Final_solutions_99 _

Final_solutions_99 _ - ngh Instructor/TA: . c; mam/Jaw May...

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Unformatted text preview: ngh Instructor/TA: . c; mam/Jaw May 12, 2007 Instructions: Please write your work, including formulas, in the spaces provided. All of your work must be shown to receive any credit. Round all dollar values to the nearest cent, and all other numbers to the nearest 0.001. your final answers. 1. [12 points] Graph the following system of equations on the grid below. b. yS—x —x+2yZ—-6 ys—J x2-7 4‘ Label every line. \ (9+ 9““ \“e ‘ Shade every discarded region. \ Pit. gimmdm Label the solution set with the letters F.R. \ pi pep/L, \ Anorak , /% Ix” V. ill/(:1 $95 3 VaflWfllllI—IIIIIII nan ‘ v ERRED“?! vwwn Illpnapul lied-mg": : r . . 3’ . . . . : I Mlnjmllltllillgliltllfll III-llllllrllllilllll lllllllll IIIIIIIIIII [2 points] Find an equation of the line through (—3, 5) {Z If? [4 points] Find an equation of the line through (2,—1 1) units of x. W Z; ([59 3 \/ lummnazumIBMMIMIllllllll .nmnnnmm-nmulnmIMIlull ,fiflflflfllflhfllflfllfllllllll . unmannmnmlnmlmuunlllll gm muugnnmumglmuI-nlullll «enummwlummnln . u. .mnwlmmmmlunul; _ .” EEIIMIMIMMflwwlmlfiflmlflflfim “Humanmumwmummnummmwmmmu.a Human-Imuwwmuwmmalwmnnflfl v illl-llllfilfiQIMHHMflfi llazllyznnmmlmmmum: Iliuir4nnlnmmlnmmm ,‘flflIIHMEMIEIM »t_,mmlllpmul-ullnlmn Inflfifillflflmllllfll ' I IMHIIIIIIIEI. ~// 2( ‘%X+b ’ MWW lam-amulfiflw Inna-mum r I I I I I E I I Ill-Illa, IIIIIIII IIIIIIII y=-—y' ; fl and parallel to the line y = 9. . and increasing at a rate of 2 units of y for every 3 4. Page 2 of 10 Math 110 - Final Exam May'2007 3. Cathy’s Card Shop recorded the number of Mother’s Day cards sold for the in the following stem and leaf plot. 1 past 10 days. The results are given 1 8i 0 8 2 8~ 2 ~1 3 3 ‘ 4 :5 a a. [2 points] What is the least number of cards Cathy sold in one day? to b. [3 points] What is the median number of cards Cathy sold per day? 2’13 2.2. s ‘2. MW...) c. [3 points] What is the mean number of cards Cathy sold per day? /%+_/o+/8+r~+53 ' ' 4n. m L...”— ~ .- 20. “i (0 ..... _. [6 points] Jan ordered corsages for Happy High-School’s graduation. Rose Corsages cost $6.50 each, while carnation corsages cost $5 each. She ordered a total of 100' corsages and spent $560. How many corsages of each typedid she order? -Define variable(s), -Set up equation(s) and -Solve. 6. Page 3 of 10 Math 1 10 5. Answer the following questions about Dan’s dairy business. a. [4 points] The demand for Dan’s ice cream is 180 quarts weekly if the quarts are $2 each and 300 quarts weekly if free! What is the weekly linear demand equation for Dan’s ice cream? , (Letx = price, y = quantity) C 2/ I 8'0) , x . WWW ow WWW-.. a w _ . x 0-; e, (£0 “33 b. [4 pomts] Dan 8 ice cream supplier Will sell Dan 40 quarts of ice cream weekly if they are marked $2 each and 200 quarts weekly if they are marked $4 each What is the weekly linear supply equation for Dan’s ice cream? ~ .»~ : 8C) 7< 4* (Z I H o ) r q , “N‘s. (sh 100). A O W%0(L) ' QED ' f‘ \O :— _ z 2 O o __ u 0 1 l2 0 a —-Z-» . r o . :. 90 9c - l 2 o. I 3-3 a. c. [3 points] At what price should each quart of ice cream be marked so that there is neither a surplus nor a shortage of ice cream? (539 slow)! \a, Z d 9 ma. not + 11- — inrAne) fifig 30% “(2,0 : «mo 76 4 we :9 my [How e %10 v< =1 $3» Ml Ifn(A) = 23. MB) = 17, n(C) = 32 and n(A UB) = 35, find: a. [3poinls] 21(AflB)" I H(AUI?>) = YNA) + V303) ’ “(A n5)v 35 = 13 m Anni) r- 5 (lat), b. [3 points] n(A x C’) " FHA). 10(5) :, 2,3137— : 323(0 (5gp. .. __ ._ 1W___——__—_u__-_____._——____w w Page 4 of 10 Math 110 — Final Exam May 2007 7. [13 points] Model the following situation, DO NOT GRAPH and DO NOT SOLVE. A local farmer raises only steers and heifers. He wants to raise no more than 175 animals. He spends $150 to raise each steer and $138 to raise each heifer. He has $22,000 available to spend on raising these animals. Due to personal preference he has decided to raise no more than twice as many heifers as steers. Each heifer produces $45 profit while each steer produces $53 in profit. [How many steers and how many heifers should the farmer raise to maximize his profit? Clearly identify: the variables, objective and constraints. :7 t...» . f A », .. ~ 1 (x (yer KZPD- WOXtmv'De P 3 53X + q v a: m an - at?) 8. A survey of students’ eating habits was conducted. Let S denote the set of all students surveyed and let B, L and D be subsets of S where: B = the set of students who eat breakfast, I t L = the set of students who eat lunch and D = the set of students who eat dinner. Using set notation find an expression in terms of B, L and D for each of the following subsets: a. [2 points] The set of students who ate breakfast, lunch or dinner. BULUD. b. [2 points] The set of students who did not each lunch. L’ ‘ c. [2 points] The set of students who ate only dinner,__ D n e’ n L.’ [M d. [2 points] The set of students who ate lunch and dinner, but not breakfast. L n D n 6’ Page 5 of 10 Math 110 ‘ Name: Section: 9. The following table shows the average price of a two-bedroom apartment in downtown New York City from 1994 to 2006. (t = 0 represents 1994.) [Yeart l———-—— l _——L 4.. 8 I I v 1 l i ' J l Pricep in millions I 0.38 l 0.40 l 0.60 0.95 i 1.20 J 1 60 l 2 a. [4 points] Find the least-squares, “best-fit” line for this data. Letx = year, and y = price. y : “+40 7< + .lTNa 0 b. [4 points] According to the model found in part (a,) in what year would you expect the price to be 2.5 million dollars? (Round to the nearest year.) y:2.5 x. Auto—x +.|?~fa w.) 7( :, Mafia 9 20‘ Li Q9” c. [4 points] What is the slope of the mode] found in part (a) a_nd_ specifically what does this represent in terms of this model? V .... mwnmwmu wm: yew!“- El? .h 1? [XML mermaam Ma .1qu Muliicm (We? 004.9) PM [La/mar. @5) , d. [3 points] 15 the line found in part (a) a good fit? Justify your answer. rt: u pl 1} (71‘s @3 , @723 Page 6 of 10 ‘ Math 1 10 — Final Exam May 2007 10. A group of students from three universities was asked to pick their favorite college sport to attend of the choices: football, basketball and soccer. The results were as follows: 1 [Football Basketball Soccer Total One student is picked at random. (You may leave your answers as unsimplified fractions.) a. [2 points] What is the probability that the student chose basketball? 3-19.. @137 375 we b. [2 points] What is the probability that the student was fiom UNC and chose football? 3) 5 <2 (33 3. 4 5 c. [2 points] What is the probability that the student chose soccer or was not from UMD? (no 4-“ — no ,2 2.93 '1wyi‘w,‘ u “Tm...MW...»...Wm::m—«mww m R; 33 ‘5 :F S d [2 pomts] What IS the probability that the student was from Duke, given that he/she chose basketball? P( D | [3,) ; n( p n _ 7» S a (Mia W E: ‘ W e. [2 points] Are the event's/“chose soccer” and “fiom UNC” mutually exclusive? (Justify your answer with computations.) N0: D(Sfl UNC): 2‘5 ¢o~ t ... .5 11. [5 points] Sixty percent. of all of the paintings in Anne’s Artistic Creations were painted by Anne. Furthermore. 75% of the paintings in her shop are watercolors, given that they were painted by Ann. What percentage of the paintings in Anne’s shop are both watercolors and were painted by Anne? W: WCtxfrchW‘b ’ g ,,,,,,,, i”; i“: WM ) 5" PA” “A; t b An , Fir Fem *,.a “Li P(A) ' ' w as = 'P/ A} pyA) $.00 [Wk mr?§3”” ($53 WW. A) w.?5. J Page 7 of 10 Math 110 Name: Section: For problems 10—] 3 indicate the formula neededto answer the question, give the value for each ofthe known variables in the formula and solve. Formulas are available at the bottom ofthe pages. 12. [5 points] To pay for her tuition, Isabelle borrowed $5000 for l 1 months at a simple interest rate of 6.1% per year. How much interest did she pay? 3 5 o ‘ Pt: ' w W7” T“ F’V r t: Ural) ii m” = sacow(.oz_9t)<_‘fl£w' r: . 0 La \ , , ................. ~ Z? 9‘ s 8 Cw. j filial warmth l 13. [5 points] What is the future value of a 10 year investment of $15,000 at 0.31% monthly rate, compounded monthly? m+ w JC1’0 tiFv:«P\/(l+.—\g) PV‘: '5 00° ( M } {240 = V000 ‘ . cast my Y’=(.003\)(12_) ; #3 {Hm m. m 2 I2. a. ‘ ,, ._ _, = z.) 7- L4 (0. ‘1 9 (lg/7r ' irii’ Mot/“ix I INT = PVrt FV = PV(1+ rt) FV = PV(1+ ’W‘)'"’ W = (1+ )m —1 I” — 1—(1+—n;) W ~———-—-—,. 1 L m! ___1 ' FV = PV(1+ +PMT£Lm—)—-—— PV =‘FV(1 + Jim: +er r m m Page 8 of 10 ‘Math llO—Final Exam May 2005 14. [5 points] What is the future value of an ordinary annuity at the end of 40 years if $375 is deposited monthly into an account paying 5.3% per year, compounded monthly? , : ., mi ''''''''' ~ t “0 cw. pm-r t we) —\ am PM T‘ = 3? 5 WWW—mm ‘ m V 3 (l+.l.03‘%2-) ml ,, :41 ; h I 70 53A 2_ = Colo? loci", 15. The Smith’s are planning on buying a new house. They take out a 30 year, $400,000 mortgage at 6.8% per year, compounded monthly. . l a. [5 points] How much are their monthly mortgage payments? + __ ..m r » it» " PV 3 £400 om r: , 0498 Lloa 000 = Pm'r (1m (H 'W‘g/lz) ] W1 3 I2. a." P-mr == 2 cm. to Q b. [4 points] How much total interest will the Smith’s have paid over the life of the loan? (zomfl'vflta) (30) ~-—-—— gm; goo INT=PVrI FV=PV(1+rt) FV=PV(1+T;;—)m' ref/=(1+I%1w—)m—1 (1+—,§1-""—1 FV = PV(1+ %)mt + PMT-——,—,-—-—— P‘V = FV(1 + + PMT—————r————— 717 m Page 9 oflO Math 110 ' ' Name: Section: 16. In Harry’s House of Flowers the probability of selecting a floral arrangement that contains roses is 0.78, the probability of selecting an arrangement that contains carnations is 0.85, and the probability of selecting an arrangement that contains both roses and carnations is 0.68. a. [4 points] \Vhat is the probability of selecting an arrangement that contains neither roses nor camations? K7: mafifia [>(RUC) : .:}8 + a 3’8 ‘— obg ” ‘‘‘‘‘‘ A C = v t. - q s (tritl Pm) = .as ‘ Pair—w“ @ t~ PCKue) [4.05 b. [4 points] What is the probability of s cting an arrangement that contains roses, but not carnations? P(K)"’ P(({flC) r K "infill ,,,,,,,,, W‘ C 17%“- .1125? v: \o 010 92%.); {:2 17. [4 points] According to the weather service, there is a 15% chance ofrain in Portland tomorrow; there is a 30% chance of thunderstorms in Chicago tomorrow and there is a 4.5% chance ofboth rain in Portland and thunderstorms in Chicago tomorrow. Are the events, rain in Portland tomorrow and thunderstorms in Chicago, tomorrow‘in'dependent? Show computations to justify your answer. [Q: m2“ an pCJt'"+\Ft/\(L~ “mu ta» T:- ‘wadrrsJW/(M M Chwafiv, Page 10 of 10 Math 1 10 - Final Exam May 2007 18. [6 points] Use the given infomia‘ti‘on to complete the solution of this partially solved Venn Diagram. m _,/"‘>g_f/mm’” fig“: a. n(A) = 26 i ‘ 72(8) = 14 ; 3L o f n(C) = i [IN/".1". g f: 7 \1 /: K S, 1:57 ‘ ‘9 \1 I Ill/4... f ‘7 . ‘ ’\ xxx x "fig/r. l ‘ ~97 ivy» imwm—J’/ 19. The local volunteer fire department has decided to raise money by raffling a itelevision worth $800, a spa treatment worth $180, 2 gift baskets worth $100 each and 3 restaurant certificates worth $60 each. A total of 5000 tickets are sold for $5 each. a. [5 points] Create a probability distribution for winning this raffle. n = ami- Nim'h 800 I so 1 oo (a O O VQS l7?» 553 "5 \ x L t j: Ltq a 3 Pw’b /5000 $000 2/5000 SO 00 5000 m C“ ~ i113“ fa cit—£33m b. [3 points] What is the expected value of winning this raffle? P a :3 ‘ 5 .L—v 'fl r ( M '-- q. 543;?“ + l :'2 3 3379: m: 4 ’3 .5553an + b J 50m; J : - 2 “a (04 o _ “WWW...” “" $ —— (1!, ?. Z 8' '::.~ m. 4’ (“I pi t€ expa‘crot 339.321 valve.) Please write the honor code below, then sign it. «1993 m ) ( I £300 “I pledge on my honor that I have not given or received any unauthorized assistance on this examination.”(signature) ...
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Final_solutions_99 _ - ngh Instructor/TA: . c; mam/Jaw May...

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