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Unformatted text preview: Name: Section #: . Instructor/TA: Math 110 Final Exam December 14, 2006 Instructions: Please write your work, including formulas, in the spaces provided. All of your
work must be shown to receive any credit. Leave answers as exact fractions, except when stated otherwise.
your ﬁnal answers; 1. Edna’s ElfWear shop makes and sells wool, cotton and polyester elf hats in red, green or white.
Edna has the following number of hats in stock. Red Green White Total Wool 20 55 35 110
Cotton 45 4O 15 100
Polyester 30 36 4 70
Total 95 131 54 280 One hat is selected at random:
(You may leave your answers as unsimpliﬁed fractions.) a. [3 points] What is the probability that the hat chosen is cotton?
' loo i,
Z, 0 Es b. [3 points] What is the probability that the hat chosen was not green? l—‘lél. : 280 2,20 9mm, ‘ [A . V,
c. [3 points] What is the probability that the hathas polyester, given that the hat chosen was
red? , 6 wk :‘ Pan new) “r 30 ) I) I. ,,,,, A. I», _q___.—S
' ‘ Pt Km) d. [3 points] What is the pro ability that the hat was a red wool hat?
‘ 2 o I 280 ® 6. [3 points] Are the events “red” and “wool” mutually exclusive? (Justify your answer with computauons.) NO ~‘JI/‘Aevre M '20 reek Waul Vials“ o. __n__—_ﬂ__——_~—m—mmwm_. Page 2 of 10 Math 110  Final Exam > December 2006 2. 350 students were asked about their plans for winter break. 95 planned to get a job (J), 130 planned on taking a class (L), and 210 planned to travel (T). Furthermore 60 planned on both
getting a job and taking a class, 50 on taking a class and travelling, and 40 on getting a job and
travelling. Finally, 25 planned on doing all three. a. [8 points] Solve the Venn Diagram where the letters below represent the spaces in the it?“
a u
[\l
0 ll
2w
U‘mU) II
N
U”! hooksmgouQ
ll ll " N .5; w H
11:
U b. i [2 points] Which lettered cell(s) represents the students who plan to get a job or travel? ._,,,,,,M. _...A.. .7 “Adam’s “772....” _ .__.. .M .._..__r..v_.__._...__.‘..t . ._.V______<__.___.hnK;m5_;Md} €._. .;,..394ligammw__.______‘r._..__._._._.V....rv _.V V , ,.. . _. c. [2 points] Which lettered cell(s) represents the students who plan on taking a class and travellin ?
g e t. ,
d. [2 points] Which lettered cell(s) represents the students who plan on getting a job, but not
taking a class? a ’ d ' e. [2 points] Which lettered cell(s) represents the students who did exactly two of these ms? \o,d, f. 3. [7 points] Henry is in charge of shipping dolls and trucks at ToysForTots. Yesterday he found
that a total of 72 of these items had been donated. He noticed that there were 7 ﬁmes as many ' ' t
dolls as trucks. How many dolls and how many trucks had been donated? Define variable(s), ?( = #do/IS. ] Set up equation(s) and \/ 5 # fruC KS . “M
Solve '
Answer the questions V + 7 f 72 ’ 1 z X :V ? >/ ’”
77y r y r 72 ___._.___._—_._—————__n——.———————___—._..__.__ ___—___ . ___ Page 3 oflO Math 110 Name: Section: 4. [5 points] According to the weather service, there is a 25% chance of snow in New York and a
60% chance of snow in Lake Tahoe. Assuming that New York’s weather is independent of Lake
Tahoe’s weather, ﬁnd the probability that it will snow in at least one of these cities. . _ , ‘ 4
N : Mm Ya k, (ﬂrdewndmi a Pm m r)  PIN) P( T) I
7’: LaugﬁMa @ =Q2,:S,)(.tpo) {>(N);,ZS ' . ‘ "’5 v 4
p (T) a: , we“ w N UT 1 mm + P(7') » Pf N M“) LL19 ‘ r, ,23 +.wo ~ ./5 =E7Ol‘dﬁ”
5.. [2 points] In Paula’s Purse Shop you can choose a purse style, of which there are 6, a color, of which there are 9 and a size, of which there are 5. How many different purses can you choose
from in Paula’s Shop? ‘ MCI5 6. [4 points] A die is weighted in such a way that each of l, 3 and 4 is three times as likely to come up as each of 2, 5~ and 6. Find the probability distribution. ovtzmne l a 3 4 3 i “ Pm ’ 3x 7“ 3x 3x x >9, I :2 _L 2.. .3. .1.. J X 72'.
I; (Z. I; I; [z )2” 7. [5 points] Forty percent of the students at a local elementary School are in both the choir in
the winter play. Furthermore, 85% of the students are in the winter play, given that they are in the
choir. What percentage of the students are in the choir? C 1 Cabal" c, a P/w/W) W»; Wr/ikf > ) MC) 1 PCCﬂW)= ‘[email protected] ,gg : .40 NW C») t 3’5, ’9“) a)
P“) ’ (M "w—mwww—wwwm“ Page 4 of 10 Math 110 ~ Final Exam I December 2006 8. You are playing a game in which a player tosses 3 fair, distinguishable coins. The player wins $10
if exactly two heads are tossed, wins $2 if exactly one head is tossed and losses $6 otherwise. a. [4 points] Create a probability distribution for this game, where the random variable X
denotes the winnings and losses. b. [2 points] What is the expected value of this game? , ,
2L4 ' w 7:? a c. [1 point] Ifyou play the game once, what is the probability of winning exactly $3? on; ~w__mimm“—WWW»——LMW Page 5 of 10 Math 110 Name: Section: For problems 912 indicate the formula needed to answer the question, give the value for each of
the known variables in the formula and solve. Round dollar values to the nearest cent and rates
to the nearest 0.1%. Assume 365 days in a year, and 52 weeks in ayear. Formulas are available at the bottom of the pages.
9. [5 points] A $7500 CD, certiﬁcate of deposit, will be worth $7675 in 160 days. What is its rate
of simple interest? ‘ W V W 7 __. z: .‘ P M:
?V : 35,00 hV PV ( ‘ “'" r£> \M
A C?
FV‘QWWS $975: 7500( [+139‘73r)
t z 192 
3‘05. r = 0. O 5 3 2 annwm,m_wtw 1 0. [5 points] Find the future value of a $6250 investment paying 0.63% Weekly interest,
compounded weekly, if the investment is held for 5 years. V ml
PV:(pZSO<Jﬁ9. I V :G 00(05)(52~r) C29 : QZSO (I +_ .oowvsz‘s.
m: 52.. JG :5, :y 3194040th INT=PVrt FV=PV(l+rt) 1:'V=PV(1+—,;‘T'"t reﬂ=(1+5%‘;’i)m1 . (1+7§;)mt—1 r _mt
FV= PV(1+ ’ )’"’+PMT——————.—— PV: FV(1+ _ +pMT 11—7 I I" L
777 m 1—(1+7;'7 "’1‘ Page6 of 10 Math 110 — Final Exam December 2006 1 1. [5 points] Henry will retire in 38 years and has decided to start an ordinary annuity. He wants the
annuity to be worth $400,000 when he retires. How much should he deposit quarterly into this
annuity if it pays 5.3% per year, compounded quarterly, to reach this goal? EV:— u/oo ooo]@ :' (1+0wf”rt) (ED~;
Fv : On FV" Pmr/ v/M . é = 3%, ‘mr ‘
r = , o s 3 ,«M 400000 “* PMT( mca. .éﬁi wﬁﬂ ’
Pm't“ 2 <5 2 8 . 80 12. Jane and John are buying a house and have taken out a 30 year mortgage at 9% interest per year,
compounded monthly. Their monthly payments are $1350.. {lpoints}.Altlhatistheorigjnalamountoﬁtheinmortgagel. .. .. , /¢_N 'P V _, Pnn't" WWWWMWW ____ .v
:.C>'”1 [Kl ‘7’“
3 t Z .4240
m Wm __ (550 I __(l+,a‘1/:z)
PmT‘ '5 lBSO ‘Oq/lzf mm
Fx/ = o ‘1 lb77ao,ez G; b. [2 points} How much total interest will Jane and John have paid Over the life of the 10 PAH)“: ’3“E>C>* I2.” 30 1 #89 000 [Pt (NT 3 PHID— “ﬁlm’s/0‘s?” z iglgzlﬁ’ﬂz QED INT = PVrt FV= PV(1 + rt) FV= PV(1 + 7% mt ref = (1 + ———";;;'" )m — 1 . 1+Lm’—1 . 1—1+—’§—"”t
FV=PV(1+T;,—)’”’+RMT£——Q’r—)—— PV= FV(1+—I% m’+PMr——(——,—.—lll—
777 i 771‘ Page 7 of 10 Math 110 Name: 13. [12 points] Graph the following system of equations on the grid below. x510 y2g—2 yz—ix 3 —x+2yS 8 Label every line;
Shade every discarded region.
Label the solution set with the letters FR. 3 g
Gad/x lme 1 , /
. , ..... [l , A
€6tOlA Shadow v ll;
WW“ I s
Fad/l [abet "' “l ‘ , _
y "' '2. If?! v ,t q; IE a [#4. y, K ; t 4‘ My
1 J‘ W, ,2; / A, ' ﬂ . f
3’ f «r l 1’4 «4 1" ' x 4» r) n’ x
.. I , w 5."
Y 'ﬁx
T a A
l l "1 1: lo
14. [6 points] Find the slope and all interceptsofthe line: y = ~7
‘ If they do not exist or are undeﬁned, so state.
Z ply x—intercept: n one '
@P‘, y—intercept: ‘ 32 0‘" ( 0/ ' 7' ),
6P9 slope: O .
,,,,,,,, ____ . ._ .._.__ ._.___.___.____.__.__________._..._1.___.._._ Section: . —————~—1w Page 8 of 10 Math 110—Fina1 Exam December 2006 15. Vince’s Video Games must pay $450 each for a Sony PlayStation3 system (PS3). The game
store’s monthly ﬁxed costs associated with this system are $1950.
a. [4 points] Express Vince’s cost, C, in terms of x, the number of PS‘3 systems Vince buys
each month. ' C : Llsz + Meg). a». a» / b. [3 points] Vince sells each PS3 for $600. Express Vince’s revenue, R, in terms of x, the
number of PS3 systems sold per month.
C519 R =— 000 x c. [4 points] How many PS3 systems must Vince buy and sell each month to break—even? 16. [6 points] Will’s Wreaths has found that they can sell 120 wreaths at $12 each, but only 15
wreaths for $27 each. What is the linear demand equation for Will’s wreaths? (Letx = $price, and y équanﬁty.)
520: /Q/*?) +' 5 (ll/no) .
(29‘1’s>~ L: 20$;
m : /S ’/20 ,. —/05 “‘“””""”“"""”W"“ W
m 7,—  : 7 )( + 209/
w we» a W wwwwwwwwwwwww J; Round to the nearest unit.
R:C , 0, P‘: o_
\ , .. 5 z
W‘Y (000“ : L/Sox 1imsom . /SO;( /7 O O.
A “507 = 1980
_ A ._ a «X : /5‘
' at. =‘ LB, Page 9 of 10 Math 110 Name: Section: 17. The following table shows the average amount per person, spent on holiday gifts each year. Year 1970 1975 1980 1985 1990 19952000 2002'
AmountSpentin$ 80 100 130 200 210 300 500 [3 points] Find the leastsquares, “bestﬁt? line for this data Round all values to 0.001.
Let x = the number of years since 1970, and y = the average amount spent. y=/3,858x 4/9569?! a. fir y = 3.35:8” 7r — 9?: S’ ’2. 100
[3 points] What is the y  intercept of the model found in part (a) an___d speciﬁcally what does
this represent in terms of this model? @. y F]. 98 I b. H _R "W? ._ _ c. [3 points] What is the slope of the model found in part (a), and what does it represent in terms of this model?
6;, m : /3, 35 8 7% average spa/VF InCl‘ﬂWo by $/3IX? Fir ymr" on: an. d. [3 points] According to the model found in part (a,) what will be the average'amount spent
on holiday gifts per person in 2015? Round to the nearest cent. ‘ ‘ 09 y: mass/95) “2‘56” xxx: #5, QED. 909/, 29/. Page 10 of 10 Math 110 — Final Exam December 2006 18. The number ofpoinSettias sold each day at a local nursery during the ﬁrst 10 days of December
was recorded. The results are as follOws: 22, 45, 64, 8, 9, 33, 38, 45, 58, 65. a. [2 points] Create a stemandleaf plot of the number of poinsettias sold per day. I (~ 5h" " I Pl" 940% M\&“&J¢:/) \ 12
33/8
45/5
$3 (g L] , S.
b. [2 points] What is the mean number of poinsettias sold per day? Round to the nearest unit.
ZZ+4IS>+'~+GS 38? .— .—
. /0 i l 0 c. [2 points] What is the median number of omsetﬁas sold per day? Round to the nearest unit.
{,9 8/1, a z, 631/354 ..... :3} <1 5/ 6*? r “I w 19. [12 points] Model the following situation, DO, NOT GRAPH and DO NOT SOLVE. Terry’s Toys produces two types of rocking horses; Classic and Modern. Each Classic
horse requires 1 hour of cutting, 2 hours of painting and 0.5 heurs of ﬁnishing. Each Modern
horse requires 0.75 hours of cutting, 2.2 hours of painting and 0.2 hours of ﬁnishing. Terry has 40
hours available for cutting, 75 hours available for painting and 30 hours available for ﬁnishing. "
Due to demand, Terry must produce at least twice as many Classic horses as Modern horses. If ‘
each Classic horse gives Terry $12 proﬁt, and each Modern horse gives Terry $10 proﬁt, how
many horses of each type should Terry produce to maximize the proﬁt? 387 Clearly variables, objecﬁVe and constraints. ‘ x: if C/Msic\@‘ ‘ O‘cwd‘wi ‘ 'N
‘ r ' . s: 90
i ‘ ‘ i mam/Wye. i X + ’18 y a » 61!?
4M 0 2x +21),  ?f> C“
x X ,.  ’7’ )1 H 7 4 o ‘
cuﬁa23"’““:“ is 40 0.3% + 0.2y — 3m
laws 2 1,7. 75 ‘ X 3 2), ﬁHQl’TmJ‘ 0,3 0,2. 30, ~ _ X >0 
y 20 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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