect -180 No effect No effect 3000 No effect No effect -200 9 Bull's Eye Company Balance Sheets December 31, 2003 and 2002 ASSETS: Current assets: Cash Accounts receivable, net of allowance for doubtful accounts of $20,000 in 2003 and $36,000 in 2002 Inventory Total current assets Property, Plant and Equipment, net of accumulated depreciation of $24,000 in 2003 and $26,000 in 2002 Other assets Total assets LIABILITIES & STOCKHOLDERS' EQUITY: Current liabilities: Accounts payable Accrued liabilities Total current liabilities 2003 18,000 2002 22,000 175,000 102,000 295,000 225,000 132,000 379,000 41,000 64,000 400,000 44,000 231,000 654,000 47,000 32,000 79,000 67,000 21,000 88,000 Long-term debt Stockholders' Equity Common stock Retained earnings Total Stockholders' Equity Total liabilities and stockholders equity 241,000 466,000 20,000 60,000 80,000 400,000 30,000 70,000 100,000 654,000 (NOTE: The Income Statement for Bull's Eye is on the Next Page, along with some important additional information.) 10 Bull's Eye Company Income statement Years ended 2003 and 2002 Sales Operating Expenses: Cost of sales General and Administrative Expenses Depreciation Expense Interest Expense Other income and expenses, net Total Costs and Expenses Operating Income Income before taxes Income tax expense Net Income 2003 $465,000 2002 $450,000 230,000 110,000 4,000 40,000 45,000 429,000 36,000 23,000 $ 13,000 225,000 116,000 8,000 50,000 42,000 441,000 9,000 4,000 $ 5,000 Additional information: 1. 2. 3. 4. Other income and expenses in the Income statement include Bad Debt Expense of $40,000 in 2003 and $35,000 in 2002. Property, Plant &Equipment was sold during 2003 for $2,000 in cash Property, Plant &Equipment was purchased for cash of $7,000 during 2003 and $6,000 during 2002. The marginal income tax rate is 40% for 2003 and 50% for 2002 11 12 13
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USC >> ACCT >> 410x (Spring, 2008)
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BISC-220 SI Week 7 Bisc220SILeaders@gmail.com Leader: Matt www.usc.edu/si Chapter 9 Respiration (Part II): Fermentation/Control of Respiration Will cellular respiration ensue without oxygen? _ Explain why or why not! What two terms describe the c...
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Mad Dog Week 7 BISC 220 Supplemental Instruction www.usc.edu/si; bisc220sileaders@gmail.com Lecture 15 (and most of 16): Photosynthesis Our understanding of photosynthesis comes from some really sexy biochemistry. Unfortunately, we first must do a ...
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Mad Dog Week 13 BISC 220 Supplemental Instruction www.usc.edu/si; bisc220sileaders@gmail.com Exam: Friday, April 11th 1) Expansion of the lungs occurs in response to: a. elimination of elasticity within the lungs. b. relaxation of the diaphragm. c....
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USC >> MATH >> 507A (Spring, 2008)
MATH 507b ASSIGNMENT 4 SOLUTIONS SPRING 2008 Prof. Alexander Chapter 5: (2.1) Let A (X0 , ., Xn ) and B (Xn , Xn+1 , .). Using Theorem 1.2 Chapter 4 (p. 224) and the Markov property, since 1A Fn we get P (A B | Xn ) = E (E (1A 1B | Fn ) | Xn ) = ...
USC >> MATH >> 507A (Spring, 2008)
MATH 507b ASSIGNMENT 2 SOLUTIONS SPRING 2008 Prof. Alexander Chapter 4: (7.1) Let N = min{n : Xn > }, with N = if there is no such n. By Theorem 7.6, EX0 EXN {XN >} XN dP P (XN > ) = P (sup Xn > ), n so P (supn Xn > ) EX0 /. (7.2) By Theorem 4...
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USC >> MATH >> 507A (Spring, 2008)
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USC >> HIST >> 106g (Fall, 2007)
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USC >> HIST >> 106g (Fall, 2007)
Upon his visit to America, Liang had experienced the western life and culture. He had noticed some important changes that were essential for China adopt in order to transform into a modern nation. First and foremost, Liang thought that the instillmen...
USC >> HIST >> 106g (Fall, 2007)
3. Write an essay comparing the Nationalists/ GMD and the Communists/CCP from the 1920s to 1950. What sorts of people (from what social strata) tended to support each side? Along what sorts of issues and policies did they align? What do you think exp...
USC >> HIST >> 106g (Fall, 2007)
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USC >> ACCT >> 410x (Spring, 2008)
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USC >> ACCT >> 410x (Spring, 2008)
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Chapter 14 Financing with Debt QUESTIONS 1. In order to recognize a liability, a company need not know the actual recipient of the assets that are to be transferred or for whom the services are to be performed. For example, a company that provides wa...
LSU >> ECON >> 2000 (Spring, 2008)
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LSU >> ECON >> 2000 (Spring, 2008)
Chapter 27 MONEY, BANKING, AND THE FINANCIAL SECTOR McGraw-Hill/Irwin Copyright 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 27-2 Today\'s lecture will: Discuss why the financial sector is central to almost all macroeconomic de...
LSU >> ECON >> 2000 (Spring, 2008)
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LSU >> ECON >> 2000 (Spring, 2008)
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Kansas >> POLS >> 110 (Spring, 2008)
POLS 110: Introduction to U.S. Politics REVIEW SHEET: TEST #2 Test Date: Wednesday, March 5th Chapter 4 (Lowi, Ginsberg, and Shepsle) What is the Bill of Rights? What is a civil liberty? What is the difference between a civil liberty and a civil rig...
Kansas >> POLS >> 110 (Spring, 2008)
POLS 110: Introduction to U.S. Politics REVIEW SHEET: TEST #4 Test Date: Monday, May 5th GTAs: Kellee Kirkpatrick, Amber Dickinson, Whitney Court, Gail Rodriguez, Linsey Moddelmog Chapter 9 (Lowi, Ginsberg, and Shepsle) How do most citizens form the...
Kansas >> ENGL >> 322 (Spring, 2008)
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LSU >> MC >> 4900 (Spring, 2008)
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Baker KS >> HWC >> 205 (Spring, 2008)
FINAL EXAM REVIEW LOCKE Tacit consent-you give up certain rights by implied consent in order to be a part of society. In return, you get some benefits. You get protection, the right to ownership, benefits of government in an ordered society. You give...
GA Southern >> ACCT >> 2101 (Spring, 2008)
CHAPTER 1 SERIES A PROBLEMS Prob. 11A 1. CHICKADEE TRAVEL SERVICE Income Statement For the Year Ended April 30, 2006 Fees earned . Operating expenses: Wages expense.. Rent expense . Utilities expense . Supplies expense . Taxes expense . Miscellaneous...
GA Southern >> ACCT >> 2101 (Spring, 2008)
CHAPTER 4 SERIES A PROBLEMS Prob. 41A 1. SCF BS IS F ASE - SCF BS - AL IS - (a) Cash. Capital Stock . (b) Supplies . Accounts Payable . (c) Cash. Sales Commissions Earned . (d) Rent Expense . Cash . (e) Accounts Payable . Cash . (f) Dividends . Cash ...
GA Southern >> ACCT >> 2101 (Spring, 2008)
CHAPTER 11 SERIES A PROBLEMS Prob. 111A 1. Year 2003 . 2004 . 2005 . 2006 . 2007 . 2008 . Dividends $40,000 18,000 24,000 27,000 65,000 54,000 $1.20 Preferred Dividends *Arrears dividend, preferred (2004: $12,000; 2005: $6,000; 2006: $3,000) . Curren...
GA Southern >> ACCT >> 2101 (Spring, 2008)
CHAPTER 13 SERIES A PROBLEMS Prob. 131A WINNER\'S EDGE SPORTING GOODS, INC. Statement of Cash Flows For the Year Ended December 31, 2007 Cash flows from operating activities: Net income, per income statement . Add: Depreciation .. Increase in accounts...
GA Southern >> ACCT >> 2101 (Spring, 2008)
CHAPTER 12 SERIES A PROBLEMS Prob. 121A MOTOSPORT, INC. Income Statement For the Year Ended October 31, 2006 Sales . Cost of merchandise sold .. Gross profit . Operating expenses: Selling expenses: Sales salaries expense . $140,000 Advertising expens...
CUNY Queens >> ECON >> 382 (Spring, 2008)
Economics 382 Instructor: Jing Sun Homework #7 This homework is due on Tuesday April 8th at the time of the class. 1. (Complete using calculator) Wooldridge Chapter 3, problem 3.10, page 114. Answer: 3.10 (i) Because x1 is highly correlated with x2 a...
CUNY Queens >> CMLIT >> 101 (Spring, 2008)
Great Books 101W Fall 2006 Midterm Review Sheet The following questions are meant as a study guide only. Any and all material covered on this sheet is fair game for the exam. Study them carefully over the weekend and on Tuesday in class there will be...
CUNY Queens >> ECON >> 206 (Spring, 2008)
Jansen Guim Econ 206 Section AM3WA December 10, 2007 Extra Credit What is the impact of the oil price in the US economy? Due to the industrial revolution the supply of energy is very important in our society. With that said, fossil fuels are of gre...
CUNY Queens >> ECON >> 206 (Spring, 2008)
Extra credit In the years before Worlds War I, the Myopia economy grew by 4% per year even though its labor force was growing by only 2% per year. During World War I, a substantial number of soldiers were killed. Usually the soldiers were young men w...
CUNY Queens >> ECON >> 206 (Spring, 2008)
Problem Set 1 - Answers 1. Explain whether and why the following items are included in the calculation of GDP: A. Increases in business inventories B. Sales of existing homes C. The fees earned by real estate agents on selling existing homes D. Incom...
Université Stendhal Grenoble 3 >> BUSINESS >> 1101 (Winter, 2002)
Notions de Stratgie Stratgie; Concept, Mthode et Outils Dfinition de l\'entreprise : L\'entreprise est un groupe productif ayant comme objectifs de : - Exister en tant que groupe dont les membres agissent en acteurs. - Transformer - Conqurir une nomb...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Biology 350: Environmental Biology Unit I: Humans and the Environment I Defining Environmental Science A E. S. studies 1. How the earth works 2. How people interact with the earth 3. How to deal with environmental problems B E. S. tries to integrate ...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Ecological Concepts I Ecology: The study of the relationships between organisms and their environment. A Goal is to determine factors that affect the abundance and distribution of species II Ecosystems - the community and its physical environment. A ...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Biodiversity Species A A population of morphologically (structurally) similar organisms that can sexually reproduce among themselves but cannot produce fertile offspring when mated with other organisms. 1. Reproductive isolation is the key feature. B...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Climate Change I Climate A Climate vs. weather 1. Climate is the long term pattern of temperature and precipitation for a given area a) Temperature measurements include average yearly temperature as well as extreme high and low temps. b) Precipitatio...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Study Questions for Paul Ehrlich and the Population Bomb 1. What was the ironic situation that Paul Ehrlich observed in India during his visit in 1966? In the midst of famine the country was undergoing a population boom. 2. What was the world\'s popul...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Forest Resources Forests A Ecosystems that are dominated by trees B Structure can be viewed as vertical layers 1. Canopy formed by the tallest, oldest trees 2. Under-story of younger trees and tall shrubs 3. Floor covered in herbaceous, flowering pla...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Renewable Energy Options I Solar Energy A Greatest benefit is that it is free other buildings a) Pas...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Non-renewable Energy Energy Resources for Planet Earth A Solar 1. provides the planet with 99% of the available energy 2. Comes in two forms a) Direct solar from the sun i) Provides light & heat ii) Energy for photosynthesis, makes most life possible...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Water Resources I Earth: The Water Planet A 71% of the earth is covered in water. 1. 97.4% is salt water, 2.6% is fresh 2. Of the fresh water about 87% is frozen in polar caps and glaciers, about 22% is groundwater and less than 1% is surface water (...
Los Rios Colleges >> BIO >> 350 (Spring, 2008)
Name _ Empty Oceans, Empty Nets Study Questions Where is life in the ocean most concentrated? Over the continental shelf (near shore which makes it more accessible to humans) What is the first and simplest reason fish stocks are collapsing at faster ...
Lee >> BUSN >> 341 (Fall, 2008)
PRODUCTS AND SERVICES Macy\'s sells a wide-ranging assortment of merchandise that\'s helps customers express their personal style. It delivers fashion and affordable luxury to its customers at more than 800 locations in 45 states, the District of Colum...
Lee >> PED >> 341 (Spring, 2008)
Dave Mason 1-21-08 PED341 Andrea Hudson When searching for a manager, there are certain traits that one should look for. However, some are more important than others. In my opinion, organization and experience are two of the most important and effect...
Lee >> PED >> 341 (Spring, 2008)
David Mason Administration of P.E. and Sport Ms. Andrea Hudson With the addition of two new feeder schools and new athletic facilities, I strongly believe that the organization of an intramural and sport club program would be extremely beneficial to...
USC >> EE >> 201L (Spring, 2004)
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USC >> EE >> 201L (Spring, 2008)
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USC >> EE >> 201L (Spring, 2008)
ee102_midterm1_Sp2005_Q5_4_alternative_solutions.fm 5 Alternative solutions to Q#5 of EE102L Spring 2005 Midterm #1 Serial Voting Machine: We want to design a serial voting machine which inspects THREE votes serially. In this design we need to prod...
USC >> EE >> 201L (Spring, 2008)
CBUX Au =< Bu ...
USC >> EE >> 201L (Spring, 2008)
step 6 to 7 is a \"No Branch\". ...
USC >> MATH >> 425B (Fall, 2007)
MATH 425b MIDTERM 2 SOLUTIONS SPRING 2008 Prof. Alexander (1) Let A = f (x). Then f (x + hn + kn ) - f (x) = A(hn + kn ) + o(|hn + kn |) = Ahn + Akn + o(|hn | + |kn |) = [f (x + hn ) - f (x) + o(|hn |)] + [f (x + kn ) - f (x) + o(|kn |) = [f (x + hn ...
USC >> MATH >> 425B (Fall, 2007)
MATH 425b ASSIGNMENT 1 SOLUTIONS SPRING 2008 Prof. Alexander Chapter 7 (1) Suppose fn f uniformly. Let > 0. There exists an N such that |fN - f | < . Since fN is bounded, there exists an MN such that |fN (x)| MN for all x. Then for all x, |f (x)| ...
USC >> MATH >> 425B (Fall, 2007)
MATH 425b ASSIGNMENT 2 SOLUTIONS SPRING 2008 Prof. Alexander Chapter 7 (8) Since |cn I(x - xn )| |cn | and |cn | < , the series defining f converges uniformly by the Weierstrass M -test (Theorem 7.10.) Letting fn (t) = n cn I(x - xn ), this means th...
USC >> MATH >> 425B (Fall, 2007)
MATH 425b ASSIGNMENT 3 SOLUTIONS SPRING 2008 Prof. Alexander Chapter 7 (20) Let > 0. There exists a polynomial with |P - f | < (sup norm), say P (x) = N n n=0 cn x . f is bounded since it is continuous on the compact set [0, 1], so there exists M suc...
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