Finite mathematics & Applied calculus

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1 1. Let A = , B = Finite mathematics & Applied calculus, C = , D = undefined. A + B =. Evaluate each of the following expressions, if it is defined. If an expression is not defined, enter A T = A + C T = D + 3A = Copyright Stefan Waner 1/9

2 2. Ballet The following table shows July purchases of white, blue, and pink tutus and leotards by the Primadonna Ballet Company: July purchases White Blue Pink Tutus Leotards During each of the subsequent months the company went through quite a large number of these items, as shown in the next table: Monthly usage White Blue Pink Tutus Leotards (a) Let J denote the matrix represented by the first table above and U the matrix represented by the second table. J 2U = (b) Which of the following is represented by the answer to part(a)? A The average monthly usage by the end of August B The remaining inventory at the end of August C The total usage by the end of August D The total usage by the end of September E The remaining inventory at the end of September F The average monthly usage by the end of September (c) The following year the company donated all remaining inventory to the local dance school and restocked with a new brand during July. However, the monthly usage was 50 percent more than the previous year. Type a formula for the remaining inventory at the end of October. Answer: Copyright Stefan Waner 2/9

3 3. Let A = , B = , C = , D = Evaluate each of the following expressions, if it is defined. If an expression is not defined, enter undefined. BA = DC = DD T = CB 2 = Copyright Stefan Waner 3/9

4 Let P =. Evaluate each of the following expressions P 2 = P 3 = P 4 = P 10 = Copyright Stefan Waner 4/9

5 5. Airport delays The following table shows the average departure delay per flight at the four busiest airports in the US during 1999: Airport Atlanta Chicago OHare Dallas-Fort Worth Los Angeles Int. Ave. delay (minutes) On a certain day, 200 flights depart from Atlanta, 300 from OHare, 150 from Dallas, and 250 from Los Angeles. Let D denote the 1 4 matrix represented by the above table, and let F be the 1 4 matrix represented by the departing flights. (a) Which of the formulas below represents the total delay in all departing flights from these airports that day? A DF T B DF C FD D D T F T E F T D F D T F (b) Now calculate the total delay in all departing flights from these airports that day using the formula in part (a). Answer: min. Copyright Stefan Waner 5/9

6 6. Ballet The following table shows the number of white, blue, and pink tutus and leotards purchased by the Primadonna Ballet Company each ballet season: Number purchased White Blue Pink Tutus Leotards Primadonna purchases from three suppliers: Logan Pirouette, Toms Tutus, and Dance Dynamics. Their prices are shown in the following table: Prices ($) Logan Pirouette Toms Tutus Dance Dynamics Tutus Leotards (a) Let N denote the matrix represented by the first table above and P the matrix represented by the second table. The (2, 3) entry of P T N is: (b) Which of the following is represented by the answer to part (a)? A The total cost of all pink leotards purchased from Toms Tutus B The total cost of all pink items purchased from Toms Tutus C The total cost of all leotards purchased from Dance Dynamics D The total cost of all tutus purchased from Toms Tutus E The total cost of all blue items purchased from Dance Dynamics F The total cost of all blue leotards purchased from Dance Dynamics Copyright Stefan Waner 6/9

7 7. Bankruptcy The following table shows the number of personal bankruptcy filings in three cities during three economically depressed months last year: Let B be the matrix represented by this table. June July August New York Las Vegas Los Angeles (a) Each month, your law firm handles 10% of all bankruptcy filings in New York, 30% of all filings in Las Vegas, and 20% of all filings in Los Angeles. Let P be the 1 3 matrix of the corresponding percentages (percentage points/100). Which of the formulas below gives the total number of filings handled by your firm during each of these three months? A P T B B PBP T C BP T D BP E B T P T F P T BP (b) Now calculate the product in part (a) would be entered as 3; 66; 7 7 Answer: Copyright Stefan Waner 7/9

8 8. Find the inverse of each matrix, if it exists. If a matrix is singular, enter singular Copyright Stefan Waner 8/9

9 9. Consider the following system of linear equations: p q = 2 q r = 0 r s = 3 s = 1 (a) If we write this system in the form AX = B, then A = X = B = A 1 = (b) The solution is: p = q = r = s = Copyright Stefan Waner 9/9

Research Update: Race and Male Joblessness in Milwaukee: 2008

Research Update: Race and Male Joblessness in Milwaukee: 2008 by: Marc V. Levine University of Wisconsin Milwaukee Center for Economic Development Briefing Paper September 2009 Overview Over the past decade,