MATH 1300: Finite Mathematics EXAM 1 15 February 2017

Transcription

1 MATH 1300: Finit Mathmatics EXAM 1 15 Fbruary 2017 NAME:... SECTION:... INSTRUCTOR:... SCORE Corrct (A): /15 = % INSTRUCTIONS 1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All xam pags must rmain stapld. Do not sparat or rmov any pags. You will hav 60 minuts to complt this xam. 2. This xam has 10 pags, including th covr sht. Thr ar 15 multipl choic qustions. Th answrs on your scantron ar your FINAL answrs. If you chang an answr, ras your old answr thoroughly. Only final answrs on your scantron will b gradd. 3. Som potntially hlpful formulas can b found on pag 10.

2 MATH 1300 Spring 2017 Exam 1: Nam... (A) 2 MULTIPLE CHOICE: Mark your FINAL answrs on your scantron. 1. An amount of $600 is dpositd into a savings account at 3% intrst compoundd monthly. How much intrst is arnd during th first fiv yars? (Answrs ar roundd to th narst cnt.) a $ b $96.97 c $ d $ $ Considr a $250,187.42, 30-yar mortgag at intrst rat 6% compoundd monthly with a $1500 monthly paymnt. What is th unpaid balanc at th nd of 25 yars? (Answrs ar roundd to th narst cnt.) a $ b $232, c $77, d $24, $25,000.00

3 MATH 1300 Spring 2017 Exam 1: Nam... (A) 3 3. A singl dposit of $5000 is invstd into a savings account arning 6% intrst compoundd smi-annually. If th initial dposit was on January 1, 2017, how much mony will b in th account on July 1, 2022? (Answrs ar roundd to th narst cnt.) a $ b $ c $ d $ $ If somon 20 yars old dposits $5000 ach yar into a savings account for 50 yars at 8% intrst compoundd annually, how much mony will b in th account whn this prson rtirs at ag 70? (Answrs ar roundd to th narst cnt.) a $61, b $2,868, c $736, d $228, Non of th abov

4 MATH 1300 Spring 2017 Exam 1: Nam... (A) 4 5. A loan of $180, is to b amortizd ovr a 6-yar trm at 6% intrst compoundd monthly with monthly paymnts and a $50,000 balloon paymnt at th nd of th trm. What is th monthly paymnt for this loan? (Answrs ar roundd to th narst cnt.) a $ b $ c $ d $ Non of th abov.

5 MATH 1300 Spring 2017 Exam 1: Nam... (A) 5 6. A bank offrs two accounts, Account A, which is 9.125% compoundd monthly or Account B, which is 9.250% compoundd quartrly. Calculat th APY for ths accounts and dtrmin which account is th bttr offr. (Answrs ar xprssd as prcntags and roundd to 3 placs.) a b c d Account A 9.516%, Account B 9.576% (B is bttr) Account A 1.410%, Account B 1.298% (B is bttr) Account A 9.516%, Account B 9.576% (A is bttr) Account A 1.410%, Account B 1.298% (A is bttr) Non of th abov. 7. Using th add-on mthod, what is th monthly paymnt for a $3000 loan at 9% intrst for two yars? (Answrs ar roundd to th narst cnt.) a $ b $ c $ d $ Non of th abov

6 MATH 1300 Spring 2017 Exam 1: Nam... (A) 6 8. Considr a 15-yar $100,000 5/1 ARM having a 3% margin and basd on th CMT indx. Suppos th intrst rat is initially 6% and th valu of th CMT is 5.1% fiv yars latr. Assum that all intrst rats us monthly compounding. What is th monthly paymnt for th first 5 yars? (Answrs ar roundd to th narst cnt.) a $ b $ c $ d $ $ For th mortgag in qustion 8, what is th monthly paymnt for th 6th yar? (Answrs ar roundd to th narst cnt.) a $ b $ c $ d $ $961.43

7 MATH 1300 Spring 2017 Exam 1: Nam... (A) Us th Gauss-Jordan limination mthod to find all solutions of th systm of quations: { x + 2y + 3z = 5 2x + 3y 4z = 2 a x = 11, y = 8, and z = 0 b c d x = 17z 11, y = 10z + 8, and z = any ral numbr x = 17z 11, y = 10z + 8, and z = any ral numbr x = 11, y = 8, and z = 7 Thr ar no solutions. 11. Find th invrs (if it xists) of th matrix A = a b c d [ [ [ [ ] ] ] ] [ ]. Matrix A dos not hav an invrs.

8 MATH 1300 Spring 2017 Exam 1: Nam... (A) Us th Gauss-Jordan limination mthod to find all solutions of th systm of quations: x + y + z = 2 y + 2z = 4 x + 2y + z = 2 a x = 2, y = 4, and z = 2 b x = 0, y = 0, and z = 2 c x = 2, y = 0, and z = 0 d x = any ral numbr, y = any ral numbr, and z = 2 Thr ar no solutions. 13. Us th Gauss-Jordan limination mthod to find all solutions for th following systm of quations: { 2x + 2y = 4 3x + 9y = 18 a x = 4 2y, y = any ral numbr b x = any ral numbr, y = 2 c x = 2, y = 0 d x = 0, y = 2 Thr ar no solutions.

9 MATH 1300 Spring 2017 Exam 1: Nam... (A) 9 Qustions 14-15: It is found that th numbr of marrid and singl adults in a crtain town ar subjct to th following statistics: { 0.8x + 0.6y = m 0.1x + 0.7y = s whr x and y dnot th numbr of marrid and singl adults, rspctivly, in a givn yar, and m and s dnot th corrsponding numbrs for th following yar. Suppos that this yar thr wr 100,000 marrid adults and 50,000 singl adults. 14. How many marrid adults wr thr last yar? a 110,000 b 60,000 c 80,000 d 40,000 Non of th abov 15. How many singl adults will thr b nxt yar? a 110,000 b 50,000 c 75,000 d 100,000 Non of th abov

10 MATH 1300 Spring 2017 Exam 1: Nam... (A) 10 Potntially Hlpful Formulas F = (1 + i) n P P = F (1 + i) n r ff = APY = (1 + i) m 1 F = (1 + i)n 1 i R P = R = 1 (1 + i) n i P (1 + rt) 12t R

11 MATH 1300: Finit Mathmatics EXAM 2 15 March 2017 NAME:... SECTION:... INSTRUCTOR:... SCORE MC:(A) /12 * 7 = LA: /16 = Total: /100 = % INSTRUCTIONS 1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All xam pags must rmain stapld. Do not sparat or rmov any pags. You will hav 60 minuts to complt this xam. 2. This xam has 9 pags, including th covr sht. Thr ar 12 multipl choic qustions worth 7 points ach and 1 long answr qustion with six parts worth 16 total points. Only your scantron will b gradd for th multipl choic sction, what you put on your scantron is your FINAL answr. If you chang an answr on th scantron, ras your old answr thoroughly. 3. Blank grids for th multipl choic linar programming problms ar providd adjacnt to ach qustion. Thy ar providd for convninc only and will not b gradd. Th graph for th long answr qustion will b gradd.

12 MATH 1300 Spring 2017 Exam 2: Nam... (A) 2 MULTIPLE CHOICE: Mark your FINAL answrs on your scantron. Qustions 1-2: Kyl is choosing btwn a combination of brands of cat food to fd his cat. H dtrmins that th combination should mt crtain minimum nutritional rquirmnts: 36 units of protin, 35 units of fat, and 20 units of taurin pr wk. Brand A provids 4 units of protin, 7 units of fat, and 10 unit of taurin, and costs $3.50. Brand B provids 9 units of protin, 5 unit of fat, 2 units of taurin, and costs $4.00. Kyl wants to provid for his cat whil minimizing his total costs. Lt x b th numbr of cans of food A that h buys pr wk and y b th numbr of cans of food B. 1. Which of th following is an inquality associatd with this problm? a 10x + 2y 20 b 4x + 9y 36 c 7x 5y 35 d 3.5x + 4y 10 Non of th abov Which of th following is on of th vrtics of th fasibl st? a (9, 1) b (0, 4) c (0, 10) d (0, 9) Non of th abov

13 MATH 1300 Spring 2017 Exam 2: Nam... (A) 3 Qustions 3-4: An invstor has $18,000 to invst in thr typs of stocks, low-risk, mdium-risk and high-risk. Sh invsts according to thr principls. Th amount invstd in low-risk stocks will b at most $2000 mor than th amount invstd in mdium risk stocks. At last $8000 will b invstd in low-risk and mdium-risk stocks combind. At last $10,000 will b invstd in mdium-risk and high-risk stocks combind. Th xpctd yild for ths invstmnts ar 4% for low-risk stocks, 5.5% for mdium-risk stocks and 7.1% for high-risk stocks. Th invstor wishs to maximiz th yild on th invstmnts. Lt x b th amount to b invstd in low-risk stocks and y b th amount to b invstd in mdium-risk stocks. 3. Dtrmin th objctiv quation for this problm. a Maximiz Y =.04x +.055y + 18,000 b Maximiz Y = x.016y c Maximiz Y = 18, x.016y d Maximiz Y = x +.016y Non of th abov How much should th invstor invst in ach typ of stocks? a b c d $0 low-risk, $8000 mdium-risk, $10,000 high-risk $0 low-risk, $0 mdium-risk, $18,000 high-risk $5000 low-risk, $3000 mdium-risk, $10,000 high-risk $10,000 low-risk, $4000 mdium-risk, $4000 high-risk Non of th abov

14 MATH 1300 Spring 2017 Exam 2: Nam... (A) 4 5. If n(a) = n(a B), which of th following statmnts about A and B must b tru? a b c d A is a subst of B B = A B is a subst of A B A = Non of th abov 6. Lt U = {a, b, c, d,, f}, A = {d,, f}, B = {a, d, } and C = {a, c, d}. Which of th following is (A B) C? (A B) C = a {a, b, c, d,, f} b {a, d,, f} c {b, c} d {b} Non of th abov

15 MATH 1300 Spring 2017 Exam 2: Nam... (A) 5 7. If n(a B) = 42, n(a) = 100 and n(b) = 50, find n(a B). n(a B) = a 108 b 150 c 42 d 192 Non of th abov 8. Which of th following is th shadd rgion blow? R S T a R S T b (R S) T c (R S) T d R S T (R S) T

16 MATH 1300 Spring 2017 Exam 2: Nam... (A) 6 Qustions 9-10: A mrchant survyd 135 popl to dtrmin th way thy larnd about an upcoming sal. Th survy showd that 60 larnd about th sal from th radio, 80 from tlvision, 30 from th nwspapr, 20 from radio and tlvision, 15 from radio and nwspaprs, 10 from tlvision and nwspaprs, and 10 from all thr sourcs. 9. How many popl larnd of th sal from tlvision only? a 60 b 80 c 25 d 10 Non of th abov 10. How many popl larnd of th sal from both radio and tlvision? a 140 b 20 c 100 d 0 10

17 MATH 1300 Spring 2017 Exam 2: Nam... (A) Us D Morgan s Laws to simplify th xprssion (S T ). a S T b c S T S T d S T 12. Lt U = {Finit Math studnts this smstr}, A = {studnts who lik multipl choic qustions}, and B = {studnts who lik long answr qustions}. Dscrib th following st using st-thortic notation: {studnts who lik long answr qustions but not multipl choic qustions}. a A b c B A A B d A B Non of th abov

18 MATH 1300 Spring 2017 Exam 2: Nam... (A) 8 LONG ANSWER: Show complt work blow to rciv full crdit. Qustion 13: A coff roastr has warhouss in St. Louis and Topka and rcivs ordrs from coff shops in Kansas City and Columbia. Th St. Louis warhous has 500 lbs of coff and th Topka warhous has 700 lbs of coff. Th Kansas City coff shop rqusts 400 lbs and th Columbia stor 350 lbs. Th cost of shipping from St. Louis to Kansas City is $4 pr pound and St. Louis to Columbia is $2 pr pound. Th cost of shipping from Topka to Kansas City is $2.50 pr pound and th cost of shipping from Topka to Columbia is $3 pr pound. Lt (x, y) corrspond to x pounds of coff shippd from St. Louis to Columbia and y pounds of coff shippd from St. Louis to Kansas City. Th coff roastr wishs to find th (x, y) that minimizs th company s th shipping costs. a) Writ th st of six inqualitis that (x, y) must satisfy. x 0 y 0 x 350 y 400 x + y y x points if corrct, 1 point ach for th last four fasibl st b) Writ th objctiv quation x + 1.5y minimiz 2 points if corrct, 1 point partial crdit for minor arithmtic mistaks c) Us th grid providd to graph th fasibl st. s graph abov 3 points if corrct, 1 point for bounding rctangl, 1 point for diagonal lins, 1 point for idntifying fasibl st d) Idntify th vrtics of th fasibl st. (0, 400), (350, 0), (0, 50), (350, 150), (50, 0), (100, 400) 3 points if corrct, 0.5 points for ach vrtx

19 MATH 1300 Spring 2017 Exam 2: Nam... (A) 9 ) Which valus for x and y minimiz th cost of fulfilling th ordr? (350, 0) 2 points if corrct f) How much coff should thn b shippd from Topka to Columbia? 0 pounds 2 points if corrct

20 MATH 1300: Finit Mathmatics EXAM 3 19 April 2017 NAME:... SECTION:... INSTRUCTOR:... SCORE Corrct (A): /15 = % INSTRUCTIONS 1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO BY YOUR ROOM LEADER. All xam pags must rmain stapld. Do not sparat or rmov any pags. You will hav 60 minuts to complt this xam. 2. This xam has 9 pags, including th covr sht. Thr ar 15 multipl choic qustions. Th answrs on your scantron ar your FINAL answrs. If you chang an answr, ras your old answr thoroughly. Only final answrs on your scantron will b gradd.

21 MATH 1300 Spring 2017 Exam 3: Nam... (A) 2 MULTIPLE CHOICE: Mark your FINAL answrs on your scantron. 1. An xprimnt consists of flipping a fair coin 6 tims and obsrving th squnc of hads or tails. How many diffrnt outcoms hav at last 3 hads? a 42 b 22 c 1 d 63 Non of th abov 2. In downtown Columbia, a studnt must walk 5 blocks south and 7 blocks ast (with no backtracking) to rach hr dstination, but sh wants to stop at Sparky s along th way as in th pictur blow. How many diffrnt routs ar possibl? a 792 A b 300 S c 400 d 3600 Non of th abov B

22 MATH 1300 Spring 2017 Exam 3: Nam... (A) 3 3. A child is dciding on his favorit and scond-favorit crayons from a box. If h can prform this task in 4032 ways, how many crayons ar in th box? a 4032 b 2016 c 64 d 63 Non of th abov 4. A class has 20 studnts of which 6 ar sniors. How many diffrnt committs with fiv mmbrs can b mad if xactly two mmbrs of ach committ must b a snior? a 1820 b 15,504 c 65,520 d 5460 Non of th abov

23 MATH 1300 Spring 2017 Exam 3: Nam... (A) 4 5. A numbr is said to b a palindrom if it rads th sam way backwards and forwards (for xampl, ). How many tn-digit numbrs ar palindroms? a 8,100,000,000 b 9,000 c 100,000 d 90,000 Non of th abov 6. An xprimnt consists of tossing a coin fiv tims and obsrving th squnc of hads (H) and tails (T). What is th probability of th vnt HHHHH? a b c d 1 0

24 MATH 1300 Spring 2017 Exam 3: Nam... (A) 5 7. Suppos that Pr(E) = 0.6, Pr(F ) = 0.7 and Pr(E F ) = 0.6. Find Pr(E F ). a 0.30 b 0.70 c 0.10 d 0.42 Non of th abov 8. Gamblrs usually giv odds against an vnt occurring (th odds of an vnt not happning). Say a booki givs 5 to 6 odds against a crtain vnt happning. What dos th booki bliv th probability of th vnt to b? a b c d Non of th abov

25 MATH 1300 Spring 2017 Exam 3: Nam... (A) 6 9. A box contains 10 computr disks, 2 of which ar known to hav bad sctors. An inspctor rmovs 3 disks at random from th box and tsts thm. What is th probability that th inspctor discovrs at last on disk with bad sctors? a b c d Non of th abov 10. Six popl ar slctd at random. What is th probability that at last two of thm wr born on th sam day of th wk? (Answrs ar roundd to 4 dcimal placs.) a b c d Non of th abov

26 MATH 1300 Spring 2017 Exam 3: Nam... (A) A man, a woman, and thir four childrn randomly stand in a row for a family pictur. What is th probability that th parnts will b standing nxt to ach othr? (Answrs ar roundd to 4 dcimal placs.) a b c d Lt S b a sampl spac and E and F b vnts associatd with S. Suppos that Pr(E) = 0.4, Pr(F ) = 0.3 and Pr(E F ) = 0.2. Calculat Pr(F E ). a b c 0 d 5 6 Non of th abov

27 MATH 1300 Spring 2017 Exam 3: Nam... (A) An urn contains 8 grn balls and 5 whit balls. A sampl of 4 balls is slctd without rplacmnt from th urn. Dtrmin th probability that all four balls in th sampl ar th sam color. (Answrs ar roundd to 4 dcimal placs.) a b c d Non of th abov 14. A ranchr obsrvs his hrd of cattl and dtrmins 45% of thm ar brown and 55% ar black and whit. Furthrmor, 61% of th cattl that ar brown ar fmal and 28% of th cattl that ar black and whit ar fmal. What is th probability that a randomly slctd mmbr of th hrd is both black and whit and mal? (Answrs ar roundd to 4 dcimal placs.) a b c d

28 MATH 1300 Spring 2017 Exam 3: Nam... (A) Considr a population in which 5 in vry 10,000 popl hav tubrculosis (TB). Suppos thr is a skin tst availabl whr popl with TB tst 98% positiv and 2% ngativ, whras popl without TB tst positiv 1% of th tim and ngativ 99% of th tim. Dtrmin th positiv prdictiv valu (PPV) of th tst, whr PPV of a mdical tst is th probability that a prson has TB givn that thy had a positiv rsult on th tst. (Answrs ar roundd to four dcimal placs.) a b c d Non of th abov