Exam_solutions_1_A

Exam_solutions_1_A - Name E: 2 Section Math 110, EXAM 1A,...

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Unformatted text preview: Name E: 2 Section Math 110, EXAM 1A, 2/20/04 Show All Work! For Problem #5, round answers to 3 decimal places. (3) 1a.Find the slope of the line through the points (-3, 6) and (2,-1). m=‘/2*Y' wl—(o .— W = ’7' t -— , X2.“‘X\ 2.4%) 5 \ Li 0;» ® ® (6)b. Find the x and y-intercepts of -2x — 3y = 17. 56+ X=O ® 36+ y=o "3y = 1?- ‘Zx =1?- y—intercept 49/3 = “5"”?- x—interceptw - np/i :" 8'5 @ (3)c. Find an equation of the line passing Frl ough (12,9) and parallel to the line y = -17. W @ (3)d. Find an equation of the vertical line through (39,51). x=3<1 2. The number of annual sales of new, in-ground swimming pools in the United States increased from 125 thousand in 1997 to 155 thousand in 2001. (10)a. Find a linear model for the number y, of sales of in-ground swimming pools in the year x, with x = 0 corresponding to 2000. WWW (29 y:7,$x+I‘-FL5 \(t’ac. . V 5 6—5125) (v55) 30 _ m: = ’_ 73 If‘(~’3) Li" y = 7.5 x + lo 1S8 < $30) + b a. b = “+711 5 @ (4)b. Use your model to predict the number of in—ground-pool sales in 2010. 20m -"'> X = ’0 QB y=7,s(\o> +I‘+'+.S @ = 222.5 vikuJSomL @ 3. Barbara’s Bonnets sells straw hats for $5.00 each. It costs Barbara $1.50 to produce each hat and $7000 per month in fixed costs. (4) a. Find the linear equation for total cost, C, in terms of x, the number of hats produced. C = [.5x 1' 71300 (2)b. Find the linear equation for revenue, R, in terms of x, the number of hats sold. ‘2:- 5x @ (4)c. How many hats must be produced and sold to break-even? Rag @ Sx=~ LSX 4 =,Looo ® 3.5x: r000 hacks. {S X = 1000 (4)d. What is Barbara’s profit (loss) if she produces and sells 2600 hats? Wm l3 = rz—c Vii?) : 5(21900) —-(.|.s (moo) + qooo) ZS® = fi. 2 l 00 (12)4. Solve the following systems of linear equations algebraically. If there is no solution, so state. a. 2x+3y=l3 *3 b. 2x+y==5 3x+5y=23 “-1 -10x=5y-25 2 @ Zx + y = 5 (as 5) “'3‘, ~[0x-6>,=—Z$ GI) »"l0X «My~ = “'le -yz—q /0x+5yé2'> w? @ 0=O MANY Selecth @ -x=~Lr (29 (x, 5-220, 5.The following table shows the number of spring bouquets sold at varying prices. ‘ \ E ( x \V Price (in $) 7 5 20 6 2 9 8 21 Number of Bouquets Sold 15 18 3 14 30 12 14 2 (5)a. Create a stem-and-leaf plot of the number of bouquets sold. 0 3.7— l 5J8/4121L+ ‘ E 2. a“; ‘ 3 O gr (twig-levies? (5)b. What is the median of the prices? 2,5, LNG“)? 9, 2° 2/ ‘ Q; i 7* 3 == 7, 5 (5)c. What is the mean of the number of bouquets sold? IS+ 8 + I +2. I 4- 4 _: fl = ,8, _ 3’ ,t ‘ b V n, , E s. (5)d. Using least—squares egression, find the best-fit-lime data (let x be price, ybe number of bouquets sold). - ‘ S, __: mlcymp+ 2 23”“) -. \[fi’L/ss + 2 53 Gin-1E)- Line. X 7 (4)e. According to the model found in part (d) how many more (fewer) bouquets can you expect to sell if you increase the price by one dollar? Bird” ‘ib Se.// /./55 (about /) 4" R’W‘f/L b n+3. .___... W76 @ (4)f. According to the model found in part (d), how many bouquets would you expect to sell if they are Juiced at $10 each? ’79 X=Io é}; \/=—I,ISS(l0) +2435? == V5.10? ‘3 \. A bowl” '3 UC‘l’S. (4)g. According to the model found in part (d), at what price per bouquet would you expect to sell 20 bouquets? @ yzzo @ }’ 20= 4.75"» am?“ '4,758= —-/./SS)< Q}; X: $4.12. (13) 6. Donna is ordering sandwich platters and dessert platters for her dorm’s leap-year party. Each sandwich platter costs $18.50 and each dessert platter costs $12.75. Donna has ordered 3 times as many sandwich platters as dessert platters. If Donna spent a total of $887.25 on her order, how many platters of each type did she buy? (Define variable(s), set up equation(s) and solve.) X = 4* Sandwich WWW“ y: it. cles>ger+ FM‘Afl’S ‘ @ ISLE>OX 4» 12.315, = 8851,25 69 X :3)! '5 13.50 (3y) 4— lZ,?Sy = 8851,25 ® @825 y = 8831,23 3 @ V 3’3 pans) ‘ :3? 36} SWdMndq Phi-{’6 m7 dCSSer-i— Phi-“PS. HONOR PLEDGE: I pledge on my honor that l have not given or received any unauthorized assistance on this examination or assignment. Please write the exact wording of the pledge, followed by your signature, in the space below: Signature ...
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Exam_solutions_1_A - Name E: 2 Section Math 110, EXAM 1A,...

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