DOC111510

DOC111510 - M GP 11 06 Finite Math Review 3< L U H 0 Prof...

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Unformatted text preview: M GP 11 06 Finite Math Review # 3 ,. ;_<__ L U H 0 Prof. Nicoli —Suco $16 “*“In addition to this review, I recommend that you attend all classes, complete and review all homework assignments, and take any steps you consider necessary for yourself to succeed in the course. Find the mean for the list of numbers. Round to the nearest tenth. 1) 73,43,73,95,43 133 4’ “(3+73 1L atri’q's ; 7:} nfl Answer: 65.4 S 5 2) 15,13,6,10,8,1,6 KW (13 4/9 ”" [0* g + { *é‘ : S‘l DELLA—.— w#—«"W W Answer: 8.4 ‘9' 9V 3) 16,6,27,16 (Lgka 91+” 6( ‘ 3L Answer: 16.3 (.1 L1 Find the mean for the frequency distribution. Round to the nearest tenth. 4) ' 4) Value Frequency \(0 C74} —\/ \’l (D) 4’ 71.1 U7") + La (“3" J.— 3 37b) 16 2 17 10 24 12 29 11 35 6 - \Om ,/ ’2 u, 3 S /‘ Answer: 24.9 q t 5) Value Frequency (C03L'L) A" 95%6.) +11°6U+3I3MJ 163 207 220 313 347 OJHBNONN Answer: 253.0 _}_§__ 6) 6) Value Frequency 16 18 23 27 33 4O Hmwpuap—n Answer: 25.0 7) 7) arm, Value Frequency k 133 193 237 279 366 372 NM ‘ (Y M «M NUJLHOJVFH Answer: 269.6 2?. (a Value Frequency 5r 1’ 8) W n- 8) 13 18 23 28 33 009me Answer: 23.6 Find the median. S 9) 9,1,28,15,21,44,40,30 ‘ \q‘l§)u‘1%'3b)qolwq 9) Answer: 24.5 3-! +er 7 10) 456, 1,4,/ 24, 3% 371 99 l 10) 2L— 58’ 11) 7% 910’ 11) Answer: 58 12) 5,2,26,16,50,41,35 M7 4/ 36¢, 12) L Answer: 26 lswms, 23,23,510 23,2 3” 7 13) Answer: 24 7/ Find the mode or modes. F 14) ____W 14) 5, 9, 35, 3, 2, 8, 77, 1, 4, 16 Answer: No mode 15) L Answer. 26 16.41, 7.5.88, 7.99, 7.62 16) Answer: 7.25 Find the range for the set of data numbers. (IQ 17) 23, 31, 11, 48, 57 3’ ’71, /1( .7 (46 17) Answer: 46 /£ 18) 18) 8, 19,4, 14, 9 /(/(/f e ( §/ Answer: 15 19) 113, 556, 130, 659, 421, 261 é S? ’ H 3 .' Answer: 546 Find the standard deviation. 20) Lm/lmsflafiz 17, 9, 8, 19 : (o 9.» Answer: 3.5 21) won/11, 14,8, 194, 213, 269 “MK 21) SMOM x 534 Answer: 58.4 W 1— Z/ozlfi I 2(X — 292.1) a Y] a 0' g 8 22)6&34,86,46,4&z€7ms,§a 22) $11.06;?me Answer: 21.1 W :- (ja'q : ggqg' = ’7: Ci \l 3 23) V15 [email protected]<{J97%12 23919553 Q: 3.? Answer: 3.7 lg: ‘ I: fl! 9c ‘ (g 1 W; 0\ \J as Solve the problem. 0 . ‘ ’7‘] 7 /o 24) Fmd the percent of the area under the standard normal curve between 2 = 1.41 and 24) _____.._ z=2-83- f“ l,‘// —> .7309- / \ x .119 :4. H10? ; ,0??: 77% Answer: 7.7% 9' <33 .9 A“: #:2— ml My 25) 26.7% 25) Find the percent of the area under the standard normal curve between z = 0.54 and z=1.91. 5%,) .5057; Answer: 26.7% SHIN //9,,_> 'quc/q ,qu’lfi -— “Q 0541': -2665 : 6, 26) Find the percent of the area under the standard normal curve between 2 = -2.36 and 26) __q.—_3_'_S__/'7_. z=-0.14. 2.24 —~> 9 490? \ Answer: 43.5% 4‘1707~ ’Om: Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 3 2 A, 27) A machine produces bolts with an average diameter of .30 inches and a standard 27) deviation of .01 inches. What is the probability that a bolt will have a diameter greater than .32 inches? PCX> .375 .37, —,'5D ’ .01» , L :_ ,0\ Answer: 7L1 mm) = . 57- 5047,; .0293; 23% 110 .37, | L 28) The mean clotting time of blood is 7.35 seconds, with a standard deviation of .35 seconds. 28) What is the probability that blood clotting time will be less than 7 seconds? Answer: 16% i E 337%; "95;; «‘ 4/;ch ’7'” PL X42): .s_,3ws c .152} >l§«7°7° 6 29) The average size of the fish in a lake is 11.4 inches, with a standard deviation of 3.2 inches. 29) AT 0 Find the probability of catching a fish longer than 17 inches. ‘\ Answer: 4% \ l7 ' “"4 : 53,13 3 ( a) . ‘4 H ‘4 \a .2 3 3’7" 3 ’2 ‘ o I’CK >1?) = -3 -.‘1S"I‘i : 4W” ’- 7'04 30) A certain grade egg must weigh at least 2.5 oz. If the average weight of an egg is 1.5 oz, 30) with a standard deviation of .4 oz, how many eggs in a sample of 9 dozen would you expect to be over g. i. 3 :2- g...‘ . g“ '0 the2.5025ize? ————"—‘ LL? “ 2's— > \.5 L: a Li I - ,Lf‘fly: . €069. : o6 7° ch>a5>=5 A, I,“ . N ‘1 new» flat): U0? OCQol-B : [03“ ,DbQ'L : oééflé 6% 0/ 31) The me montHly income of train at a local mill is $1100 with a standard deviation of 31) i a $150. Find the probability that a trainee earns less than $900 a month. Pam) :, 5:91:32 9m - “00 -Mo _, — L1. . I #33 «3 , Wm An 29% E f g '- F ' ‘ SW61' ’2' -’ 3 1 =’ 7.13%: 5‘0 [too Answer: 1 egg Solve the equations: 32)21t+4=12t+10 91tqr1: 32) 2 ta 2/3 Answer: 3 'i It ’ bl ‘Hrv g 1573 Q 3' a, ‘\ ‘1 3 W .. s, MN.~W‘—__WMN_~M_” _“~~_~H.‘¥n‘www¢‘.fl. ....i— —' “"’ ‘7‘ "mfln'flufi\ l ‘Rq flofimlh“: ' ‘Mzwu‘q»\‘ 33)31b+15=11b a”? MS: {a 33)_,4_2;7Z¢p__ — ' 3 ( Answer: -% [0 (O L: : - b- ’ ’ Z ‘7‘, ’20 a ‘7 w m ‘ A v, M... Ma“ an...“ 34)4(y+5)=5(y-6) (y‘LJOCMS 34)_5t'4§_Q_ 317’ 7 7 Answer: 50 35)5(2z-3)=9(z+4) Log—K; a +1, 35) %:-S’( ,qck 448/ 7.. Answer: 51 z 3 8’ - - . - :5 36Q'72L4) 2? 3P “ 32 36) _?:_____°- 1' - 7" "Si-L 3‘: “EL Answer: —32 X x/\ co . 37)r;6=r;8 E QCN/o)¢ r+$ (4 37)_£;Ef.__ , I Q A Q P21“ If“ (‘ Answer: —4 —r r f): 4/) {HMLX 3:8{18 =1+A>6quryu) 38) >(:”/L/J x-4 x+4 ' ______..— (?(x+‘4):(><m3(>c«w) A» leVJt/t) o Sk—‘Zr2x— /6d’ Answer: 12,-14 “flu/Tl : X;_ Hp +70 K,g/O OI’OWL/qxxrnj fl, wry»--w—M‘”’“““’" I ye-fr'?’ I ‘- XL + 7-D); r 67(0 X 47,90 2 e , - L flax .72 W»? - M y+ 3 =% “J _“M_4WMM~_ fl“; 5 "Q : 3 a 3 Answer: -6 +3) 3 (23+ (0 — “‘33 M i U (‘v5 , - j? *6 I M 3_7\C/;< :( «J; , x;- 40 l—X—ZJ ‘ \ 40) a .«e =7>< ~-~—- Answer: -2 y L _b( k ;X )(_‘_—L 2 Max 5—a 3 7 b - . —=— Cl ‘7 “ u E “(a +4 a)! H(Sw)+3a’39 ale—ma? 4” 'L0 '20 Answer—8 lo'L/q434; 2? 1:9 4;,3 r, :7 W6 3 LL I ~ 9&7“) y) PM 39(qu Zq, x 42) X"? 1k ~7y Answer: 24 2 t t: Z G 43 Tube) (Jug/(23(2) c 43)———L— Answer: 2,6 '7’762, 0 , t2, ?6 H1 Graph the linear equation. 44) 2y=x+8 44) 45) ______ Answer: 46) 2y+8x=—2 CZfiyygfz ,7, 46) Find the x-intercepts and y—intercepts of the graph of the equation. 47)x+y=5 (“398V M o ; 5 47) Answer: x-intercept: 5; y-intercept: 5 48)x+y=-7 Answer: x-intercept: -7; y-intercept: -7 49) 2x+y=10 Answer: x—intercept: 5; y-intercept: 10 50) -2x+y=2 Answer: x- intercept: - 1; y— intercept: 2 Find the slope of the line, if it is defined. X24 “K \ 51) Through (7, -3) and (9, -5) 51) _;l____ An . 1 " 6* 'L 3 ; CE" 2: ’( swer. — q a 1 Z 52 Thr h —9,- -9, ' UNDEFINED ) oug ( 3) and( 5) +r~5 ' 1 : LRUQ£WJ 52) _________ Answer: Undefined ,4, f. r 1 O 53) Through the origin and (—2, 6) Q, r o .g g g f 3 53) _ "i _ Answer: —3 V 7 '0 fl 2 I “4/ 4_( '2 A 3 a ’ ” 54) Through (-9, —5) and (-6, 9) Ci 4 —l S \ k4 54) __ 3 2 I” "' ’7' Answer: 45 a V Q ++ q 3 Find the slope and the y—intercept of the line. ‘ q 2 3 55)4x+5y=23 U‘fiq/ 33:13 55) E 4 23 ~ M Y — W V Answer:rn=——~;b=— ‘ ,My 7? 5 5 in: ,qy+33 3: j, +~ fflw ooooooo N s r r , m mm » anwmwmw wwwww W ,,,,,,,, K at L :L 7. 56)4x-5y=22 56)_7"2_/__5'_'> 3—‘- . _ 4 _ 22 H X ' $ \) ’t " I Answer.m—g,b—-—5—— «(4% HM); ' ‘EECALW*EF ormmwm ,/,#—~\\2____k~wm _; :? <r’ «FM Wwoo ~ ’—*“ , ,‘ 57) -4y= —2x — 22 N ~~ ~—«--~m~»w«~*"’” 57) M“ L 9 3 7? An 1.b 11 J43’ 23141 5W“ “‘7' ‘7 «T "4 "W H , J f 9 “ 1x "1’ Decide whether the pair of lines is parallel, perpendicular, or neither. 58)3x-6y=—13 3x/chyls fivgjxqj {Vi} lit/3 58) per “a” 18x+9y=9 “3% “l /(I /(, Q, L (JO Answer: Perpendicular / 6 M7j 7; ‘7 9 9 46526 % 7 WV 7/ 0M ' 2,( bppt5l maogm$ ' W and A / x I ‘7 7 7 MMWWW “”‘\\~«Rg a :rzx +7 lfwwwwworwrwww \ 3X - = 8 kmnxm“\\\ J m T; ' L If, aha/w 32x+ 12y: -1o fl pppppp X as ——m— Answer: Perpendicular 0?: 9 " g 3 ¥“ ‘6 m; "’8! 7 g (9 K Jr Kj 7 C V’IO 3/ 10 fi v? P. ch/flonéf) 312M473 / ’33\’ “i {13(09 m / / ‘3 AL I ‘1 ‘1 ‘1 60)12x+4y=16 * 3f 3 60) p461 “cl = - XL 4’ . 5 9 / Answer: Parallel 8/ 5 61) The hne through (3, —5) and (—1, 7) and the hue through (6, -13) and (-2, 11) 61) ._ .____ Answer: Parallel m: 7’7C: \l’ err} m; \l"\3 52—5- ‘3 ’ P3 ' l ’7, ~49 v r * 62) 62) The line through (-20, 5) and (-4, 7) and the line through (-5, 5) and (7, 4) Answer: Neithermjr v .2;— “— «L m —/ 445g .:_ “I “(~00 lb 5 VHS, AIL Find an equation of the the line satisfying the given conditions. . "1~ oCx-z) +120 -4 ,- 63) Through (2, -9);m = 0 3 r ’ 3 _, 63) _- Answer: y = —9 64) Through(0,5);m=% 5—5 3 £504) 7(3)- 3': Answer: —8x + 9y = 45 65) Through (o, 2);m= —% 3 —& Answer: 7x + By = 16 lw 66) X: 66) Through (4, -3); undefined slope-51> V‘Qf‘l‘i“, Answer: x = 4 67)<9,0)and<1,5) W W A 3—0: —;(x-e) 67) S—MEQAS" Answer: 5x+8y=45 («7 ’3’ Q - '5- b‘r- 8 3' FX 1"}, 68)(—1,10)and(—1,-4) 53 "SA/t“f 68) x;- Answer:x=-1 “Iv-(O ‘ 7, ‘__—.——-—~ ’7, I ‘ ‘ m _, : (ll/\d s.) / I'M-é, 11 69) (-3, 4) and (5, 4) my k“l “’l a ,2)— ; 0 anoeifil RN” 69) é————:L{ <73 Answer: y = 4 5—H Find an e uation of the the line satis 'n the 'ven conditions. A ‘1 f” g‘ A, +8 -2778 4XX3=’15' 70) Through (—7, —6); perpendicular to -8x — 9y = 2 ~—) W‘ Z "’3‘ ’ :fi— “(q ( c7 70) Answer: 9x — 8y = -15 Peflwjfl‘iv M =3 r. g N 6 8 5—40 = %(xr9) :> ’53 +9: 132$ tug? :gf «if-ix +63 S '3 3 71) Through (-7, 9) and vertical 1) ‘ 9 j 71) X z " ? Answer: x=-7 3? 72) Through (3, —4); perpendicular to 5x — 8y = -17 ' 59’8‘33‘47 (5% t :5? 72) 8 x4“; :Lf Answer28x+5y=4 RfewnM=Tg~ 59§X+g you»; ,. -q :32(x :5) a, mix +2.9 V 5 ’5 W ’5 3‘ steamer Solve the problem. +3; 3 10 “king #10 D 73) The bank's temperature display shows that it is 23° Celsius. What is the temperature in 73) _—Z_2:_{__ Meme“? F > 3g «L W 1 6103) +3L : 4/14. 1‘ 32 Answer: 73.4° Kr . . . . . _ 2%0’0 74) Suppose the sales of a partlcular brand of apphance satisfy the relatlonshlp S(x) — 100x 74) ________ + 800, where S(x) represents the number of sales in year x, with x = 0 corresponding to‘ 1982. Find the number of sales in 1998. h fig 3» X -,~ be ( hag ~( an) Answer=24°° gm): 100w) MW: [0617 +800 75) =HI +62% 75) Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $9000 in 1982 and 64,500 in 1987. Let 44x = 0 repr3sent 1982. Find the equation giving yearly sales S(x).( O ’ ‘3 000) (3) G ‘6 5.019 __ a 00° _: H, “300; Answe“ 50‘) = “'1me Mm ’ €000 : Wu 1 N, [no 9' 7m : H, (W \fl'n“+ j.“ (9 5 as» (5(00X +700 Solve and graph the inequality and graph the solution. 76)a+3<10 91113“? 0.47. 76) g ’01; 0787(ou firmj?) Answer: (— co, 7) 891011121314 01234567 12 77)8x-729x—16 ‘CgK/ELZ‘W”! 77)’ac 9 WM qf‘QQSfiIOHVLI) Xefi Answer: (—oo, 9] 2345678910111213141516 Solve the system of two equations in two variables. 7%(;(+9y=12)r(0 /(a «$43 :’?L )c +701): )0? 78) a) / x+8y=-20 \é" zrkgl I «M Answer: (-6, 2) —' L/ 6:} .J 4/ J" x ’ ‘1 (Q X g I i 3"” . er 9 z 79) 4x + 6y = 5 3 ’3 3 79) infigwh Sp! Jim/‘5 12x+18y=15 dlewfl c, "3' Answer: [- %y + 751—, y] for any real number y '5’ o a a 80) A10 313(979‘5)”. 9x—6y=8 ’J’SF 8, .. Oeri Answer: No solution o +b 7 ‘4 LE, an‘awhmw / Z + 285;: UL y 4(4) = ’“9 8mm— 7 7x-3y=-12 733$,(Z X-‘ 1462 Answer: (0,4) g 5 “Lo 9 7 L/ k 4’! 9 2 u’ a 0 Multifgiy both sides of each equation by a common denominator to eliminate the fractions. Then solve the s stem. ( V ’2[ D éézé'%=-18>(0 ’23,; —-,‘08)(/( ?:,L{3L 32) 3 ~35+ZX=_9 >30 97x 7V0? : £ch 37x 4’j=~32q .4 9 ’ V I (fix =7sé Answer: (— 12, 0) a 6 3 X:’/L 13 Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z. G 8/ 1' " 3 ) l ’3 ‘3 83) x+ y+ Z: 4 now—3 JR +3}=\(O aficiagb‘ 83) )3 x—y+ 22:12 “who; —.—.’.u4)~( ’ ‘ ' 3x+y+ 2:127“ “7"‘2’8 j +E=O 3(4)!» alto K: "i 3 “he Answer: (4, —2.67, 2.67) g+ 34:11,, by, M3 ; .114 3b? (A + 3+ “3/3 v L03 Z4:- i‘; WWW A #7 A 1~~~A<~>-ex 3/? )2 + ‘53.r 8‘: V34 3 3 r A ¥ v. \ ’ mow/.- _ 84) X+ y + Z = '4 5 “Do \\ ~ V“WWW(WWWMM_W__“WWW,”WNWW-.. 84) C ‘ 4 _ X—y+2z=-6 9~[+?5~?:"-‘i0 . 3X43 $40 4x+y+ “45”” «\’9x +3} =—q—y\ ~51- 4:,53r QM) (Sic—u) Answer: (1, —1, -4) .. ' 2+3%-—\o fl::"+r3 f: ::-”i /———’—\ 3 3. 4 A2. W M y mwwwwwww v m“ _ 85)(x—y+22=-1A7' 33/(432’3’43’ 85) {OJ’ZI‘SD 3x +z=—3 r ' AX“ 2+q%2-% ' - = V- x+2y+z=—7 ¥+ +2: =_q_ Ling—“LL72— §X+C'3)="3 Answer: (0, —2, —3) ’ 5:1? {5:3 5' 7? : '3 3 x5? 733 «\Kfix + :2; = ’3)'\ 33,40 W D WWW-mm» W“ ~ 3-61-4 - -7. _ - 86) X ' y + Z: ‘3) m away «Mm- ' -WEI;,W,W«my—W‘””” saw“ 3 o<x+y+zj 5 a”: f .1023 «rag 1; W X+y_z__1 '1 :2 v”\ta%:1_ —2,4r‘3+3’5 . _ X a .1 Answer. ( 2,4,3) L 9:}, 9% g 4/" C 5 m ~ WMNWMM “3: a 21er My, 4 WWW-M 87) x + 2y + 4z = 16 MW“ 87) / , 5y+4 =124 33+ my?! 531+ WW Sg;to 3:4 Z = N100 “((0:76 H 8+Lr:»l® H 12sz “.5; Answer: (4,4, 1) ~51 “(L Solve the problem. 88) What—is file size of the matrix? 88) Z X 3 '4 6 52] 2m; x 3 Lawns -4 -8 1 Answer: 2 x 3 89) EL. 89) What is he size of the matrix? 7/"> 1 HM w; mm; Answer:1x4 14 Perform the i ' o eration where possible. —7 1 6 2 Ex ’5 0 9 ) [ 2 5 ‘ 1 ] ,5 q 90) _______— V Answer: —1 3 3 7 -2 ] Wit db LJIL & a‘é W T Lblvwws ____————- 91)[34]+[ 9 Answer: Not defined [—fi] ’3 92) 0 4 ' 74 a '1’ O 92)_————— 6—4 32 3 40 Answer: ’ 2» t 3 93) __'___.__— 7; 94) _____.. l5 ’l0 "S Perform the indicated operation. 95) LetA = [ '3 i Find 4A 95) ________ Answer: H .3 ’ J—VL ['12:] M L 15 96)LetB=[-136-3]. Find-43 *'((\ -’S (a —3] : [,4 ‘2 —Z.l( a] 96) Answer: [4 -12 -24 12 ] [ 4] 1 ( L‘ ,. Z 97) Let C = -2 - Find [—] C. ’7, ’7’ W -\ 97) _______ e 2 1’2, 12 (9 Answer: 98)LetA= 23 andB= 04 . Find4A+B. 1+ 2,3 + o “ 9s)____ -16 lg V‘ c.) W332] $011393] 9 [3? £23] 3 .FindC-3D. ‘ _ z " 99)___— -2 ‘3 3‘ L - 99)LetC=[_3 Answer: 100)LetA=[-12]andB=[10]. Find2A+73B. ZA>7L CH 11 1 (3191 100) Answer:[14] 38*300] p C3 0:) (224314: 0:3 : m3 Given the matrices A and B, find the matrix product AB. 101)A=[';:],B=[jg] FindAB. 2'3 0+3 101) Answer: 7* 3 £61 0+3 4‘ 2' 102)A=[g B=[j(1’] FindAB. (7 + 1 0 fig 102) Answer: [-13 'i] = [9L *2 /[0'{ 0+! '11 l Graph the linear inequality. 105') 3x + y s -5 17 103) ______ <5 "(p-IL / —8 43 O .- 0 4H0 3 l_q I1+b 104) —, 3 "5L *l a 4049 35% 9 ”<0 351 105) ...
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This note was uploaded on 03/07/2011 for the course MGF 1106 taught by Professor Nicoli-succo during the Spring '08 term at FIU.

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DOC111510 - M GP 11 06 Finite Math Review 3< L U H 0 Prof...

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