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MACH05 Test 3Prof Howard (3-16)

Name

Show all work for credit. Turn in all scratch work in a neat and orderly fashion.

1. The table gives the percent p of African voters who have supported Democratic candidates forpresident for the years 1960-1996.

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a. Is the percent p a function of the year? Explain.

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b. Let p = [(x) denote that p is a function of the year. Find [(1992) and explain what it

means. ~ ( \ q q2.") :: ~ 2- ~'MU\'CQ.V'\

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c. What i~x if [(x) = 94? What does this mean?--\(, c;<"'1) = 9q

~~ -:LV\ \q(,,'1 'N d/O of' f\<fou.n p,"'U,cc,n v"WS SVff~d;/ ,)

. \)~c-rC{.r'~ CQrlJ,'<k~~ R>r r~s~~+.d. What ISthe domamof the functiondescribedin the table?

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a scatterplotin the window[1955,2000]by [60, 100]. Whichshapebest fits the data'(!inear:'Auadratic,or cubic)?

~f. Calculate the linear regression equation.

Year Democrat (%)1960 681964 941968 851972 871976 851980 861984 891992 821996 84

g. What is the slope and what does the slope mean in the context of the problem?

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h. Does a linear function model the data in the table exactly? Explain.

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i. Use your equation in part fto predict the percent of African American voters who supportedDemocratic candidates for president in the year 1982.

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~~ 2. A business property can be depreciated for tax purposes by using the formula"- y + 3000x = 300,000, where y is the value of the property x years after it was purchased.

a. Find the ~ercept of the graph of this function. Interpret this value.YeJ:trs $11}ce pv.af.ase

~ 1'- 3000{o) ~ 3oopoo

y -;:: 3DO, Oc)O ( \ ~ "J-n-\io.! fU.n:.~~ va jUt,iso 300000)--/ €J 113cP, 000 .

u ~ b. Find the x-intercept of the graph of this function. Interpret this value." .oA. I .-Iy 0 + 3000 X ::3()OOOO :=:) X = /OD .A.f# 100 YeAr.s J VQ I~ OT f(l) f / r IJ 2ero.

~ 3. The mean time in prisony for a crime can be found as a function of the mean ~ntence lengthx, using y, = 0.5S4x - 2.886, where x and yare in months. If a convicted criminal served 17mon

~hs, ow longAras the criminal's sentence length ordered by the judge? Solve by a methodof your.choice. {

0. Q (0l\1ean l7 == . 55Lf X - ~ .150

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(rro~c:. ) / 35. 9 f'11on/J5X

4. Use the graph to solve an equation where Yl > .Y2. Each tick mark represents one unit.

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5. Match the slopes with the appropriate lines shown below. Place your answer in the boxesprovided.

1m=-

5m=-3

m=2

m=O

~eao-b m = fjJ~

6{

3x - 4y = 21. 2x + Sy =-9

a. Solve by the substitution method.

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..3\ 3X-4~ ~:2.~ ::> X ==

72}(~

J (~HiY) + 5 y :=-9

:t2: -+j~ +sy:=-?.3 3

1.f2.. ~ J. ~ -+-~ \I ;; -<1

"3 :3 / 3 I

j3; :r~ y = -93 8 -,~- I~ 3 3~t ::: -;L3 ~:: -3

b. Solveby the elnninatiOiimethod.

S (3x -L{~l2-

l11) l (=<xt' 5 Y = -1) (-3)

to J. - gy -:; Lj2

-jbx -1'5'{ =.27

-~~9y:=-.3

3x-Lj(~3)=-al

3x +I~ =.;21

3x==Q

(0

c. Solve by graphing. ~I = ~ 3)( -+ 1. \ ) / -Lj

Yz= (-;}.x-q)J5~.