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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 x27
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
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Mlnjmllltllillgliltllﬂl
IIIllllllrllllilllll
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
.nmnnnmmnmulnmIMIlull
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Inﬂﬁﬁllﬂﬂmllllﬂl ' I IMHIIIIIIIEI. ~// 2( ‘%X+b ’ MWW lamamulﬁﬂw
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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 HighSchool’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 33 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 twobedroom 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 leastsquares, “bestﬁt” 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? 319.. @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. pmr 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." Pmr == 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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