The transitive closure R^T of a relation R is the smallest set conta.pdf

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The transition matrix of a Markov chain is: [ .96 .04 ] [ .27 .73 ] If it starts in state 2, what is the probability that it will be in state 2 after 2 transitions? Solution The transition matrix is [P=([.96,.04],[.27,.73])] and we are asked to find the probability that if we are in state 2 we are again in state 2 after 2 transitions. The entries [p_(i,j)] are the probabilities of going from state i to state j. To find the probabilities after m transitions we look at [P^m] . [P^2=([.9324,.0676],[.4563,.5437])] . The probability of starting in state 2 and ending in state 2 after 2 transitions is the entry [p_(2,2)] in [P^2] which is .5437 ----------------------------------------------------------------- The probability is approximately .5437 ---------------------------------------------------------------.

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The trial balance of the Wall Fashion Center, Inc. contained the following accounts at December 31, 2007 the end of the company’s calendar year. WALL FASHION CENTER, INC. Trial Balance 31-Dec-07 Debit Credit Cash $ 16,700 Accounts Receivable 33,700 Merchandise Inventory (Beginning) 38,000 Store Supplies 5,500 Store Equipment 85,000 Accumulated Depreciation-Store Equipment $ 18,000 Delivery Equipment 48,000 Accumulated Depreciation-Delivery Equipment 6,000 Notes Payable 51,000 Accounts Payable 48,500 Common Stock 80,000 Retained Earnings 30,000 Dividends 12,000 Sales 746,600 Sales Returns and Allowances 4,200 Purchases 503,600 Purchase Returns and Allowances 6,900 Purchase Discounts 3,700 Freight-in 10,800 Salaries Expense 140,000 Advertising Expense 26,400 Utilities Expense 17,000 Repair Expense 9,100 Delivery Expense 16,700 Rent Expense 24,000 $ 990,700 $ 990,700 Adjustment data: Store supplies on hand totaled $3,500. Depreciation is $9,000 on the store equipment and $7,000 on the delivery equipment. Interest of $11,000 is accrued on notes payable at December 31. Other data: Merchandise inventory on hand at December 31, 2007 is $45,000. Salaries expense is 70% selling and 30% administrative. Rent expense and utilities expense are 80% selling and 20% administrative. $30,000 of notes payable are due for payment next year. Repair expense is 100% administrative. The beginning balance of accounts receivable is $31,250. The amount of total assets at the beginning of the year is $199,700. Instructions 1)Journalize the adjusting entries. 2)Prepare a multiple-step income statement and a retained earnings statement for the year and a classified balance sheet as of December 31, 2007. 3)Journalize the closing entries. 4)Prepare a post-closing trial balance. 5)Prepare the following ratios and show all support for your computations: a) Current Ratio b) Quick Ratio c) Working Capital d) Accounts Receivable Turnover e) Average Collection Period f) Inventory Turnover g) Days in Inventory h) Debt to Total Assets Ratio i) Gross Profit Ratio j) Profit Margin Ratio k) Return on Assets Ratio l) Asset Turnover Ratio 6) Based on the ratios computed in 5 above, answer the following questions and use the financial statement ratios to support your answers where appropriate: Do you feel that the company is able to meet its current and long term obligations as they become due? Comment on the profitability of the company with respect to the various profitability ratios that you computed. Would you lend money to this company for the long term? Comment on the ability of the company to collect its receivables and mange inventory. 2004 2005 2006 Industry Average Liquidity Current 1.09 1.30 1.80 1.42 Quick 0.89 1.08 1.28 1.10 Working Capital $ 10,000.00 $ 13,500.00 $ 18,000.00 $ 20,000.00 Leverage Debt to Total Assets (%) 52.03% 48.52% 43.61% 40.00% Times Interest Earned 1.50 3.50 4.75 5.00 Activity Inventory Turnover (sales) 12.56 13.85 14.02 19.98 Fixed Asset Turnover 9.50 .

The trial balance of Watteau Co. does not balance.WATTEAU CO. .pdf

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the trassh bag case Solution Tests show the trash bag has a mean breaking strength µ close to but not exceeding 50 lbs The null hypothesis H0 is that the new bag has a mean breaking strength that is 50 lbs or less The new bag’s mean breaking strength is not known and is in question, but it is hoped it is stronger than the current one The alternative hypothesis Ha is that the new bag has a mean breaking strength that exceeds 50 lbs One-sided, “greater than” alternative H0: µ = 50 versusHa: µ > 50 State the null and alternative hypotheses H0: ? ? 50Ha: ? > 50where µ is the mean breaking strength of the new bag Specify the significance level ? ? = 0.05 Select the test statistic Use the test statistic A positive value of this this test statistic results from a sample mean that is greater than 50 lbs Which provides evidence against H0 in favor of Ha Determine the rejection rule for deciding whether or not to reject H0 To decide how large the test statistic must be to reject H0 by setting the probability of a Type I error to ?, do the following: The probability ? is the area in the right-hand tail of the standard normal curve Use the normal table to find the point z? (called the rejection or critical point) z? is the point under the standard normal curve that gives a right-hand tail area equal to ? Since ? = 0.05 in the trash bag case, the rejection point is z? = z0.05 = 1.645 Reject H0 in favor of Ha if the test statistic z is greater than the rejection point z? This is the rejection rule In the trash bag case, the rejection rule is to reject H0 if the calculated test statistic z is > 1.645 Collect the sample data and calculate the value of the test statistic In the trash bag case, assume that s is known and s = n1.65 lbs For a sample of n = 40, x = 50.575 lbs. Then Decide whether to reject H0 by using the test statistic and the rejection rule Compare the value of the test statistic to the rejection point according to the rejection rule In the trash bag case, z = 2.20 is greater than z0.05 = 1.645 Therefore reject H0: µ = 50 in favor of Ha: µ > 50 at the 0.05 significance level Have rejected H0 by using a test that allows only a 5% chance of wrongly rejecting H0 This result is “statistically significant” at the 0.05 level Interpret the statistical results in managerial terms and assess their practical importance Can conclude that the mean breaking strength of the new bag exceeds 50 lbs.

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The TOTOM Company sells one product with a variable cost of $5 per unit. The company is unsure what price to charge in order to maximize profits. The price charged will also affect the demand. If fixed costs are $100,000 and the following chart represents the demand at various prices, what price should be charged in order to maximize profits? Units Sold Price 30,000 $10 40,000 $9 50,000 $8 60,000 $7 A. $10 B. $9 C. $7 D. $8 Solution B. $9.

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The Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $298,000 at the end of each of the next two years. At the end of the third year the company will receive payment of $640,000. The company can speed up construction by working an extra shift. In this case there will be a cash outlay of $630,000 at the end of the first year followed by a cash payment of $640,000 at the end of the second year. Use the IRR rule to calculate the (approximate) range of opportunity costs of capital at which the company should work the extra shift. (Round your answers to 2 decimal places.) The Titanic Shipbuilding Company has a noncancelable contract to build a small cargo vessel. Construction involves a cash outlay of $298,000 at the end of each of the next two years. At the end of the third year the company will receive payment of $640,000. The company can speed up construction by working an extra shift. In this case there will be a cash outlay of $630,000 at the end of the first year followed by a cash payment of $640,000 at the end of the second year. Use the IRR rule to calculate the (approximate) range of opportunity costs of capital at which the company should work the extra shift. (Round your answers to 2 decimal places.) Solution We have following cash flows: C1 C2 C3 Current arrangement (298,000) (298,000) 640,000 Extra shift (630,000) 640,000 - Incremental flows (332,000) 938,000 (640,000) Using the IRR, function we get IRR 1= 15.21% IRR2= 67.32% Therefore, capital cost would be in between 15.21% to 67.32%. C1 C2 C3 Current arrangement (298,000) (298,000) 640,000 Extra shift (630,000) 640,000 - Incremental flows (332,000) 938,000 (640,000).

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The three essential pieces of information in the abstract section of an informal document are A. buffer, appeal, and background. B. purpose, scope, and summary. C. conclusion, recommendations, and next step. D. ethos, pathos, and logos. Solution Ans ( B ) Purpose : for the report - why are you writing it ? Scope : what range of information does the report contain ? Summary : what main information does the reader most want or need to know..

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The ThisInstructorIsSoNice Company expects to have net income of $18 million for the year, and to pay out $3.5 million in dividends to common stockholders. There is no preferred stock. What is the expected \"addition to retained earnings\" for the year? Solution The calculation is: + Beginning retained earnings Nil + Net income during the period $18.00 - Dividends paid (3.50) = Ending retained earnings $14.5 million.

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The terms of trade refers to: What goods are exported. What goods are imported. The volume of trade. The prices at which trade occurs.A What goods are exported.B What goods are imported.C The volume of trade.D The prices at which trade occurs. Solution Hi, The correct answer is option (D), The prices at which trade occurs Eplanation: Terms of trade (TOT) refers to the relative price of exports in terms of imports and is defined as the ratio of export prices to import prices..

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The textbook (Engineering Materials - Properties and Selection) divides wear into 3 categories: adhesion, abrasion, and surface fatigue. For each of these, list the type of wear found in each. Solution Wear :- Wear is a erosion of material from its derivative and orginal position on solid surface performed by action of another surface Different types of wears 1) Adhesive wear 2)Abrasion wear 3) Surface fatigue 1) Adhesive wears These can be found between surfaces during fictional contact and generally refers to unwanted displacement and attachment of wear debris from one surface to another Generally adhesive wear occurs when slide over or pressed with each other , which promote material transfer ex - Sheet metal forming 2) Abrasion wear Abrasion wear forms when one material slides over other surface . Abrasion differs from type of contact ex- Deep grove like surface over metal 3) Surface fatigue This process is which surface of material is weakened by surfac loading . Which is a general material fatigue . Fatigue wear is produced by wear materials are detached by cyclic crack growth of micro cracks of surface.

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