Final_solutions_ _

Final_solutions_ _ - Name Section Instructor/1A.1 Math 1 0...

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Unformatted text preview: Name: Section #: Instructor/1A.: .1! Math 1 0 Final Exam May 13, 2004 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 the nearest 0.001. your final answers. 1. Mary recorded the number of balloons she sold daily for 10 days. The results are given below. ' I \ ' r I ll, 18,24,10, 24, 13, 12, l6, 40, 26 a. [3 points] Make a stem-and-leaf plot of the data. b. [3 points] What is the mean number of balloons Mary sold per day? .WM_WMM~.WM._.M- c. [3 points] What is the median number of balloons Mary sold per day?_,__,_, m , ,/ f [z , x3 ,Upa, w 3% m, 2w W “p; («dams Mug ,1, I? t hi?) 2. [7 points] A nursery can sell 1,200 red oak seedlings per season when they are priced a t $9, and 1000 seedlings when they are priced at $1 I. What is the linear demand equation for red oak seedlings? (9/ ”00) g? W ”WWW/9 W 11> (W 22 r: (H, “200) Mac; -{zfmww4 b {I ll ”7 W [QQQLLEf-Eiam b m 2 M20 l1 [1,“? 1‘... 1 x ‘5 MW 2,62%? :3- ”/m = __ UPWW‘AK My) 0 W ” f /00/9 + 2/00 ,P> Page 2 of 12 Math 1 10 - Final Exam May 2004 a. [3 points] Determine an equation of the horizontal line through (—3,-5). 1 ea b. [3 pointsiéaehfi Determine an equation of the line through the point (3,—8) and parallel to the line x i ’4. x=3_ @1 4. The Homestar Company makes and sells hummingbird feeders. Yearly fixed costs are $37,500 and variable costs are $2 per unit. a. [4 point] Express the company’s cost, C, in terms of x, the number of feeders produced per year. C 2 2x + 317300 <21 @ b. [2 points] Homestar sells each feeder for $6. Express the company’s revenue, R, in terms of x, the number of feeders sold per year. R = (a x - <2? . :IHHWWNNFIIII-Ill __ .. hallmmmigfllllllufilu o x : unnummflro .m 2 2 “Mmuhuuucw T , e . i- .Imfimnvals: 2 . s w u 5 w ywunflul-“mulfiflwfi-nr. m Yam: ELIE, .3 .m m. 2 C a=.!lmum.ifiqu€m “I w ‘Da ,/ . , ,, , d ,, :. E $.3an . e x/ «\l ‘ x 1‘ : ‘. 1 Im R. : M: H , n . ; : m A 0 F a. 2. a, : m m x r F. x .m m . g cl t . a e ., w . u - _ n I § h .m m . 0 g h 4 m m .u _ .. w d w >_ e W. 0 fl u) m ”a m m N .m M R rm. w n d m 0 “0 W. W. m 3 l e w. m m >_ S . . . u .m .hL lel )//.2...m-_w:.m Mm h “Mm (W03aum.n.nw__wqmfl.m_ \9 I «IVJIMITv .|.1ql.|t\4|.. . h m m 2 m _ . o m+iT x/\ HI. 2 2.-.»..- .ruLLLWt. r. G . . . 3 C wrr.mnr..rp:-2.:frf2-rfirrr H «1. 1|... 1 S t f n O O 3 D. e g B 8 .Il P 5. [..w_ Page 4 of 12 t x. . 4~\ ) 30$ MathllO-Final Exam May2004 >\‘ A324“; “ii 436% / ,3? 6. [4 points] The supply and demand equation for a new sweeper are given by $07) = p — 8 and / i D(p) = 90 — 3p, respectively. Find the equilibrium price. 3077/)! : ciflVM/td (i?) H P ‘ “l % {1'32} Pg 13 $2450 6,) 7. [9 points] Mayor Green is purchasing azaleas and peonies for the new Town Center. Each azalea costs $18 and each peony costs $12. If the mayor buys 42 plants and spends a total of $588, how many azaleas, and how many peonies can he buy? -Define variable(s), -set up equation(s)and ~solve. "N x = final/en; w?) y: a peonies *f—W'fl—‘iW—‘Wm ,(_ 5 (u) 2 /" Maxim'rje \ngs‘» Page 5 of 12 Math 1 10 Name: Section: [14 points] Model the following situation. but DO NOT GRAPH and DO NOT SOLVE. A carpet manufacturer produces two kinds of rugs, Oriental and braided. Each of which must be designed, produced and packaged. Each Oriental reggires 10 hours to design, 8 hours to produce and 0.6 hours to package and returns a profit o®5fiiach braidedwre . uires 1 hour to design, 2 hours to produce and 0.] hours to package and returns a profit of $8." he carpet manufacturer has 30,000 hours available for designing, 40,000 hours availaBTéTor producing and 120 hours available for packaging. Due to demand, the manufacturer must make at least as many braided as Oriental carpets. How many carpets of each type should be produced to maximize profits? Clearly identify: - the variables, - objective and - constraints. x y W ,,,,,,, I...“ X ,; O (‘ P\’T\‘5‘\ W38 f—‘f’ mwumw WWWWWW‘Wfi-‘g MMMMMMM ME} 0 OCJO , / A6 52V“) m M) l r y 7 bfm ided V03 5 , r t - > D Pmcwcc g 2" 6”" £4 0 w k“ gym (I \c: age 0' (.0 O 9 i i j tiff. 61> x! ”P; Lfix 4- 3)’ /0x + y .4. 300053 @md’x ?; 4wa 0 04px +0.1)! 4* ‘x/ 2 >< @@ )x :0 ' f,“ A “9 (yzo) ml mreamr ”—r—‘mT—T—l—m_ Page 6 of 12 Math l 10 - Final Exam May 2004 9. The following table shows the number of violent crimes committed during an unusually hot summer. EEEWWNW 21. 92:95‘19‘6156"ioo"“f64'% lNumberofCrimesl 4.1.131. “chitin: l8 16% 21 { a. [3 points] Find the least-squares, “best-fit” line for this data. Letx = temperature, and y = number of crimes. y~11fif§flx ‘—«/)Lw‘i<pl @ b. [3 points] According to the model found in part (a.) how many crimes would be expected to occur on a 1 10° day? Xrllo . @ Y: VSM (no) Mllul‘iwl = germ @ “haul 30 C(me’3 ® 0. [3 points] What is the y - intercept ofthc model found in part (21) fl what does this represent in terms ofth__i_s model? ..Tl’\.f2/\,..Q fillrfiuld be __1 “(0670] CYW€$ 07L, _<i 0“ 00 (My . 5 10. 11. Page 7 of l2 Math 1 l0 Name: Section: For problems l0-l 3 indicate the formula needed to answer the question. give the value for each of the known variables in the formula and solve. Formulas are available at the bottom of the pages. [5 points] A 3-year bond costs $7,500 and will be worth $8445 upon maturity. What is its annual rate ofsimple interest? , ”W a ‘22 5 O<> “ FV :: ($9 “l 5 [Weam t 3 FV= PV(\+V*3 <9 (aims: 7500 (w 3w) gill-1936 ysoo +- ZZSOOV‘ 7 LI SW 2 Z {:57} if?) (R 69 . :: Y” \ l1 2:? m OH 2. WW) Ll" 2' 0/3» J [6 points] What is the future value of a 25 year investment of $l0,500 at 5.18% per year, compounded monthly? tr25 : 05/3 ””"Z Y ml!“ @ FV: pv(l+ lm) 8 .2325 . '1 310230001“ 9%" ® INT: PVrI FV= PV(I +‘rz) FV= PV(1+ ,—§,— "1' r47: (1 + 5%)“ -1 +_’_'_'"l._1 ]_(]+_r_)—ml FV= PVU +~%)”"+PMT—(——L7r)—-——— PV= [fl/(l +7;-;— "””+PA{T—-—-_r——m-—- 77 m WNW—.mpwsmmmlmum..+am.,.mw...,wm~n ..... «M.».uwwh‘mn..m.\mwwmww.aW-Mwmmm-m-m.~”Mum"...-mu-m-~.,»~,m..-,mmmwymlw. ....... WWW—WWWWWWWWW Page 8 of l2 Math ] lO-Final Exam May 2004 12. [5 points] What is the present value ofa 6 war investment at 0 13% per quarter, compounded quarterly, ifthe value ofthe investment upon matucltgs $6750? m'l' l rzéooti’zXLl) €19 Fl/s- PV(H Am) {so _ G) 5&%g0:pv(i+(oot3XJ/> .3 ' :[email protected];5o ®[ W:— $é764+2.?3 <Q, ”25> $0? r“; 1.20613} 13. a. [7 points] The Smith’s are planning on retiring in 30 years. How much money should they deposit monthly into their retirement annuity to accumulate $350,000 If the annuity pays 5.8% per year, compounded monthly? / i?“ ’ 053 I2- 30 ® it; 2 go 350 000—:— 77/727" x “W - / 33061200 '0‘33/12, F V: @ ecldfi r” ,m ,n . .i V‘ V“ f” ' 3:330 ('11: amt-:32 73:; WW7“ ( ‘37 964. "Y i :1? a”) a 253"} :7?“ / :51», ‘ it i a «a W “ til; I ( Pv <2) . WW mew ’ , GE) [M V/ )er l .. , a m -. 17V "’ W77 ( WWW Y7m b. [2 points] How much total interest will the Smith’s have received over the 30 years? 70w, pay/MW} = (301,7?)(IZX30) “r 35/930 3001.20 360006 ~ /3o em,” =22 jig/foam” WWW rat's”; 7L y r ,r m rnnm n IAT=PVH FV=PV(l+rt) Fl =PV(] + ,—,—,)' w: (1 +--— m -——-)' 1+L””_.] 1_]+_r_~nu FV=PV(l+—,’;7)””+PMT—(-————’—nr-——— PV= Fl(l+ r)‘”“+PMT———-(-—.—r—"-7—)—— 777 771‘ W__________.___.___________ . . __ 1 WT- __ . ____.__ .. a”. Page 9 of 12 Math l 10 Name: Section: 14. Let S = {Honda Toyota‘ Dodge. Black. White. Tan. Sheila, Susan, Steve} be the universal set, and let A = {x e S : x is a car} B = {Honda, Black, Tan, Susan, Steve} C = (Honda, Toyota, Tan, Sheila} and D = {x e S : x is a color}. Find each ofthe following: a. [2 points] 3’ ‘1 E’Fajo‘fa/ Dodge.) (Al/wk) ‘Sl’wJa. u? (29 b. [2 points] Ama m 5% @ c. [2points] COB “"1 7%da, T4773. €1.10) d. [2 points] A x D Elm. blag; (235:2) (3:12th a“ Mile, um: Wig (“WM Tm \émndu T03 ,W. . 4A WM) CVMTUYA'A) 63» My) . 15. Your favorite restaurant offers 45 desserts. 30 desserts contain chocolate, 20 desserts contain fruit and 8 desserts contain neither chocolate nor fruit. 8. [3 points] How many desserts contain chocolate or fruit (or both?) ® {Vl (“eel/her) = M3) ' Naomi”) Q == 43 - n(CUF) @ mam?) == 3? b. [3 points] How many desserts contain both fruit and chocolate? G) / nefCuF) = I’l(() + rm?) MW/t’fiF’) 3? —‘= $0 + 20 —n(C/7F) @ mane): 13 ® _.__.._'_____.___.____~‘__T.__‘______.___.____.W__._ Page IQ of l2 Math I l0 - Final Exam May 2004 16. A group of students was asked to pick their favorite type ofmovie. The results were as follows: ‘M _ __ Fantasy ; Science Fiction j Horror x Total {Elementary SchoolStudents ‘ 807': 40 5 5 ”125 l Mid—ctiés'ciiéélstudent; ' “lol "so ' '60 156i :Fié'tséliwlStildéms if: .. 2° 45.. ' ._.,,651'§1.3¢'l BT93” ._ “0' _._'.35., 139? 375.. One student is picked at random: a. [2 points] What is the probability that the student picked was in high school? “0/95 @ b. [3 points] What is the probability that the student chose horror movies and was in elementary school? I". ‘9 ... :3) “/3322; t’ c. [3 points] What is the probability that the student was in middle school or chose science fiction? - ' 4' “ ' a: ‘ O 129 + 13>: .... fix a, 2.3.3:. 576 322—5 we): $125 \~ ® (a? d. [3 points] What is the probability t at the student chose horror movies. given that he/she was in middle school? tMH/l/Vl) :1, a), y ,1. ”MW /20 7- ”H’M) @ e. [3 points]. Are the events “horror movies” and “was in high school" mutually exclusive? (Justify your answer with computations.) h<homar mum fl Ml“ swat) '5 {a5 94 O @9 60 NOT [MW/muggy ”closure..- 6; ##M—fi—“w—T—T—fir—mfl Page ll of 12 Math ”0 Name: Section: 17. You are playing a game in which 2 distinguishable 6-sided dice are tossed. You win $30, ifthe sum of the dice is 2, 3 or i 1. You win $5 if the sum of the dice is 4 or 12. Otherwise you lose $10. ‘1 a. [5 points] Createaprobability distribution for this game. m 30 l f5 _ __"/O 635/“ WWW i m U ‘2 (t,3)(z,z)(a,\) __ lg k f Ii 4 loge.) (2,») i MM) 6}) fi‘tih’mee lgglwl 9;; l l g; rwb l ”/50: [4/30. 29/369 “:69 em" b. [3 points] What is the expected value of this game? ECU : 3O (S/gip) -l— 5(4/39) +~-/-/O)(2;7/39) Q?) r“ ”mo/3L0 == ”2.3/8 (Q; c. [2 points] lfyou play the game once, what is the probability of winning at least $5? WWW) + an 30) M Li/azp + ‘S/ae Page l2 of II! Math l 10 - Final Exam May 2004 18. [5 points] There ts an 85% chance that I travel to California this summer. There Is a 70% chance that l w ill paint my fence this weekend. Assuming that my traveling to California 15 independent of my painting the fence, what IS the probability that I will do neither? (PCC) 1': . Caps]; Farrow” P(F) "“3 a?!) F4"? W’neaw , - lMCPPWdeA-l’ m» Pccmr) Pm par) (sgmo) 01;) = l 595 P(CUF)—~ PM.) + PW)” Puma) ® “Pd/her“ 2:: . 33 + ' :70 .. , 66$ 5:; 0755 WWWfi-‘J'Pttcmo’l vi "Pi/CUP? .5. was: w .096 (in?) 19. [5 points] Eighty percent of all adults who are college graduates got ajob within six months of graduation. If 30% of all adults are college graduates AND got ajob within 6 months of graduation, what percent of all adults are college graduates? A:- ' ailf’at’ LR‘FMCQ E: flat- sob w/m to WW» NAME) = 030 .5 PHI/I8) ® NEW) PM) p337)?" :39 ~ p(,q)=—,,3?5 ® Please write the honor code below, then sign it. “l pledge on my honor that l have not given or received any unauthorized assistance on this examination."(signature) _~_T—-__——V—F——I ...
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