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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 yintercepts 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, inground 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 inground 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—groundpool 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 $7000 per month in ﬁxed costs.
(4) a. Find the linear equation for total cost, C, in terms of x, the number of hats produced. C = [.5x 1' 71300 (2)b. Find the linear equation for revenue, R, in terms of x, the number of hats sold. ‘2: 5x @ (4)c. How many hats must be produced and sold to breakeven? Rag @ Sx=~ LSX 4 =,Looo ® 3.5x: r000
hacks. {S X = 1000
(4)d. What is Barbara’s proﬁt (loss) if she produces and sells 2600 hats? Wm
l3 = rz—c Vii?)
: 5(21900) —(..s (moo) + qooo) ZS®
= ﬁ. 2 l 00
(12)4. Solve the following systems of linear equations algebraically. If there is no solution, so
state.
a. 2x+3y=l3 *3 b. 2x+y==5
3x+5y=23 “1 10x=5y25
2 @ Zx + y = 5 (as 5) “'3‘, ~[0x6>,=—Z$ GI) »"l0X «My~ = “'le yz—q /0x+5yé2'> w? @ 0=O MANY Selecth @
x=~Lr (29 (x, 5220, 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 stemandleaf plot of the number of bouquets sold. 0 3.7— l 5J8/4121L+ ‘ E
2. a“; ‘
3 O gr (twiglevies?
(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 bestﬁtlime data (let x be price, ybe
number of bouquets sold).  ‘ S, __: mlcymp+ 2 23”“)
. \[ﬁ’L/ss + 2 53 Gin1E)
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 leapyear 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 dCSSeri— Phi“PS. HONOR PLEDGE: I pledge on my honor that l have not given or received any
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