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All Textbook Solutions for Mathematical Applications for the Management, Life, and Social Sciences

1REIs it true that 3{x:x3}?Are A={1,2,3,4} and B={x:x1} disjoint?4RE5RE6RE7RE8REIndicate whether each given expression is one or more of the following: rational, irrational, integer, natural, or undefined. (a) (b) 0/6 (c) 6/010RE11RE12RE13RE14RE15RE16RE17RE18RE19REWrite an inequality that represents each of the following. (a) (1,16) (b) [ 12,8 ] (c)21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63REIn problems 63-73, factor each expression completely. 4(x2+1)22(x2+1)365RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97RE98RE99RE1T2T3T4T5T6T7T8T9T10T11T12T13TIn a nutrition survey of 320 students, the following information was obtained. 145 ate breakfast 270 ate lunch 280 ate dinner 125 ate breakfast and lunch 110 ate breakfast and dinner 90 ate all three meals Make a Venn diagram that represents this information. How many students in the survey ate only breakfast? How many students skipped breakfast?15TCampaign Management A politician is trying to win election to the city council, and as his campaign manager, you need to decide how to promote the candidate. There are three ways you can do so: You can send glossy, full-color pamphlets to registered voters of the city; you can run a commercial during the television news on a local cable network; and/or you can buy a full page ad in the newspaper. Two hundred fifty thousand voters live in the city, and 36 of them read the newspaper. Fifty thousand voters watch the local cable network news, and 30 of them also read the newspaper. You also know that the television commercial would cost 40,000; the newspaper ad, 27,000; and the pamphlets mailed to voters, 90 cents each, including printing and bulk rate postage. Suppose that the success of the candidate depends on your campaign reaching at least 125,000 voters and that because your budget is limited, you must achieve this goal at a minimum cost. What would be your plan and the cost of that plan? If you need help devising a method of solution for this problem, try answering the following questions first. How many voters in the city read the newspaper but do not watch the local cable television news?2EAGP1Campaign Management A politician is trying to win election to the city council, and as his campaign manager, you need to decide how to promote the candidate. There are three ways you can do so: You can send glossy, full-color pamphlets to registered voters of the city; you can run a commercial during the television news on a local cable network; and/or you can buy a full page ad in the newspaper. Two hundred fifty thousand voters live in the city, and 36 of them read the newspaper. Fifty thousand voters watch the local cable network news, and 30 of them also read the newspaper. You also know that the television commercial would cost 40,000; the newspaper ad, 27,000; and the pamphlets mailed to voters, 90 cents each, including printing and bulk rate postage. Suppose that the success of the candidate depends on your campaign reaching at least 125,000 voters and that because your budget is limited, you must achieve this goal at a minimum cost. What would be your plan and the cost of that plan? If you need help devising a method of solution for this problem, try answering the following questions first. Complete the following chart by indicating the number of voters each promotional option reached, the total cost, and the cost per voter reached. NumberofVotersReachedTotalCostCostperVoterReachedPamphletTelevisionNewspaper4EAGP11CP2CP3CP4CPCHECK POINT Let A=={ 2,3,5,7,11 } ,B={ 2,4,6,8,10 } and C={ 6,10,14,18,22 }.Use sets to answer the folowing. Which of A,BandC is equals to D={ x:x=4n+2fornaturalnumbers1n5 }?6CP7CP8CPIn problems 1-4, use or to indicate whether the given object is an element of the given set. 12{1,2,3,4,...}In problems 1-4, use or to indicate whether the given object is an element of the given set. 5{x:xisanaturalnumbergreaterthan5}In problems 1-4, use or to indicate whether the given object is an element of the given set. 6{x:xisanaturalnumberlessthan6}In problems 1-4, use or to indicate whether the given object is an element of the given set. 3In problems 5-8, write the following sets in a second way. {x:xisanaturalnumberlessthan8}In problems 5-8, write the following sets in a second way. {x:xisanaturalnumbergreaterthan6, lessthan10}In problems 5-8, write the following sets in a second way. {3,4,5,6,7}In problems 5-8, write the following sets in a second way. {7,8,9,10,...}9E10EIs AB if A={a,b,c,d}andB={a,b,d}?Is AB if A={6,8,10,12}andB={6,8,10,14,18}?13EIn problems 13-16, Use notation to indicate which set is a subset of the other. E={x,y,a,b},F={x,1,a,y,b,2}15EIn problems 13-16, Use notation to indicate which set is a subset of the other. D={a,e,1,3,c},F={e,a,c,1,3}17E18E19E20EFrom the following list of sets, indicate which pairs of sets are disjoint. A={1,2,3,4}B={x:xisanaturalnumbergreaterthan4}C={4,5,6,...}D={1,2,3}If A,B are disjoint sets, what does AB equal?In problems 23-26, find AB. A={2,3,4,5,6}andB={4,6,8,10,12}24EIn problems 23-26, find AB. A=andB={x,y,a,b}In problems 23-26, find AB. A={x:xisanaturalnumberlessthan4}andB={3,4,5,6}27E28E29E30E31E32E33EIn problems 31-42, let. A={1,3,5,8,7,2}B={4,3,8,10}C={2,4,6,8,10} And U be the universal set of natural numbers less than 11.Find the following. AB35E36E37EIn problems 31-42, let. A={1,3,5,8,7,2}B={4,3,8,10}C={2,4,6,8,10} And U be the universal set of natural numbers less than 11.Find the following. (AB)39E40E41E42E43E44E45E46EDow Jones Industrial Average The following table shows information about yearly lows, highs, and percentage changes for the years 2000 to 2012. Let L be the set of years where the low was greater than 8000. Let H be the set of years where the high was greater than 11,000. Let C be the years when the percentage change (from low to high) exceeded 35%. (a) List the elements of L, H, and C. (b) Is any of L, H, or C a subset of one of the others (besides itself)? (c) Write a verbal description of C'. (d) Find H' U C' and describe it in words. (e) Find L' C and describe it in words. Dow Jones Industrial Average Year Low High % Change 2012 12,101.46 13,610.15 12.5 2011 10,655.30 12,810.54 20.2 2010 9686.48 11,585.33 19.6 2009 6547.05 10,092.19 54.1 2008 7552.29 13,056.72 72.9 2007 12,050.41 14,164.53 17.5 2006 10,667.39 12,510.57 17.3 2005 10,012.36 10,940.50 9.3 2004 9749.99 10,854.54 11.3 2003 7524.06 10,453.92 38.9 2002 7286.27 10,635.65 46.0 2001 8235.94 11,332.92 37.6 2000 9796.03 11,722.98 19.7 Source: Dow Jones CompanyJob growth The number of jobs in 2000, the number projected in 2025, and the projected annual growth rate for jobs in some cities are shown in the following table. Consider the following sets. A = set of cities with at least 2,000,000 jobs in 2000 or projected in 2025. B = set of cities with at least 1,500,000 jobs in 2000. C = set of cities with projected annual growth rate of at least 2.5 (a) List A,B,andC (using the letters to represent the cities). (b) Is any of A,B,orC a subset of the other? (c) Find AC and describe the set in words. (d) Give a verbal description of B. ProjectedAnnualJobsin2000Jobsin2025RatesofCities(thousands)(thousands)Increase(%)0(Orlando)109822072.83M(MyrtleBeach)1332562.64L(Atlanta)271548932.38P(Phoenix)195336752.56B(Boulder)2334202.38 Source: Based on data from NM Data Services, Inc.Carbon emission controls Suppose that the following table summarizes the opinions of various groups on the issue of carbon emission controls. Use this table for problem 49and50. WhitesNonwhitesOpinionRep.Dem.Rep.Dem.TotalFavor10025030200580Oppose2501501010420Total350400402101000 Identify the number of individuals in each of the following sets. (a) Republicans and those who favour carbon emission controls (b) Republicans or those who favour carbon emission controls (c) White Republicans or those who oppose carbon emission controlsCarbon emission controls Suppose that the following table summarizes the opinions of various groups on the issue of carbon emission controls. Use this table for problem 49and50. WhitesNonwhitesOpinionRep.Dem.Rep.Dem.TotalFavor10025030200580Oppose2501501010420Total350400402101000 Identify the number of individuals in each of the following sets. (a) Whites and those who oppose carbon emission controls (b) Whites or those who oppose carbon emission controls (c) Non-white Democrats and those who favor carbon emission controlsLanguages A survey of 100 aides at the United Nations revealed that 65 could speak English. 60 could speak French, and 40 could speak both English and French. (a) Draw a Venn diagram representing the 100 aides. Use E to represent English-speaking aides and F to represent French-speaking aides. (b) How many aides are in EF? (c) How many aides are in EF? (d) How many aides are in EF?Advertising Suppose that a survey of 100 advertisers in U.S. News, These Times, and World found the following. 14 advertised in all three 30 advertised in These Times and U.S. News 26 advertised in World and U.S. News 27 advertised in World and These Times 60 advertised in These Times 52 advertised in U.S. News 50 advertised in World Draw a Venn diagram representing the 100 advertisers. How many advertised in none of these publications? How many advertised only in These Times? How many advertised in U.S. News or These Times?College enrollments Records at a small college show the following about the enrollments of 100 first-year students in mathematics, fine arts, and economics. 38 take math 42 take fine arts 20 take economics 4 take economics and fine arts 15 take math and economics 9 take math and fine arts 12 take math and economics but not fine arts How many take none of these three courses? How many take math or economics? How many take exactly one of these three courses?Survey analysis In a survey of the dining preferences of 110 dormitory students at the end of the spring semester, the following facts were discovered about Adam's Lunch (AL), Pizza Tower (PT), and the Dining Hall (DH). 30 liked AL but not PT 21 liked AL only 63 liked AL 58 liked PT 27 liked DH 25 liked PT and AL but not DH 18 liked PT and DH How many liked PT or DH? How many liked all three? How many liked only DH?Blood types Blood types are determined by the presence or absence of three antigens: A antigen, B antigen, and an antigen called the Rh factor. The resulting blood types are classified as follows: type A if the A antigen is present type B if the B antigen is present type AB if both the A and B antigens are present type 0 if neither the A nor the B antigen is present These types are further classified as Rh-positive if the Rh-factor antigen is present and Rh-negative otherwise. Draw a Venn diagram that illustrates this classification scheme. Identify the blood type determined by each region of the Venn diagram (such as A+ to indicate type A, Rh-positive). Use Google or another source to find what percentage of the U.S. population has each blood type.CHECK POINT Decide which of the following are undefined. (a)40(b)04(c)44(d)44442CP3CP4CP5CP6CPIn Problems 1and2, indicate whether the given expression is one or more of the following types of numbers: rational, irrational, integer, natural. If the expression is meaningless, so state. 10 9 93 40In Problems 1and2, indicate whether the given expression is one or more of the following types of numbers: rational, irrational, integer, natural. If the expression is meaningless, so state. 06 1.2916 1.414 963E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29EIn problems 29-32, express each inequality or graph using interval notation and name the type of interval.In problems 33-36, write an inequality that discribes each interval or graph. [3,5)32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48ETake-home pay A salesclerk's take-home pay is found by subtracting all taxes and retirement contributions from gross pay (which consists of salary plus commission). Given the following information, complete parts (a)-(c). Salary =300.00 Commission =788.91 Retirement = 5 of gross pay Taxes: State =5 of gross pay Local =1 of gross pay Federal withholding =25 of (gross pay less retirement) Federal Social Security and Medicare = 7.65 of gross pay Find the gross pay. Find the amount of federal withholding. Find the take-home pay.Public health expenditures The expenditures E for government public health activities (in billions of dollars) can be approximated by E=5.03t2+100t+1380 where t is the number of years past 2000 (Source: Centers for Medicare and Medicaid Services). (a) What t-value represents the year 2010? (b) Actual expenditures for 2010 were $2879 billion. What does the formula give as the 2010 approximation? (c) Estimate the expenditures for 2015.51EHealth statistics Using data adapted from the National Center for Health Statistics, the height H in inches and age A in years for boys between 4 and 16 years of age are related according to H=2.31A+31.26 To account for normal variability among boys, normal height for a given age is 5 of the height obtained from the equation. Find the normal height range for a boy who is 10.5 years old and write it as an inequality. Find the normal height range for a boy who is 5.75 years old and write it as an inequality.53ECHECK POINT Complete the following. (a) x3x8=x? (b) xx4x3=x? (c) 1x4=x? (d) x24x3=x? (e) (x4)2=x? (f) (2x4y)3=?2CP3CP1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43EIn problems 37-48, compute and simplify so that only positive exponents remain. (3m2y1)3(2m3y1)45E46E47E48E49E50E51E52EIn many applications, it is necessary to write expressions in the form cxn, where c is a constant and n is an integer. In problems 49-56, write the expressions in this form. 1x54E55E56E57E