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# Finite Mathematics MGF 1106

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This 17 page Class Notes was uploaded by Ella Simonis on Wednesday September 23, 2015. The Class Notes belongs to MGF 1106 at University of South Florida taught by Karol McIntosh in Fall. Since its upload, it has received 49 views. For similar materials see /class/212661/mgf-1106-university-of-south-florida in Mathmatics at University of South Florida.

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Date Created: 09/23/15

MGF 1106 Final Exam Review sections Time of Common Final Exam Place of Common Final Exam Sections only Those students with a final exam conflict with another highernumbered course please contact your instructor Make sure to get early to the final exam No final exam make ups Will be given Please bring a photo ID to the nal mam Calculators Calculators no cellphones may be used an the nal exam but they CANNOT be shared Content The Final Exam consists of 55 multiplechoice questions Here is a chapterbychapter breakdown of the content of those 55 questions and also some suggested review problems You should be familiar with the terms listed under vocabulary Chapter 2 We will select 8 questions similar to the ones below Concepts empty set universal set subset intersection union complement Venn diagram 1 Write the set xix is a counting number less than 8 using the listing roster method 21 27 2 How many subsets does the set A 51 b c d have 21 57 Let U 51 b c d efAa c e Bb d ef and Ca b if Find each speci ed set 3 a AnBUC b CUA nB 2219 4 Let U 1 2 3 4 5A 2 3 4 and 1 4 5 2228 Find aA B bB A Draw a Venn diagram and shade the region in the gure representing each speci ed set 5 AUB A B 235 n 4 I 6 A 0339 6 23 7 7 Use the numbered regions ofthe diagram to identify the set c m A UB 23 10 cquot 1 a I 2 so 8 8 Draw aVenn diagram that satis es the equation A m3 B 23 29 9 Given A B abA B c2A B gh and A UB df use a Venn diagram to find the following 23 37 aABandU bAUB c A B 10 Suppose that rtA15 nA m3 5 and nA UB 30 Find nB 24 3 11 quot L L39 39 39 39 or people in L t quot 39 24 10 Dimmmeun 1A lC 0 ISK 551 mi Purchming P l 14 7 o n o Quillily 011141th 1 7 i 21 53 ll SalcslS E 8 4D 0 0 0 Manllfi39lculring 1M 5 7 0 9 23 37 Jnnlinn al Ill 1 n D 6 8 ll n41 ldlnhlh mlrn v tL i rlencul ll7 mlw 1th Allied my M mhkmm iUi unskilk d a A NS 391 S U P cM A39 SK39 ILS A39 C39 12 In a sulvey conducted in a certain US city the data in the following table were collected 24 14 White Black Dlller 0 I Im om l W 1B l DverSlD JU H 50 15 IO 370004511000 M7 40 15 15 Under 157000 LLI 30 35 2G Find the number ofpeople in the following sets suM bM c OUB W dLUO eH B39 13 below End the followlng a We h hm c hams 14 on checklng wrth 100 rnyestors to see who owned electxl eompany stoek an 24 21 transportatron stoek 27 or munlclpal bonds M the numbers shown m the dlagram below were found 24 25 41 a hmquot tb tm h trnpnttut c How many had one or two ofthese types oflnvestments but not all three7 d Howmany had atleast two ofthese types ofrnyestments7 e How many had none of these types ofrnyestments7 Chapter 3 We wlll seleet 9 questrons slmllar to the ones below Cuneepts negauon eomuneuon dlsjunchon condlnonal eontraposrtrye lnverse eonyerse blcondmonal De Morgan39s laws truth table equryalent statements symbohe logo premlseconcluslon valldlnvalld argument 15 Let p be RmkylovesLucy and q be LucylovesRlckyquot lee ayerbal translatron of the statement pn q 31 24 16 lee the negatron ofthe statement Some basketball players are not 6ft tall 31 37 17 lee the negatron ofthe statement Ertherhe ls bald orhe has a loan forehead 31 39 18 Let g be Hels agentlemanquot andlet s be He ls aseholarquot Wnte ths statement m symbohe form He ls agentleman and a seholar 32 9 19 Consider the statements p and q 32 11 p It is raining q I will go to the beach Write the statements in parts a and b in symbolic form a It is raining but I will go to the beach b It is raining or I will go to the beach c Assume that p is true and q is false Find the truth values of the statements given in parts a and b 20 Consider the following statements 32 23 g I go to college j I join the army Suppose that g is false and j is true Write a statement in symbolic form and find its truth value of the statement I go to college or I do not join the army 21 Construct atruth table for the statement N pv N q 32 31 22 Use a truth table to show that the two given statements are equivalent pvq andpAq 3245 23 Construct atruth table for p gt q lt gt p v r Note the importance of the parentheses to indicate the order in which items are grouped 33 15 24 Construct atruth table for p gt q A r 33 17 25 Let p be I will buy it and let q be It is a poodle Translate If it is a poodle then I will not buy it into symbolic form 33 25 26 Which of the following statements is logically equivalent to If Mary is in Tampa then she is in Florida 33 55 a Mary is in Florida or she is in Tampa b If Mary is not in Tampa then she is not in Florida c If Mary is in Florida then she is in Tampa d If Mary is not in Florida then she is not in Tampa 27 Let h be honk and u be you love Ultimate Write A necessary condition for loving Ultimate is to honk in symbolic form 34 19 28 Use an Euler diagrams to determine the validity of the argument 35 7 All professors are wise Ms Brown is a professor Ms Brown is wise 29 Use an Euler diagrams to determine the validity of the argument 35 15 No mathematics teacher is wealthy No panthers teach mathematics No panthers are wealthy 30 Symbolize the argument using the suggested abbreviations and determine the validity of the given argument 36 6 If prices go up u management will scream s If management screams then supervisors will get tough I Hence if prices go up supervisors will get tough Given the two premises below what conclusion will make the argument valid 36 41 31 IfI drive to work then I will not be late IfI am not late then I do not lose any pav a If I am not late then I drive to work b If I do not lose any pay then I drive to work c If I drive to work then I do not lose any pay d IfI do not drive to work then I lose some pay Chapter 8 We will select 11 questions similar to the ones below Concepts quadrilateral trapezoid rectangle square triangle obtuse acute right isosceles equilateral scalene similar right angle Pythagorean theorem circle sphere radius diameter circumference perimeter area surface area volume 32 Name the quadrilateral 82 13 33 Classlfy the mangle as sealehe lsosceles or equllateral and as acute nght or obtuse 82 25 35 1h hls gure 755 ls parallel to A8 Cenam lengths are glveh Fmd the mlssmg length mdlcatedby ablank um w I39 m RI 3 J 6 7 shadow 8 a long How tall ls the telephone pole7 82 37 37 The playlhg surface of afootball eldls 120 ydlong A player Jogglhg aroundthe perimeter othe surface covers 346 yd How wlde ls the playlhg surface7 83 14 38 Fmd the clrcumference of 83 17 Frrst g1ve the answer rh terms of JK theh ea1eu1ate the approxrrhate answer usmg Jr e 3 14 39 The clrcumference ofa 1rcle1s 15sr em Fmd the 64ameter and the radms of Lh1s erre1e 83 31 40 Fmd the area ofeach regmn 84 4 9 h rm n m y E 1 1n and 41 Fmd the shaded area 84 15 42 A reetahg1e has a dAagonal 17 t1orrg anda 1ehgth of 15 1t How w1de1s1t7 84 17 43 Fmd the herght ofa mangle of area 70 1h2 1f1ts base1s 20m long 84 32 44 State whathappehs to the area ofarectangle 1fboth rts armehsrorrs are 84 39 a doubled h mpled c rhu1trphed by a constant k 45 a Ithe edges ofa eube are doubled rh 1ehgth whathappehs to the Volume7 85 9 b What 1f the 1ehgths are mpled7 46 For areetahgu1ar sohdthat 1s 20m long 10 1h w1de ahd8rh h1ghfmd 85 11 a the volume V b The tota1 surface area S 47 Fmd the volume ofa sphere ofradws 61h 85 25 48 A basket ball with a 30in circumference is tightly packed into a cubical box for shipment 85 36 a What is the volume of the ball b What is the smallest possible volume for the box c What percent of the space in the box is occupied by the basketball Chapter 10 We will select 5 questions similar to the ones below Concepts sequential counting principle permutation combination withwithout replacement order 49 In Connecticut auto license plates carry 3 digits followed by 3 letters 101 16 a How many arrangements are possible for the 3 letters b How many arrangements are possible for the 3 numbers c How many different license plates can be made using 3 numbers followed by 3 letters 50 Social Security numbers consist of nine digits 101 19 a If the first digit cannot be 0 how many Social Security numbers are possible b How many Social Security numbers are possible if there are no restrictions M 4 51 Compute 102 16 52 Six coins are tossed in how many ways can you have at least one tail 102 36 53 How many of the first 100 natural numbers are multiples of 2 or multiples of 5 102 39 54 How many license plates using six digits can the state of Vermont issue if repetition of digits is 102 41 a permitted b not permitted c In the 1990 census the population of Vermont was about 600000 Why do you think Vermont allows repetition of digits in its license plates It now uses three letters and three numerals 55 If 20 people all shake hands with each other how many handshakes are there 103 20 56 How many different 5card poker hands are possible using a deck of 52 cards 103 25 57 There are 4 vacancies on the scholarship committee at a certain university In order to balance the men and women on the committee 1 woman and 3 men are to be appointed In how many ways can this be done if the following are available to serve 104 11 a 7 men and 8 women b 5 men and 2 women Chapter 11 We will select 10 questions similar to the ones below Concepts sample space experiment event outcome probability odds independent events conditional probability 58 A single ball is taken at random from an urn containing 10 balls numbered 1 111 10 through 10 What is the probability of obtaining a ball that is either less than 5 or odd 59 In a survey conducted on a Friday at Quick Shop Supermarket it was found that 650 of 850 people who entered the supermarket bought at least 1 item Find the probability that a person entering the supermarket on a Friday will purchase 111 45 a at least 1 item b no item 60 Use the following survey table which gives the numbers of males and females falling into various salary classifications On the basis of the information in the table find the probability that a person selected at random from those surveyed is a female with 111 49 a an average income b ahigh income Low Average 300 160 460 61 A committee of 2 is chosen at random from a population of 5 men and 6 women What is the probability that the committee will consist of 1 man and l woman 112 10 62 Assume that 2 cards are drawn in succession and without replacement from an ordinary deck of 52 cards Find the probability that 2 kings are drawn 112 11 63 An urn contains 5 white balls and 3 black balls Two balls are drawn at random from this urn Find the probability that 112 22 a both balls are white b both balls are black c one ball is white and the other is black 64 Two dice are rolled Find the probability that the sum of the two faces that turn up is between 0 and 13 113 3 65 A single card is drawn from a deck of 52 cards Find the probability the card chosen is the king of hearts or a picture card ack queen or king 113 13 66 The personnel director of Gadget Manufacturing Company has compiled the following table which shows the percent of men and women employees who were absent the indicated number of days Suppose there are as many women as men employees 114 9 Sex A bsences Days Men Women 0 20 20 1 5 40 20 6 10 40 20 11 or more 0 40 Total 100 100 a Find the probability that an employee missed 610 days given that the employee is a woman b Find the probability that an employee is a woman given that the employee missed 6 10 days 67 A recent survey of 400 instructors at a major university revealed the data shown in the following table Based on the data what are the probabilities of the following 114 19 a An instructor received a good evaluation given that the instructor was tenured b An instructor received a good evaluation Good Poor Status Evaluations Evaluations Tenured 72 168 Nontenured 84 76 68 A computer repair shop has estimated the probability that a computer sent to the shop has a bad modem is the probability that the computer has a bad CPU is g and the probability that it has a bad drive is If we assume that modems CPU s and drives are independent nd the probability that 115 3 a a modem a CPU and a drive in a computer sent to the shop are bad b only a modem and a CPU in a computer sent to the shop are bad c none of the three partsmodem CPU or drive is bad 69 A company has estimated that the probabilities of success for three products introduced in the market are i and respectively Assuming independence nd the probability that 115 31 a the three products are successful b none of the products is successful 70 Find the odds in favor of obtaining a vowel when 1 letter is chosen at random from among the 26 letters of the English alphabet 116 7 71 Ifthe correct odds in favor of Johnny s winning a race are 3 to 2 what is the probability that Johnny wins 116 15 Chapter 12 We will select 12 questions similar to the ones below Concepts sample frequency distribution frequency relative frequency measures of central tendency mean median mode measures of dispersion range stande deviation normal distribution circle graph regression line prediction correlation 72 A student has a mean score of 88 on five tests taken What score must she obtain on her next test to have a mean average score of 80 on all six tests 122 14 73 The table below shows the distribution of families by income in a particular urban area 122 15 Portion Annual Income Families 120000 001 a What proportion of the families has incomes of at least 25000 b What is the median income range c Find the mean of the lower limits for the annual incomes d Find the amount below which 36 of the families have lower incomes 74 In a mathematics test given to 50 students 25 earned scores of 90 Most of the other students scored 80 and the remaining students scored 30 Which of the following statements is true about the distribution of scores 122 17 a The mode is the same as the mean b The median is greater than the mean c The mode is greater than the mean d The mean is greater than the median 75 Out of 10 possible points a class of 20 students made the following test scores 0 0 l 2 4 4 5 6 6 6 7 8 8 8 8 9 9 9 10 10 123 11 a What is the mode b What is the median c What is the mean d Calculate the standard deViation to the nearest hundredth e What percent of the scores lie within 1 standard deViation from the mean 139 What percent of the scores lie within 2 standard deViations from the mean 76 The daily numbers of pounds of garbage for 6 different households were 123 15 6 217 3 5 9 Find the range mean and standard deViation of the weights 77 numbers7 Explam 123 27 78 Two elasses eaeh wlth 100 students took an examlnauon wlth amaxlmum posslble seore of 100 In the rst elass the mean seore was 75 and the standard devrauon was 5 In the seeond elass the mean seore was 70 andthe standard devratlon was 15 Whleh ofthe two elasses do you thnk had more seores of 90 or betterv Why7 123 30 eom rtrs shown m the next gure 124 1 than g mm 3 4mm 2 1mm 0 t ii iii 0 en 9H m nu an no in him pee H we new Hughllm a What ls the mean herght offarmerBrown39s com7 b What ls the standard deyratron from the mean7 c What pereent of the eornstalks ls between 90 and 110m tam d Abouthow many stalks are between 80 and 90 m tam 80 Suppose that sueh apuzzle ls glven to 1000 ehrldren eaeh chlldls tamed and agaph ofthe umes ls made Suppose the graph ls anormal eurye wrth amean ume of120 see and a standard deyrauon of 15 see 124 3 z Abouthow many of the ehrldren flmshedthe puzzle m less than 90 see7 h Howmany tookmore than 150 see7 c1fyou rated as averagequot all the ehrldren wrthrn 1 standard deyratron from the mean how many Ehlldren would fall lnto ths elassl eauon7 81 For a certain standardized placement test it was found that the scores are normally distributed with a mean of 200 and a standard deviation of 30 Suppose this test is given to 1000 students 124 4 a How many are expected to make scores between 170 and 230 b How many are expected to score above 260 c What is the expected range of all the scores 82 Assume a normally distributed set of test scores with a mean of M 100 and a standard deviation of 15 Find the probability that a person selected at random will have a score between 124 29 a 100 and 110 b 100 and 130 83 Assume a normally distributed set of test scores with a mean of M 100 and a standard deviation of 15 Find the probability that a person selected at random will have a score 124 31 a between 55 and 145 b less than 60 84 Assume a normally distributed set of test scores with a mean of M 100 and a standard deviation of 15 Find the probability that a person selected at random will have a score between 110 and 130 H int In problem 82 you found the probability that the score will be between 100 and 110 and the probability that the score will be between 100 and 130 You should be able to see how to combine these two results to get the desired probability 124 33 85 In Florida the daily water usage per person is normally distributed with a mean of 110 gal and standard deviation of 10 gal Between which intervals will 95 and 99 of the daily water usage lie 124 44 86 A company specializing in leisure products surveyed 500 people and found their fav01ite activities were as follows 125 39 75 read 60 had family fun 250 watched TV 65 had other activities 50 watched movies Make a circle graph for this data 87 TheU 5 Department ofLaborupdated ltstheoreucalbudget forareured eouple The hlgh budget for sueh a eouple ls appomoned approxlmately as follows 125 41 Food 22 Ho g 35 Transponatlon 11 c1 mg 6 Personal care 3 a1 care 6 Other famlly eosts 7 Mscellaneous 7 1neome taxes 3 Make a euele graph to show thls budget 88 1 h many the bottom7 12 5 24 89 The table below shows the marnage rate y for 1000 Ameneans from 1980 to 2000 Swim us muons mm farchlmSlalNlrs a Make agraph fonthe olata 125 28 h Predlct the mamage rate for the year 2005 h m w Wouldyouexpecttommy7 Hmt Followthepatteml n 1 r y on the bass ofthe rst score x on the fusttest Suppose Mana scores a 90 on the rsttest What wouldbe the pnedleted value ofher score on the nal exam7 127 15 z 81 h 89 c 91 d Cannot be determlned 91 Th n r r m A 1 L exhaust ofcars per mlle dnven 127 17 e E Cm van nannnne 10g dnver z 1 1 c10 h 22 d 14 92 1271s Hugh The scattergram 1nd1cates z a posmve assomanon between hexght and volume h a negauve assomauon between hexght and volume cne1Lher a or b 11 no assomanon between hexght and volume In addition to doing the problems above make sure you understand all the answers to the problems posed on the exams and other graded work you did during the semester Comments on taking a multiple choice test 1 You will be gridding your answers on a scantron sheet using a 2 pencil The exams will be machine graded so it is important that you clearly mark your intended answer If you decide to change your answer on a problem erase the previous answer thoroughly Also make sure you have only shaded in one oval for each problem 2 You will have two hours to take the exam This should be plenty of time but you might want to skip problems that you don t immediately understand and come back to them later However if you skip problems like this be sure to mark the oval corresponding to the appropriate problem 3 There will be no penalty for guessing so don t leave any answers blank Ifyou need to guess at an answer first try to eliminate one or two of the four options 4 Double check everything Often the answer that corresponds to making a simple mistake will be one of the options given and there will of course be no paltial credit 5 Look at each of the options given Sometimes the answer may become apparent to you after you see the choices available

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