Math 167 Review for Test 4 Chapters 7, 8 & 9

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1 Math 167 Review for Tet 4 Chapter 7, 8 & 9 Vocabulary 1. A ordered pair (a, b) i a of a equatio i term of x ad y if the equatio become a true tatemet whe a i ubtituted for x ad b i ubtituted for y. 2. The of a equatio i the et of all olutio of the equatio. 3. The of a equatio i two variable i the et of poit that correpod to all olutio of the equatio. 4. The graph of a equatio of the form y = mx + b, where m ad b are cotat i a. 5. The graph of a equatio of the form y = mx + b ha (0, b). 6. If a ad b are cotat, the the graph of y = b i a ad the graph of x = a i a. 7. Suppoe that a quatity y chage teadily from y1 to y2 a a quatity x chage teadily from x1 to x2. The the of y with repect to x i the ratio of the chage i y to the chage i x, deoted by! "#! $. % " #% $ 8. A cotat rate of chage of oe variable with repect to aother implie a betwee the variable. 9. Aume (x1, y1) ad (x2, y2) are two ditict poit of a o-vertical lie. The of the lie i the rate of chage of y with repect to x. I ymbol: m =! "#! $ = )*+, % " #% $ ) A icreaig lie ha lope, a decreaig lie ha lope, a horizotal lie ha a lope equal to, ad a vertical lie ha lope. 11. The of a liear equatio i y = mx + b. 12. The of a relatio i the et of all value of the explaatory variable. 13. The of the relatio i the et of all value of the repoe variable. 14. Each member of the domai i a, ad each member of the rage i a. 15. A i a relatio i which each iput lead to exactly oe output. 16. A relatio i a fuctio if ad oly if each vertical lie iterect the graph of the relatio at o more tha oe poit. We call thi requiremet the. 17. A i a relatio whoe equatio ca be put ito the form y = mx + b where m ad b are cotat. 18. The repoe variable of a fuctio f ca be repreeted by the expreio formed by writig the explaatory variable ame withi the parethee of f( ). We call thi repreetatio. 19. For a data poit (x, y), the i y ad the (writte y0) i the value obtaied by uig a model to predict y. 20. For a give data poit (x, y), the i the differece of the oberved value of y ad the predicted value of y. (Oberved value of y - Predicted value of y = y y0 ) 21. Suppoe ome data poit are modeled by a lie. A data poit o the lie ha. A data poit above the lie ha. A data poit below the lie ha. 22. We meaure how well a lie fit ome data poit by calculatig the. 23. For a group of data poit, the i the liear fuctio with the leat um of quared reidual. It graph i called the ad it equatio i called the. 24. The i the liear regreio fuctio for a group of data poit. 25. A i a graph that compare data value of the explaatory variable with the data poit reidual.

2 26. If the lope of a regreio lie i greatly affected by the removal of a data poit, we ay the data poit i a. 27. ted to be ifluetial poit whe they are horizotally far from the other data poit. 28. The i the proportio of the variatio i the repoe variable that i explaied by the regreio lie. 29. A i a equatio that cotai two or more variable. 30. For a umber c, if a < b, the ac < bc. 31. For a umber c, if a < b, the ac > bc. 32. A i a iequality that ca be put ito a form mx + b < 0 where m ad b are cotat ad m ¹ 0. Exercie 1. Fid the y-itercept ad graph the equatio by had for y = 4x Worldwide ale of iphoe are how i the table below for the lat three moth of variou year. Year Worldwide Sale (millio) Let be worldwide iphoe ale (i millio) for the lat three moth of the year that i t year ice a. Idetify the explaatory ad repoe variable. b. Cotruct a catterplot by had. c. Graph the model = 11.6t 37.6 by had o the catterplot. Doe the lie come cloe to the data poit? d. Ue the model to etimate worldwide ale of iphoe for the lat three moth of Did you perform iterpolatio or extrapolatio? e. Compute the error i the etimatio you made i part (d). f. Ue the model to etimate worldwide ale of iphoe for the lat three moth of Did you perform iterpolatio or extrapolatio? 3. For the 60 player picked i the 2014 draft for NBA baketball, let h be the height (i iche) of a player ad let w be the weight (i poud) of a player. For height betwee 72 ad 87 iche, icluive, a reaoable model i w = 6.54h a. What i the lope? What doe it mea i thi ituatio? b. What i the w-itercept? What doe it mea i thi ituatio? c. Graph the model by had. d. Predict the weight of draft-pick Shabazz Napier, who i 6 feet tall. 4. For fall emeter 2014, part-time tudet at Ceteary College paid $575 per credit for tuitio ad paid a madatory part-time tudet fee of $15 per emeter (Source: Ceteary College). Let T be the total cot (i dollar) of tuitio ad the fee whe takig c credit of coure.

3 a. Idetify the explaatory ad repoe variable. b. Fid the lope of a liear model. What doe it mea i thi ituatio? c. Fid a equatio of the model. d. Graph the model by had. e. What wa the total oe-emeter cot of tuitio plu part-time tudet fee for 9 credit of clae? 3x For f ( x) = -2x + 5; g( x) = ; h( x) = -2x 2 + 3x, fid the followig. 4 x + 1 a. f (-4) b. f (3) c. h(2) d. h (-1) e. g (1) f. g(-2) 6. a. Fid f (-2). b. Fid f (4). c. Fid x whe f ( x) = 0. d. Fid x whe f ( x) = -1. e. Fid the domai of f. f. Fid the rage of f. 7. a. Fid f (2). b. Fid f (-4). c. Fid x whe f ( x) = 4. d. Fid x whe f ( x) = 3. e. Fid x whe f ( x) = 0. f. Fid the domai of f. g. Fid the rage of f. 8. Let be the umber of drive-i movie ite i the Uited State at t year ice The fuctio = 4.9t model the ituatio well for the period a. Rewrite the equatio = -4.9t uig the fuctio ame f. b. Fid f(3). What doe it mea i thi ituatio? c. Fid f(0). What doe it mea i thi ituatio?

4 9. The mea umber of viewer of Fox prime-time TV how wa 9.1 millio viewer i 2010 ad decreaed by about 0.8 millio viewer util 2014 (Source: Niele). Let f(t) be the mea umber (i millio) of Fox prime-time viewer at t year ice a. Fid a equatio of f. b. Fid f(3). What doe it mea i thi ituatio? c. Etimate the percetage of America who were Fox prime-time viewer i The U.S. populatio wa millio i that year. 10. Fid a equatio of the lie that ha m ad cotai (5,4). Write the equatio i lopeitercept A form. 11. Fid a equatio of the lie that cotai the two give poit. Write the equatio i lopeitercept form. Roud the lope ad the cotat term to two decimal place i eeded. a. (-5, 4) ad ( 2, 10) b. (4.5, 2.2) ad (1.2, 7.5) 12. Let E be the erollmet (i thouad of tudet) at a college t year after the college ope. Some pair of value of t ad E are lited i the table below. Age of College Erollmet (year) (thouad of tudet) t E a. Cotruct a catterplot. b. Decribe the four characteritic of the aociatio. c. Fid a equatio that decribe the aociatio betwee t ad E. d. Graph the equatio you foud i part (c) o the catterplot. e. Fid the E-itercept. What doe it mea i thi ituatio? f. What i the lope? What doe it mea i thi ituatio? 13. The price of ki retal package from Gold Medal Sport Ò are how i the table below for variou umber of day. Let p(x) be the price (i dollar) of a ki retal package for day. Number of Day Price of Package (dollar) a. Cotruct a catterplot. b. Decribe the four characteritic of the aociatio. Compute ad iterpret r a part of your aalyi. c. Graph p() = o your catterplot.

5 d. Fid p(8). What doe it mea i thi ituatio? e. Fid whe p() = 130. What doe it mea i thi ituatio? 14. A racquetball i dropped from variou height, ad the bouce height i recorded each time. Let f(x).be the bouce height (i iche) of the racquetball after it i dropped from a iitial height of x iche. Drop Height (iche) Source: J. Lehma Bouce Height (iche) a. Cotruct a catterplot. b. Fid the liear regreio equatio for f. Doe the graph of f come cloe to the data poit? c. Fid the um of quared reidual for the regreio lie. d. Fid f(18). What doe it mea i thi ituatio? e. Fid the reidual for the predictio you made i part (c). What doe it mea i thi ituatio? f. Fid x whe f(x) = 30. What doe it mea i thi ituatio? 15. Solve the formula for the pecified variable. a. x= µ + z (Solve for z) b. (Solve for ) c. (Solve for ) x = y- y1 = m( x-x1) x1 16. The price of a adult oe-day ticket to Walt Diey World wa $46 i 2000, ad it icreaed by about $3.75 per year util 2012 (Source: The Walt Diey Compay). Let p be the price (i dollar) of a ticket at t year ice a. Fid a equatio of a liear model to decribe the ituatio. b. Solve the equatio foud i part (a) for t. c. Ue the equatio foud i part (b) to etimate i which year the price of ticket were $70, $75, $80, $85, ad $ Subtitute the give value for the variable i the compoud iequality. a. x- t < µ < x+ t ; x = 26.9, t = 2.528, = 4.9, = 20 pˆ(1 - pˆ) pˆ(1 - pˆ) b. pˆ - z < p< pˆ+ z ; pˆ = 0.45, z= 1.645, = Solve the iequality. Decribe the olutio et a a iequality, i iterval otatio, ad o a graph. 1 2 a x b x <