Math 1313 Final Exam Review

Transcription

1 Mth 33 Fl m Revew. The e Compy stlled ew mhe oe of ts ftores t ost of $0,000. The mhe s depreted lerly over 0 yers wth srp vlue of $,000. Fd the vlue of the mhe fter 5 yers.. mufturer hs mothly fed ost of $00 d produto ost of $.50 for eh ut produed. The produt sells for $0 per ut.. Wht s the ost futo? C F. Wht s the reveue futo? R s. Wht s the proft futo? The fd the proft loss f 300 uts re produed d sold. R C d. Wht s the rek- eve pot? Mth 33 Fl m Revew

2 3. Solve usg the Guss-Jord lmto roess. y3z 0 yz 0 4y5z 7 4. The followg mtr row redued form. Gve the soluto, f t ests to the system of equtos: Solve for d the Mtr equto d Fd the trspose of mtr Mth 33 Fl m Revew

3 Let d 0. Fd Fd the verse of the mtr 4 6 d If d D d 0 the. d D 9. veyrd produes two spel wes whte d red. ottle of the whte we requres 4 pouds of grpes d oe hour of proessg tme. ottle of red we requres 5 pouds of grpes d hours of proessg tme. The veyrd hs t most,98 pouds of grpes d llot t most 60 hours of proessg tme to the produto of these wes. ottle of the whte we mkes $.00 proft, whle ottle of the red wes mkes $0.00 proft. The ompy wshes to mmze ther proft. Set-up the ler progrmmg prolem. Mth 33 Fl m Revew 3

4 0. Mmze the followg Ler rogrmmg rolem: M = 3 + y s.t. +3 y +y 8 0 y 0 Step : Grph the fesle set. 3y y 8 Step : Fd the orer pots of the fesle set. 3y y 8 Step 3: Fd where the optml soluto ours d the optml vlue. Corer ots M = 3 + y Mth 33 Fl m Revew 4

5 . Dve vested sum of moey 3 yers go svgs out tht hs se pd terest t the rte of 4.5% per yer ompouded mothly. Hs vestmet s ow worth $5,7.4. How muh dd he orglly vest? Idetfy the prolem.. Steve ought r for $30,000. He put dow 0% d fed the le. Hs k hrged hm 5% ompouded mothly for 5 yers. Wht s the mothly pymet? Idetfy the prolem. 3. Gry deded to sve some moey for hs dughter s ollege eduto. He deded to sve $300 per qurter. Hs redt uo pys 4.5% per yer ompouded qurterly. How muh moey wll he hve vlle whe hs dughter strts ollege 0 yers? Idetfy the prolem. 4. Mke pys $300 per moth for 4 yers for r, mkg o dow pymet. If the lo orrowed osts 7% per yer ompouded mothly, wht ws the orgl ost of the r? 5. wts to hve $5,000 sved whe she grdutes from ollege so tht she wll hve dow pymet for ew r. Her redt uo pys 5% ul terest ompouded mothly. How muh moey should she depost eh moth to hve the moey vlle whe she grdutes 3 yers? Mth 33 Fl m Revew 5

6 6. George deded to depost $4,000 to py for ruse he pls to tke yers. Hs k pys 3.5% ul terest ompouded semully. How muh wll he hve ths out t the ed of two yers? 7. Gve the Ve Dgrm, fd:. [ C ] =. [ ] = 8. I group of 300 hudred studets, 5 re tkg mth lss, 75 re tkg hstory lss, d 70 re tkg oth lsses. How my studets ths group re tkg mth lss oly? Mth 33 Fl m Revew 6

7 9. survey of 500 people ws tke to determe ther preferee s soft drks. Of the 500 people surveyed, 33 lke Coke, 7 lke eps, 78 lke RC, 44 lke Coke d eps, 07 lke eps d RC, 8 lke Coke d RC, d 38 lke ll three types of soft drks. How my people surveyed lke Coke, ut ot eps or RC? 0. I how my wys 6 hoored guests e seted 6 hrs o oe sde of the hed tle?. I how my wys presdet, ve presdet, seretry, d tresurer e seleted from orgzto of 0 memers?. You re gog to mke serl umer whh must ot 3 dgts d letters. The dgt 0 ot e the frst dgt. Nether dgts or letters my repet. How my serls umers re possle? 3. o s tossed 0 tmes. I how my outomes do etly 0 tls our? 4. orgzto of 4 me d 6 wome eeds to mkeup fudrsg ommttee. I how my wys the fudrsg ommttee e formed t t s to ot 5 me d 3 wome? Mth 33 Fl m Revew 7

8 5. smple of 7 fuses s drw from lot otg 5 fuses of whh 5 re defetve.. Fd the prolty tht t lest oe fuse s defetve.. Fd the prolty tht t lest 4 re defetve. 6. Let d F e evets of smple spe S. Let =0.69, F = 0.36 d F = 0.5. Fd F. 7. Compes,, d C produe 0%, 40% d 50%, respetvely, of ert lultor. Reords dte tht % of the lultors produed t Compy re foud to e defetve, ½ % of those produed t Compy re foud to e defetve, d % of those produed t Compy C re foud to e defetve. lultor s hose t rdom. Wht s the prolty tht the lultor s defetve? Mth 33 Fl m Revew 8

9 8. Ur I ots 3 red d 4 whte mrles d Ur II ots 5 red d whte mrles. ur hose, wth eh eqully lkely to e hose, the mrle s drw from the hose ur. Fd the followg prolty tht Ur I ws seleted, gve tht red mrle ws hose? 9. The prolty dstruto for rdom vrle s gve elow: = Clulte the epeted vlue. p p p 30. Cosder the followg oml epermet. The prolty tht ew employee t mufturg plt s stll employed fter oe yer s 0.9. Seve people hve reetly ee hred y the ompy. C p q,. Wht s the prolty tht t most of these ew employees wll stll e employed fter oe yer?. Clulte the me, vre d stdrd devto of ew employees tht wll stll e employed fter oe yer? p Vr pq pq Mth 33 Fl m Revew 9

10 3. Let Z s the stdrd orml rdom vrle. Clulte.. Z 0.9. Z.4 3. Let Z s the stdrd orml rdom vrle. Fd the vlue of z f:. Z < z = Z > z = Use the orml dstruto to ppromte the followg oml dstruto. Cosder rdom smple of 00 drvers o terstte 0 Tes, where 9% of the drvers eeed the 70 mph speed lmt.. Fd the prolty tht fewer th 40 drvers eeed the speed lmt.. Fd the prolty tht etwee 30 d 40 drvers, lusve, eeed the speed lmt. Mth 33 Fl m Revew 0

11 Mth 33 Fl m Revew Formuls to e rovded o the Fl m Z-tle wll lso e provded y y m m y y m y F C s R C R. the 0 d If d D d D d I r t F rt m r mt F F F F 3...! 0! =!!, r r!!!, r r r C F F F

12 Mth 33 Fl m Revew S for d depedet.... where. p p p p p p Vr Vr k k k q p C, q p p pq Vr pq z Z z z Z Z Z Z