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Final_solutions_ 0_ - Name RE y Section Math 110 Final Exam...

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Unformatted text preview: Name: RE y Section #: Math 110 Final Exam Instructor/'1‘.A.: December 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 nearest 0.001. your final answers. l a. [3 points] Find an equation of a horizontal line through (—8,12). b. [5 points] Find an equation of the line through (—3,4) that is parallel to the line —2x + By = 17. Write your equation in slope-intercept form. L “~Zx+sy=i¥ 3y: 2x + l? at \/=%x +13; W”2/2, y:_§_x +‘O :L - , 41 €(S)-\’lo b=Lo Y‘Z/s K-l'q Zp'l’ lp‘h 2. [7 points] Edna’s Elf—Wear Shop has found that they can sell 120 hats if they are priced at $18 each, and only 150 hats if they are priced at $15 each. What is the linear demand equation for Edna’s Elf Hats? (Let x = price, y = quantity of hats sold.) 2% CH?) tzo) (IS,iSO) m=l§9;E!L» lS-‘IE 2)" = 32'3“ O l’ _3 i [£0 = *lOUS) + b. 300 2 \o MWWWWM...WW, \ y: —|O X + 300 uwww Wk )Pl, va Page 2 of 10 Math 110 - Final Exam December 2004 3. Carol’s Card Company makes specialty cards. Fixed yearly costs are $35,000, and variable costs are $1 per card. ‘a. [3 points] Express the company’s cost, C, in terms of x, the number of cards produced each year. ~~w~—w~_w—»~~-w,- ~~~~~~~~~~~~~~~~~~~~~~~~~~~ b. [2 points] Carol sells each card for $5. Express the company’s revenue, R, in terms of x, the number of cards sold each year. W333 2;» c. [4 points] How many cards must Carol’s Card Company produce and sell to break-even? zfll‘ ch Or 1P=R~C =0' “3*“ If _5X : x+gsooo 4X: 33000 Page 3 of 10 Math 110 Name: Section: 4. Mary recorded the number of pairs of mittens she sold daily for 8 days at various prices per pair of mittens. The results are given below. —-llm $11 mam a. [3 points] Make a stem-and-leaf plot of the price data. 02/3/U Ila/Z. «I pi 1F "‘3” mo ‘vs Masha) I O U‘EA : “LP—l3 QM WWWJ decim— L[ o b. [3 points] What 1s the mean price of the mittens Mary sold per day? // O —z + 9c [:13 :3 '35; epi' P WE Adm. c. [3 points] What IS the medianfinumber of pairs of mittens Mary sold per day? z e, 33 L)? —7/ , 7o go qsws jfi’o’ipg‘fi “ lpi' Ordei'm V ii» ' 2' W”. d. [3 pointS] Usmg least square linear regression, find the best-fit line for this data. Let x= price and y= # of pairs of mittens sold at that price. “y: 4.233 x + $18.33? [319% (‘2‘); :1} >1:~'55;L)g 1.50.3311 wmwmup I) you e. [4 points] According to the model found 1n “part d” above, how many mittens ”‘an expect to sell if they are priced at $15 per pair? x =15 0:?“ AW- U 1)) . . a.» y=~z,233(.s) + 92,573 45 Pan’s 45,0752. @ f. [4 points] What is the slope of the line found in “part d”? What does it mean in terms of this model? m: -2233 @3 \V Paula. tmrm (C‘eCrmm) L3 5”“ yam. (KPH-V "in RM. 013%} Z. RMW‘ (mare) ZP’L 'Pm‘f‘» (X Mums. 29* apt 1‘99 6. Page 4 of 10 Math 110 - Final Exam December 2004 [9 points] Mr. Smith is purchasing cookie platters and containers of apple cider for the school party. Each cookie platter costs $8, and each container of cider costs $7. If Mr. Smith spends a total of $529 and buys twice as many cookie platters as containers of cider, how many platters, and how many cider containers did he buy? (Define variables, set up equations and solve.) x: Manure, PMM y? fi- 6de ccmimnus 3x + 7y =62? X =2>/- 237 : Slq 2135" y :- 2.3 X 7: Z-(Z3) lP-\- ,440 40 wide plauers 5': 7.3 Cider" “minder; [14 points] Model the following situation, but DO NOT GRAPH and DO NOT SOLVE. Clearly identify the variables, objective and constraints. A bridal shop produces two kinds of custom wedding dresses, traditional and modern, each of which must be designed, produced and finished. Each traditional gown requires 10 hours to design, 12 hours to produce and 2 hours to finish. Each modern gown requires 11. hours to design, 9 hours to produce and 1.5 hours to finish. The bridal shop has 3800 hours available for designing, 4200 hours available for producing and 425 hours available for finishing. Due to demand the shop must produce at least as many traditional as modern gowns. If the profit on each traditional gown is $325, and the profit on each modern gown is $275, how many gowns of each type should the shop produce to maximize the profit? X: H: de‘hmfl. 6‘“?ng 7 z». tt Modem civeSSeS. x“ +01%}. deg-fit“ [0 || MWZ-E‘BOFW' 10x Hi), 9. $200 lax +qy 992.001 ea/dfl, Page 5 of 10 Math 110 Name: Section: 7. LetS = {blue, green, 1,2,3,a,b) be the universal set, and letA = {x e S I x is a word), B = {x e S | xis a letter} and C = {green,2,3,a} and D = {2,3,a,b}. Find each of the following. a. [2 points] D’ = f Elva, 3‘9”” 3 b. [2points] an =62, 3, (3 c. [2 points] A x3 = flow/ax (Limb), (gram, a), (Wm, M73 - d. [2points] 005 =0 = fame“, 2,3, 053. e. [Zpoints] AUQ : A : E Hm) yum?) ‘ 8. Helen is having a New Year’s Eve Party. Let C be the event that champagne will be served, E be the’event that eggnog will be served, and P be the event that pretzels will be served. a. [2 points] Express in words: (C U E) E‘A‘Atflr {310nm PQSOQ: 3:” eggnofi M has $PM£SL . W ‘P* b. [2 points] Express in words: (E (l P)’ I , ‘ . ‘\ p _ No?” K d £103 \V" MV‘W NOT 3““, \oa—HA eggnog) mame 31% a3 No’r' W+u g c. [2 points] Express 1n symbols: On New Year’s Eve, Helen will serve both hampagne and eggnog, but NOT pretzels. CnEnP’ 9. Let P(A)= P(B) = P(A u B) = —1——3 Find. 271 ’ 281 ’ 21 a. [2 points] P(A n B) = W A) +7 W6) ~— WADE) = 4/2,. + 75/2: " ’3/2| :EZ/zl‘ GE) b. [2p0ints]l<(AUB)'): [ __ P(AUB) (Pi; c. [2 points] P(B|A) ‘ =— (3» 2 W en A)“ P( A) (it) Page 6 of 10 Math 110 — Final Exam December 2004 10. A group of students was asked to pick their favorite holiday activity. The results were as follows: 120 Baking Cookies Attending Holiday Parties Giving Gifts 30 10 . Elementary School Students 140 . \l U'I I LII )-l A O One student is picked at random. (You may leave probabilites as unreduced fractions.) a. [2 points] What is the probability that the student picked was in middle school? l%O 3?0 b. [3 points] What is the probability that the student was in elementary school and chose giving gifts? l O "' O 0 Z 7:" 5WD ° c. [3 points] What is the probability that the student chose baking cggkies or was not in high 9 school. KR) +PCH’)" PCSCO H’) @ MO 370 -no No -20 2.80 _ f ........ ago 3?0 22% 3:}0 . @P‘l') @ “"1 NO Htto + no —8o~qo) /3?—O . _ d. 3 points] at is the probabilitiy that the student was in middle school, given that he/she chose attending arties? ?C 1WD T pmlws) == nCms n Write») : ;z,5 h (, pwhés) E Wm.) (va W e. [3 points] Are the events “chose baking cookies” and “is in middle school” mutually exclusive? Justify your answer. wt n(Bc 0 ms) 2 4o SOECHYY‘S 75¢ 2+ 3 W axuNO—V P 0 a rmmd%,ambswu =o‘fSS. Page 7 of 10 Math 110 Name: Section: 11. [5 points] Ted needs to pass calculus and chemistry to graduate. He believes his chance of passing calculus is 0.7, and his chance of passing chemistry is 0.4. He thinks his chance of passing at least one of them is 0.75. What is the probability that Ted will pass both courses? E: (A: (766‘: Ch‘C,, P3: Page chem. “E Wave») =2 PCA)+?(6)- owns) ”’3 =3 .-+ +»4 —— 9mg) 75?» Mme) = .35 12. [4 points] In December, 50% of all the flowers in Fran’s Floral Shop are roses and 40% are roses and are red. If a flower is selected at random, find the probability that it is red, given that it is a rose. RNA): NEDA) no Miro. .,, -v M PCA) '" ~ 50 13. [4 points] Find the expected value of the following probability distribution. Page 8 of 10 Math 110 — Final Exam December 2004 For problems 14-17 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. 14. [4 points] A 5-year bond costs $7,500, and offers a rate of 6.2% simple interest. What will the bond be worth upon maturity? ,, ”2’" 'PV — 7500 ‘ F'V: #2790 (i + 600,246.33) [9* P[r : 5.3092. : St 732- 5 m Fv= PV(l‘\'Y'JC) . ”9* ”A, 15. [5 points] What is the present value of a 20 year investment paying 6.15% per year, compounded monthly, if the future value is $75,000? , tZ-ZO 5‘ t :20 73000 .3 W ‘1‘ .OU'S \Q r:,ou\5 ‘2. \p’l YY\~=|Z_ I ’\>\/3 $> Zl qctO.o\\ \s‘ F’v “set—€000 ' L..____._~_____. P t‘\/-PV<H—r‘>"‘Jr ‘ [Pt 7““ pt INT=PVrt FV=PV(l+rt) FV=PV(1+7;-)m' refl=(1+—”—';%L)m—1 Lmt_ 1_1 L—mt FV = PV(1+ —,%)m' + PMTil—iM-rL—l PV = FV(1+ 7%)” + PMT—i—i-L— Tn— m Page 9 of 10 Math 110 Name: Section: 16. [5 points] Joan invests $8250 in an investment offering 0.42% per month, compounded monthly. What will be the value of her investment in 6 years? I’Z.~<a u :v: 3500 + .0304 r: o 2- : — \2. 26‘ E \00 A ‘2' ,ObOL} ‘ . 'L‘b Wx-[ PV = $1561“ ' 37—50( I + .0092.) t r Lo yy‘ == l2. m+ :$9 a} 0' 693 FV: PV(\+:;Y‘ 55.9 w; 17. ' F; a. [6 points] The Smith’s are planning on retiring in 25 years. How much money should they deposit monthly into their retirement annuity to accumulate $250,000 if the annuity pays 6.7% per year, compounded monthly? \‘Z-‘LS Mtrzs) zsoooo:o+PMT(\+39'fg ’( FV :. 2‘50 000 60‘3”“ m =11 2:30 000 =7- PWW‘ (7"?2—(0‘53) v?\l 2: O ) wt WW“; use b. [2 points] How much total interest will the Smith’s have received over the 25 years? PYWT' M 4: \P’r [ “MB Wax-L (32’53‘60flmfl28) = $7?o(08./I \*[ Rik/110% : 250 OOO‘Q7OL98’.“ 2 i/SZQSL 8:? P” INT = PVrt FV —_- PV(1+ rt) FV = PV(1+ TQ—ynt reg = (1+ ”WWW —1 (1+ 72—)” -1 1— (1 + —,g—)-m' PV = FV(1+ Til-rm + PMT r FV= PV(1+ —r%)m’+PMT , 731‘ m Page 10 of 10 Math llO-Final Exam December 2004 18. [12 points] Graph the following system of equations on the grid below. [Pi— Pa (‘ \a‘oei. -Label every line. . -Shade every discarded region. lpi' WV C WCA“ ““6 -Label the solution set with the letters ER. 6. \n a At ._ n0 x—2y24 yS—3 x2—5 yS—x |P+ Per g A iE-u' m‘ MINA 4 ‘I l‘ E 2539315351.. I ‘ ‘ (Ar QML‘V‘HNIMM iwmwnwmn E: Ammmvm H“. mnmavmwmn 51'3“!!!" hating.“ WI‘I‘LMWM RIM MEWmflI; 5 t a stigma _ “MIN?“ WWW/N“ "' MINI 5 ‘5??? mamummmmawag [MD 1W- _ ‘ ,5 'wiiw‘flflflh'm unnmmnvm‘anva lnn’tafil WMWMWJ‘“ ‘IWMW WWI mam ‘ IIEEQEEEEWIUIIIIII 'fl’fllfifl “ an 'IIIIIIIIImflWZIWI I’ V‘ an ~ I: . ‘ I g g ' V fiflfiflfigfi 5 ilfillllflifi £1215 ,1pr 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 th1s examination.”(signature) ...
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