Final_solutions_ _9

# Final_solutions_ _9 - .——9 Name t Section Instructor/TA...

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Unformatted text preview: .——9 Name: t \ Section #: Instructor/TA; Math 1 10 Final Exam December 16, 2003 Instructions: Please write your work, including formulas, in the spaces provided. All of your work must be shown to receive any credit. Round all numbers to the nearest cent or nearest 0.001. your final answers. 1. [13 points] Graph the following system of equations on the grid below EV each \H'VC,‘ 3 9+ m \clodx. l F+ pow corredc Me, “A P» termed: Shelia] - Label every line. - Shade every discarded region. - Label the solution set with the letters F.R. 2y+3x212 x52y x3~1 3,59 > | 77 a ' 0;: L- 33 - r 7 - r » v 1 (yr Gr PK, 3 , a v H 1T 3 ” _ “ "L41 4_ _ ‘ 3!, - 1 ii, I V— 7 _ 'L i “ 3"? l _____ _ "A _ 4m + A — ~— “ i‘ﬁ ‘r' - ' " i—r'r“ ‘tﬁj — r 1"”: r ,.;;i; ‘ i ‘ : fl: r l l l 3’ L l 1 i k a A X ‘ _4_‘_...._lv i- | I _ _ _ Li. _ _ i y-— , l ‘; 1}” p a 1: L — ~ L a- ‘ ‘ r- » l : ’ ‘ y ‘ __ A v w_“_ __ — ——" 5 ‘ r1:— *1 , ', i 3 «MA L a « -y «4.. vi a A i 2 J .L “J - _ —m_ I 1 A _m A— to”; 1__r ._ t _ I a i. as I i J r __ I a k“Lulwm; ._ £1” 4. __ ‘ I I TAX,“ : ;.H w A f ‘L I 3 1-..? . a... :H‘ _ _. w _ I_‘ I j: ' _ 72g. i ' ‘ _J L i: KM / . 2y+ax a: ll. 2. [6 points] Find an equation of the line throug the point (—5,4) and parallel to the line 7x + 5y 2 —2. Leave your answer in slope—intercept form (v = mx + b). l 6y :4va L{ = “ix-Sh b ,_ :~ , 5 2i” YB ’xA3/33P'b l .brvéa Page 2 of 10 Math 110 - Final Exam December 2003 3. Mary recorded the number of presents she wrapped daily for 10 days. The results are given in the following stem-andJeaf plot. 0 0,1,4,6,4,1 l 1,3,] I to b.) I a. [3 points] What is the most amount of presents Mary wrapped in one day? 832‘ 39% b. [3 points] What is the mean number of presents Mary wrapped? O+leL++Lo4Uf+\-+H+\3+H * 32- . ' ....................... m Wmmmmmmmm .: . go ,. kph NP» C. [3 points] What is the nt-cdian numlcr of presents Mary wrapped? Oibhqlet/b/“ju/li, 32. < i?" Eile~5 ~..~ 2 «gas. 4. [9 points] Elizabeth is buying candles for Chanukah this year and has decided to use only blue and white candles. She has decided to buy three times as many white candles as blue candles. If Elizabeth buys a total of 132 candles,how many candles of each color did she buy? -Define variable(s), X :bkﬂ COMM“ 1 ,3 Pig, -Set up equati0n(s) and y : “mtg (bth -Solve. 2? p35 2 pk my :5 l’fﬂ. y: 3k X_\3X :: V51 ‘ 3" LN 1’13?— . P x: 33 ‘P‘r Page 3 of 10 Math 110 Name: ________________Section: 5~ Edna’s Elf—Wear shop makes and sells elf hats. Edna can make 100 laats each month fora total cost of $6575, and she can make 200 hats each month for a total cost of$6775. a. [Spoints] Express the shop’s cost, C, in terms ofx, the number of hats made per month. ,lvl (lOO/ (Gigs) Q=Z><+b m= b7¥3~e375 lo a (03315 b. [3 points] Edna sells hats for $17 each. EXpI‘CSS the shop’s revenue, R, in terms of x, the number of hats sold per month. R=l¥x W%' C. [3 points] Express the shop’s total monthly profit, P, in terms ofx, the number of hats made and sold each month? (P: R’C 19*” I" ﬁx ~» (2x {03%) 1‘9; 3 |$x «£0395 {LPL d. [4 points] How many hats must the shop make and sell to break even? P: O o; R = C 210‘3 x = LlZS ME \Pl, hmwm__—__ Crzx + e3?5 ] lP+”W““"W“ Page 4 of 10 Math 110 - Final Exam December 2003 6. [14 points] Model the following situation, but DO NOT GRAPH and DO NOT SOLVE. A local craftsman makes two types of New Year’s displays: Party Time (PT) and Winter Magic (WM.) Each PT display requires 4 hours of woodworking while each WM display requires 2%, hours of \\'oodworking. Both types ofdisplay require 7 hours Of ﬁnishing. The craftsman has 325 hours available for \\UOLi\‘\’01’i\'lng and 590 hours available for finishing. Due to storage limitations, he can make no more than 105 displays altogether. Also, he must make at least 40 PT displays. If the craftman makes $55 profit on each PT diSplay and$95 proﬁt on each .WM display, how many displays of each type should he make to maximize proﬁt?? Clearly identify: the variables, objective and constraints. X3 #6? PT Chsplrzyj I i 2P¥s y: 7x4 7), 9 $30 X 2 40 lmaximiu P: SSX aﬂsy 2,92 xx (x2 Woecwbavvzs 7. Let S = {balk doll, game, Mary, Sean, green, blue, red} be the universal set and let/l = {x e S : x is a name} 8 = {Doll, Sean, red, blue} C = {game, ball, Mary, green} and D = {x e S : xis a color}. Find each of the following: a. [2 points] A' n E balk, a0“! 30mg) years) ﬁve) ROLE, :1 36mg b. [2 points] 8 n A 2 Pt: c. [2 points] C H S =2 C = 2 some, La“, Maura, Swen-i, d. [2points]A><D = I (yea/1)) (MAB,HUL)I (MAUK'MLL 2e*3. 212*; Zp’ts (Sean, 3mm ), (Sean, blue), (3%“; (ML) ’ Page 5 of 10 Math 110 Name: Section: 8. The following table shows the price and the number of Xmas trees sold at that price at Terry’s Xmas Tree Stand. [bile as» W “$7.50” 322‘?" [325 [355W s2; l Number ot‘Trccs? 3s: 32 r 17 1 20 3 21 30 [ 12 [18 § a. [3 points] Find the least-squares, “best—fit” line for this data. Letx = price, and y = quantity. y: #0351 x + 4\.03Uf E>P*$' b. [3 points] According to the model found in part (a,) at what price would they expect to sell 20 trees? y:ZO (Pt, 20 = ~0.%z x + Q\.07.>'+ \PL PMygq \Ft' C. [3 points] What is the y — intercept of the model found in part (a) §n_d what does this represent in terms of this model? y~m~lerwpk " LH.O7sl—l \Pbr. W exped- in: be able kc 3w:— away *5. «load; LH lacs 9r Vac. 2‘) Page 6 of 10 Math 110 - Final Exam December 2003 9. A group of students was asked to pick their favorite holiday treat. The results were as follows: i ‘ "ml-Gthgot-htotlclbooties [ ChocolateSnowmen Candied Nuts "T5151 tattoosalso. Swat: i Q Q_;.3_§-__ A1,: [git/éﬁ i M- 7 WM Middle School Students [ 55 I 65 High School Students 320 ' | :50 l ‘ Total ’ a f 110 N [ 195 One student is picked at random: a. [2 points] What is the probability that the student picked chose candied nuts? ("5/320 ‘ 'zpts b. [3 points] What is the probability that the student was ill Middle School and chose gingerbread cookies? 55/3570 2;»; c. [3 points] What is the probability that the student was not in Elementary School or chose chocolate snowmen? HOHIO + [013 _((03+50 g 330 3% 3% 3% 540 \_\V 7777777777777777 ~ l - W z. 1. pm “hi. d. [3 points] What is the probability that the student chose candied nuts, given that he/she was in high school? ; Mme n as) _ 3Q Julio ﬂaw...) WHO»: 1 1’)“ \ P‘“ e. [3 points] Are the events “Chose gingerbread cookies" and “chose candied nuts” mutually exclusive? (Justify your answer with computations.) M Ma; :atvarlka ygg, Mo cm. chose l \w 2,336, ; (it, h( {payoutth 0 not ) = O Page 7 of 10 Math 110 Name: Section: For problems 10-13 indicate the formula needed to answer the question, give the value for each v of the known variables in the formula and solve. Formulas are available at the bottom of the pages. 10. [5 points] A 5-year bond costs$12,000 and will pay a total of $3200 in simple interest over its lifetime. What is its annual interest rate? t = 5 vv: \Zooo ate/k \NT = “57—00 lNT’ PV rt \P" 3200 = \LOOO -t‘ S m r: 0.053 ‘9’" 7 5.3”?“ 11. [6 points] W hat is the future value of a 6 year investment of$20,000 at 0.15% per week, compounded weekly"? *3: L9 ‘ V1 ‘2‘» Cad/L YV= 10000 T: .0015 (5;) or Y" Zfﬁg’ "=‘ .Ol m 05 m= S'L lpi'. Fv= PV beg)“ Ital s24, ‘ = 10°0°<\+.00i$) -—-— ﬁalﬁ‘14.?$ W" INT = PVrt FV = PV(1+ rt) FV = PV(] + 7;— "" ref, = (1+ )m -1 Page 8 of 10 Math 110-Final Exam December 2003 12. [5 points] What is the present value of a 20 year investment at 4.12% per year, compounded monthly, if its future value is $32,000? {= 20 l“: oO‘HZ Va 90w» = I’L (hug. S? 2 > Fv = 31000 . -\ FV: Mum” <*- Z? S . 11:10 : ,CNIZ 32000 W (H. ‘2. ) \P*‘ 1 W: i in 03?. '53 13. The Smith’s are planning on buying a new house. They take out a 30 year,$130,000 mortgage at 6. l % yearly, compounded monthly. a. [7 points] How much are their monthly mortguge payments? -n - so ,0th {3: 30 \%0000 =PmT '1- <‘ + |z : 9 9V 3" 330000 (noon/m) Y‘ = OoOLol W” I2. VIM“: $17817”: ’ cm“) 1* \ -\' each P IV». b. [2 points] How much total interest will the Smith’s have paid over the life of the loan? INT = 78?..7‘1 (Iz)(so) —- 150 000 = 1F I53 oos- so». If]! V r"(}’" "I INT: ert FV: PV(1 + rt) FV2PV(l+—;ﬁ ref]: (1+ ‘75-) "1 Page 9 of 10 Math 110 Name: _.______________Section: 14. Your favorite restaurant offers 45 desserts. 3O desserts contain chocolate, 2O desserts contain fruit and 15 desserts contain both chocolate and fruit. a. [3 points} How many desserts contain chocolate or fruit (or both?) b. [3 points] How many desserts contain fruit, but do not contain chocolate? 5 * 59h (3m mad S: mm is (“mock w/ to) pea—t lb premath mswrf‘ 15. [5 points] A market survey shows that 40% of the poulation used brand X leaf rakes, 5% of the population gave up raking their own leaves and 2% of the population used brand X leaf rakes and then gave up raking their own leaves. Are the events of using brand X leaf rakes and giving up leaf raking independent? (Show computations to justify your answer.) Wm-PM) 3--—- mew) * 29% '2‘ MO) (.09 i=- ‘ .0; 19+, ‘01 = .02. \ 2‘3)”. Vi; -‘- tnwpendeA-‘r - ‘ 16. [5 points] Ninety percent of all students who study for their math exam pass it. If 80% of all students study for their math exam, what percent of students both study for and pass their math exam? S: shay / P: pass Wit: "i «:2 ZIP)”; \s Ptvts) : WPnS) P " Z? Pcs) ’90 = PlPoS) .8’0 Page 10 of 10 Math 110 - Final Exam December 2003 17. You are playing a game in which 3 distinguishable fair coins are tossed. You win$25, if three heads appear, and you win $15 if three tails appear. Otherwise you lose$8. a. [5 points] Create a probability distribution for this game. “Mam-..” u ..,...—.......M- \pi’ Q4 ribbed” A: ‘3. b. [3 points] What is the expected value of this game? 25 (Vg) + \S('/g) + (-8)("/2) 29% ii) hi. \P’r, (jut Crews ii: Ohmic (mm-loci" w/ mmh (a) H E”) H c. [2 points] If yOu play the game once, what is the probability of losing exactly $1.00? 0 /" “Mum. cm; m <7th {A max yaw lose exackta$1. 2915, Please write the honor code below, then sign it. “I pledge on my honor that I have not given or received any unauthorized assistance on this examination.”(signature) ...
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