Georgia State University Math Placement Practice Test Solutions

___l__tl_t___t_______n______r____|_______\g_l)___________t___s_________2__|_ _t__|___+__l_f_lt)____t_____)__|__0_____J_t|_________5____ ___t_sJ__ _____ _| _____l|____t _J'_ __ _ _ .l_" J,,.;"' ues_,c,_ re - e __'__;: -;__ ' ' J___. '_ 6, ___ ._ l I l lJ I _ _ 3 /?c__Jc__'n/,

- l __3: __-r__ 4 _c__,_,n__J_e__,__ '__lJ__ ' ,,/,) ___J b:_-3 . ') '- '

_\_, . s _J c _? _"3 _ r_-3 'CJ'_J _ __') __ _ '_ ;9_,_'3_ ____4_q-_,'? '_,__" __8___t'__m_- O' _' ''' 'iM _;___' _ -3 __- - ''' '' _ ' -_/� _.n,, , ' X ___ ___ _ _: '___ ..,_,,_ _ ,! __ '4_ ,_

4, J ,_, _ (_3,_ _6_

__ _, J ' ' 4 _ .//__y '_, _ _w____ ' ' ,'- __, __' - '__, . _ - ._!- _ __, ___7 ;,,

t_ As,, .__

_. 0_,_ /__ _u,mb cr_ , ,. , ,

___'_J! 5_ _'__ x- _,__J _J S,/Jc___?'!,_,_ t,. t__ e__4t, _on r_ __r_._ S__1c___t,. '' -},__:''_ 3x _sy__ 'I__5_ , ' _ ' ___. _,. 9J-4 soJ' ,3__syc; _ t_ t5_'__._i,r'_ \ _t_-_;, _ '_,_ ,... __._ .. , ,J_' _._ ' ' .x__5 . _ 5.y_-5_ ,

. c _ __'_ J x___ J _ / - _ _J_u' '''' _ 'hx _ _ _--e c 5 h4 __ '__. _ -s_ , t _ u e, S _q _-h__ __ _/ox__y_'_ __ ____i_ ' - _ '.

__ A_Si X___ __J!y_'_/_ i__ - 't__' __ - _' '-_ __ Jc,h _ ___ om Jc_ Jnn T rI

!_ __'_ ' , /'mp/'_J !_

_/; _.,d_7_J8 _ __ ' _ _3_

____________________________________)____________)________________________r__t_____________________________________________________x___________________________________c__t_____________________x___________________J_____s__________________________/____t_________________a__________t____r0___rl_________________________________________________l___________________________________________________________________________________________rr_________________r______________l_________)t____)_____________________)___________T____ _____ _________________ ___..__. _._%;_?._.,___.,_' _.___ -D-__J _ ' ' '_Co_l4/ey ?____e_c h_J_xpo__r,__1_5_ _ _I_ '-'' -- _ '' ' -' _''-'--";-'- ' '_-_ _ p-f__ _ _ __ C__' -, _.,- _S ._ -- - ,....3 __,2 ,. _ __ ,., _ ' . _ _ l__/_; __ ^:.. _ __ ___ __ . .c. __.. C _c _ _ -_ ,-I _, _ _' _'_',_, - ___6/',� _ ,!_Y__,_; _,__ _ , _ __ ?o /?_ \_ __o_ _r4 t,'_ _ __ç__?,y__ _ ' f____or. _ '- IJ __o J?e ..._, _ _x_+. ___y__ .-__ 0'_._,, _ r '-__. - - _ _ .__ ' -- _ ' " - '-". __/.._._.3.y _'2__Cx_._+__._ v' _o_.'I___ _y __ = 0 or 1\_+_ __- 0 ' '_ .._ __,_ __ -_,x.,__.___.______ . =___._.___,_ _xA____:_.__ . _ _. _-',_,__ - _ ,

__ /,e -_' -'_+-- =_ö- - '' ' - -'' _ ,- , ' ' ' ,_.A_s, .._ __x_ _,.,__. __ _ _ _ _., _ _ _ . _..

_ _ ___ t __.___ ' _i___Jr__,c ' __, '44 __y_\5 ?_r_c - _rr �cJu �. _J.. ;_ ; __ ; _._ __3_ ' .. 'x^_?_ __x +_ 3__. ._0___ __. _ _ .,_. _ , .. ,__ ' _ , _ _.;; _;_ _x_ _.___ _;_;x?_ _:__i___-_o_ _.:_ __ _, _ _ _ =_ " - _ , "' - __ '" _ _ '-___ X'_ -' 7_+_4q ____3j' "_--i_'' -- - '_ '_ _!_''' - _ _ '_- _- _ .-- _ _i,_(,\ _ , ,_- --_ '.X_ ,,._..___ __J -_ -_' _ __ - '

_t_tJ __x''_ /o_x_ ___ 9_._=_ __ _ ._ .__ = ' _= __ -'' __ -_ -' - ' __A_'-s'_ç' __ x_, -;__i-__�^_'_i__ ___ '-__/____"--_- ' "" '__/ ^ -"-' '' '_ _- ''' _-_''-' ' __ '"'' '''-_. . , __. _ _, __ ' ._ _._ '__ _..4_ ..._ _ ' _. __. _ ' _

_ ___ __.?.. /_u_'?.s____ .._____._.g___'_n____ .,;____e'_g__._J.,_t! êJ ' "'- '_ ' '''_,^' -'' _ '' _'; '''- _ - '' , '- '_ -' '- ^ '_ _ t _.__ _._ ?o J._em..._ ____r4__.. _ ___ y'x,_ >_ /0__ _ ' ' -_So t,._ 2..___x ''> /ù.. =- _ ' " '-''' '_ "__x __ _?,X _ - _D__e__^'c_ __,,,! /-,,,, _ _ . -

_tt_l______4y__t_d___l____r______l__y_l)/s__u__t r_n_______lt5_________ç___y___l__x__1y_r___3______r__t___ |___J__t_f_ yl _ _ _

!__ __:t' c-- - _'__' _/ X __.,_/;w_,.?y_,- __- _ A_!s__ x7' __ x___ ,M ',0 ' ./_ _,.,, ', '' -

' '- '- __3 0 '_j '�- -' ' ;-, . - ' -I--;,, ' !..S

y5__cms _r_ __4__,_unJ_ ' ' '_,,___m- ., ' ;

____J_ t7, SoJu!_ 3x4_y__!_"!' n__ _ 7_ _ _ _ l_

L_ _ _ ' ' 'J'j_ _ " _ _,J_,__.'_V _o ; 3X+_y=_ _._:_?.-_''_.' '._ :. _x _Y __I . ? -y _ f-..7_ ,_ _7_-l '' __/ ___0 _ec,; 3x_ __7x !"-J )__.. . _ '_J7_x' _'_,__. _, ,.

''_u'_'' ...3_ ' ' ' l 7_i ;__ J_ ' ..._?-'_ ' _ _- ,---' ' '''',y__' 'i___ ' _ _ ,-_J_-_^_ q'tc , T_J? _J _7C_J7)-I , .__; ' ' _,__,,-t, ,!_'Y'' ' _ J_o __, ' !' !' _"_ _ _ ' _ '', ' - ) -- -_J_,_d/_c _W_+__ M-(0D , '___w _ z *-__ .

_ _ ____ _ _ __'_, __,_, ,' J

�_ - - ' ^ '-' ''l_'_ _,,,,, _ r___y_ _ _ ' ' _ ' _ _ , . .' ' '_,, ._ __g t _e.'_?__t___ _U__ i': _ .X ' t. _J:.__ ' __-'' _ __y '_?rCel'

__ ! ._ ' . , - _' ''M _ h y_._._

_/,' ,__ 4 _ _ _ 3 l(__ _''__' ; _ ,0___

____ - ' ' ,l '3 '_'_ '' _ __'_ _ __- - _, - 3 '(r__J'_, '' ' _h(_tc__p_ v_e,_ X__ , _O __ 00 t_" ^- .y /ntc_cc__ 4_ _0, __) ! - , 'X_'___rcF_ _rn y _,' _ r,___ __ 0,__e_er.___rc . _ 0 X'__Cr' vt-

___lr___________________________c)_______t__Lt_______________________________________t___ttr____l__________t___________________________l__t_||t___________________________________l____r_r___________________________________0_t_____l________________________________pl__l_l___|____________0_________________r___t|l______________________________________lt________r________________________________|____t__t_______________________o__________________tl____________________________________/_l___tr__________________________________ltt_l_____________________________________________tl_l______________________________|_|___________________5_____________________|_r_____t__________________________________t_____l____lt__________________________l____r_____________________________t__ttlt________________________________|________+_____________________J______t|_________________________?_________t__________lr_______________________________tt_______t_______________________t_____||tt__________________________________________________________________________________t___________ __ _ _|___________t__ __________________tt________________|_|r______________________tt___tr____________________t_______________________t_l|_t___________________________ _,______?_ __ r_?..__ _?v_n_.t,-__ __ 3_x, ___ q _ _?_. J'J.n, _._;__ _ x4; _ __ _ _'nt_cr__.cp__,_ ,_ , _n__- :!':-!_';!--';_;_;!___ ;__= __;;;-':_;__ ;;';_._- _;- _;:,=; ;;__ ;;_ ;- ._;- ;' _;;_,__;;;-;;-'__-_--__;--,,,-;:':.;_;,;;- ;_ ..,_;:'=;-,;'=;

_J'____rc.._cg __''___J/._' )__ __ ._ __ _ __ ' __ _' _ :_ '... ' _ '';__1,.mrL-_r �_e___?/.' _ ___'__.q _ , _' '___.,'_._. _. ., :__.'_. _ _.!., .' _ _ !' _. _ _ _ ._'_ ? __. / _ c _ _? ,. _ _qo tu _.1 _.. ! ,. ,, _ _ _ . _ _ _ _ '. _ , ' _. _ ... _.. _ _ ' _ _ _ _ __ ' ' . !.._ __ __ '_____,_ _.'3__x_ ____h_-;___5 _ .__.___ ...__. _.._:_ _ . _.. ,__.__,_ _, _..., ,_.'..___ t. _;., ' .4..3_x +_,_ '';;. __5_ __ _ _ ._ , .. _ ._ _ _ ' ._. .... __ ' .., _. , _ , _ _ ._ ' _ _,_- '_" -',!_x._' +__ _- y^^'_h_l.,'_?. t- -' _-: '-_ '+. ''- -'- -'' ' _ = -- , - ' ' _+- _..__R,_.j__d_.l_.'_____;_..t'-_____:__.,,.__..___.,_ . _,. ;_: .__..,'' . _. . . ._'____: '_ '__3.__?.._.Iu____o_ y_.:,_ _...,.,_Xt3 !,.___ _.__,. , _ . , _ .. _'' __ .. _ _ , ___.?_.c.)_ ..._____'____ '--_'_0_! -_ . '___ ___:_- ;?_ __-___.n____.rm!_;.t?_ '____i_ _-__6'!' _"-;

.. _,_ :_._,x_:'?!J__;-__0._.__2_,__'_j_. ,4_r. _X;'_ ''.._!_,_ 3'____ _'_'___-_--_ :__--!-_.: '_.:

__l___|____K___ _Jp_s____r/y___c_7_y__y_l____xo_______g l___r__ ___/r ______ __t_ __q7__J ____ y__ __do_r_mJi_ _O_t_M_5, '_x:-_ Jo_-_, r_}_J_ .x_ _u.chr?q_ Y'_x'i_?

_ _r_\J __ Jo _x___ 5 ' __; s,.,,_,, __cxPN\.. '_o __ x_)_ _ __)_ ' - !_ _ _? ' _/ )0x -_ _or_;_;! _,,. ./_ ._ �___!' _,__ X =__

___'' ' Z_/ _rXJ__ _X t, __, _'__x_suc_____y_J_-0,__crc___J_a''; ' Co_ _ i__ t_? 'D - - ' - _- -_5; X _- '__

_, __ht'_-o_o__,c l,nc:_i__: __, ___,%J __ ,__'_, ),,.__ 5,._,n .(x_, y_) -- __r/, 4__, __X,/ y,_J_ _ (__, _).__-)_r,_ . .. _ . ' _r / '___ _____! Sot _. o__c_/___,_c _'_c_ __t1__x+ __e.r, m,_ s1 _ 4_J_ li Jn.t__rc.c_

- s/ r!__ \) -yo __ __ _ ' 'q__ ''"__ ' _! -_ _ _) -

I

_ T_us y!-_ __ + _,?_ ' ''_ ' ì Xo' _ b _�__ ''Jt _!q_ , . 'J_/ 4 __ _(___b>_.; ___ _

_' T_ere_ar_, . Y =' a_ +__ _

_g_o __c.. c_h J 0hh

w._. , __. _s ._.. s,-n -x _ne_ o_eJ,_r _'' ____ __ s ;' '''_'- O _ '';_-__; . '_ _' ._ _

__/ ?Je,___'/_ _cr_ _J_urc __,n o.nc X C_r __r_t-__yl__r __/uc_ of y _,

7- __ O _

_._ _'-_,. _S, e5,

______%_w__________l_________r____t_r___ __ ______y_c_3_____l__+__g__)__(________t___x_t4______)fx___t_____x_______y_____y) t_ ______

___v_,/ 3_-6_; l_)_ 4v,,._c,.,___!__ ;'_. AI_ __r__�_ s,(_,__ J_" _" ___ _Ç -3__C_. _ _9 y _ _ _

__ ' '' __,/J,' r ___ _/) C_ _ _qay ) _ _ _x- _! ) + _ _x , _q_/ ) _ _ '_3_ y, _ _ _! _j_ y.__ rx)+ __qyx) + C-3 _yx ) +_ _ _- _y_ '_ _ + 3_y _ __y __~- _\ __y '

__\:, _ _,,.,_ _3s_ ___ J_ _') C y _ _ _ )

v__;___ _, /s,' _/'_ __'+_y____

W _, ___-_, _' ,,%,r /_ __/Jn,!, 4 __'onh_ __, u______

3___3 +xX-l ' x__

_" _,/ ' _ _ X+ _/! 3 x /' x'____'__ ' _ _ ' 4_ = _i_ ;_ + _ _ _,,;_ _,__ _ , l ., X_ 'I// X- . X _( x t _J

____ r_ +, _ __! ' _' '_\ + __.._,. __' _X_4 , X-_ _; _x________\,

n _X__4 )_ x_l

í_'' !, _- __+_ _ I__ _î;?_' -_ _:_ __ _ +3X -___ _ _.,rN;! ____ 3 _,_ _'_. _i_ X __ _+3

�__; X' + C_

C''_ !. ' ___. c___'____c

v._'_ _,_, Ju;.,_ _o_,,,_ ___ ,,J, c, _,u,. ,_ ,e, c, ,__,,c_ _.__ _-__ C,J..,! __o y_,Js _ _s__ y_r_í _ q__0_e_ (! ___ ._! ', ' J __._,,_ - b0M'nS ^"_'_c_ 1 I,a__r = ___ J7...'_,_t-_( I _/_ _._J __ _ ,?_cc_ __ ___ vm_,)r _ _,___,_JCc,_- - q____ ___

______________________tl______t_______t_____________________t_____)___________l___________________t______________________________________________0_r___________tlt____________________________________________________________________________________________r_t_t_t_________________y_____t_______t_____________________________r_______________tl_________________________________________________l______________r________________________l_r________t______________________________t__tl_r_______________________________l______________________________r__________________________tt__________l_r__l__r__r________________r____________________l______t_t_____________________r_______)t_________tl_r_t____l__tl_________________t_____r_________________________________r______________lr__________________________)__>_____________________.2?_. Co__?e,it ___t/___ __.mt?, _'_ c_.c, _cp_r____._J te ' _ __ ,, _ .. ._ ,

_ ____; ' _.. ,,__. _ ____ .r'J' ,_Ç. m._ _;__. _ _, ._ _ , _ . ._ ' _ _ _ . .. _ _ _ ._ __ _. _ . _ _ _ __ ; _ ___

' !U __rc__ _ç,. 7_ __, ,, . , ; _ ! , , ,. í,_U, 0_ __.r_-_ _ Jnta ç_pI_r�c___ _,c , _ , i '__-_--"_'-_, ''_ _- _'-''--'_1?-_ '"'_'!'_;- '' ''- ''- - _ -''-' '----,--" _-'' - "-_' - ' _ _ - - - _ ' ''- _ _- __o(; ' _! ___ /__ ' __/' J_' _____J '' ! '' ! _ ';.i_, ' ' ' _ __ _,. __ !,'' ' ''' ;.' '

_ ' '-'_/-ì!_,_J__ ;-'! ! _'__^__/ - ' '; "-' ' , '_ - t__-_ -, ' ' '!' _'_' -_ ' . _'-'''___ ' _- - _ ' , _ _ - '_ _ _ __;:''_,__:'',_,'-____-,__;/" -_-_,; _;-', '__;- .' .:''

_4f, ?_n_c_r_t. _.____ ____; __.t.,_ h_Fr__._,r_J_, , .;_ _ _, . _ _ ' _ ,!_ .,_ _ '.,____;_,._.'q__2.__ _ _! ,___, ,_, ' ' ' __ ____ ,._ _ .;__ _

o_ J ll_ __v4 ' _ y _ r __u_ !_cc ;vc__,_,,,_ i ; , ' ' ' ' ' _ _ ' ; ' ' ' '

__(d.,.;_.__,_J_,g_ . ; ; __' x;+ '4( _ , ' ' . ' ' , , ' ;''._ _'____+_ ,_, , , ' ,

'_o/: 'y__ x+_, , , , ' ' ' ' , ' _ _ ' _' '_5x,__ ';__. ;, '_ , ' _ ,' ,'''_?;X_V_-3x_'t ! ' _' , , ' ! _ ' ! _ ' _ ' ' ; _ _-' __X'' _ ' ' ''_ '' '''' '!___'._' 'X-_!__?.9____,,..-_.;!/i'.. ,_ ';: ;';_,__, _;',.; : ,_,'.'

: _3_'__'_/_c' _ -'x'my__,1-_-' ' , ' ;_ ; ; ' . ' .'' ' , ' _ ,_'_._.'-' ,.'.,_,,____.X___'__ . _'.__,' '._ ;_ _ _ .

''_S; X_;__' ,, __._ ' . , _,_ , _, __, ' ,. ,, _ ;_;

. _. __J.e_rs'_/_J,'__ J_. _____i_.t__!_ ; _ ' _ i . _ :_ _ ' ' _ ' ' _,,!'_v__,,___?,_'__:_i___x__-_t..__,,_ _in,..,;J,í'.-''___!_ _ ,' ',_; : _ ; , ,. ' : :, ' '_; ; :_,,;

_o/T_!__C!x,__-__x_,_,_'! _, ,;; ''_' '; ','''_''..__. ._,,___,e__._____;_;!_,.__!____.__!,__,_____'j.,._.:._. ,,., .;._,_:._,_..'_ '__;_, _ _ _ _ ' ' , ' '' ,'

_ ______ _=s,c' x.____=' .._/_o__,_,__.._.j__. ,'__,_'!,_,\c,.' 'c,?'___.;iJ.'_;__ __''__..., - ' ___-:-:',,____. _ :._'_ "- _ __ '.-.'._I",...--._ - '_. -' _-.'.-'-! '_,_:".'_'' ' _!' '_ s_ / J_o ;' .' ' ' ' ''' !' '.,,__ 'J1 _ _''__ .'__ _. ;- , ; _ , _ ; ., .; . __: , ' _ .., , , . __ ;_ _ , '

__ Ju_'_,__ _ _c ___c,m?__-_\5 _ __.r X , . _ , , ' ' _ ' _ . , . , _ ' '_',____--'__-'-'_,____ .- -'_' ' ' -, _ ' __ so(__ '_x +_ ,c _ , ,. - (_;j J^= __)' , _' ' '''_ __'i)__ __/I__-7 '

_________________________________________r______t_____5__________________J______________l_r___rr_____r___________________________________________r____r____________________________l___o___________________(_________________l____t_________________________________________________________________6____________________________________________________________________________r________________t__t_______________________________________t________________t____M__lr____________________________________r___________æoJ___0_______________(_________________________________________T___________r______rr___________________________________________________________________________t________l____________________________________r_r____r___t_t________________________________r___)______t____T_____t_)D_Tt___________________________t________________)_5_________________D_____________________l______\___r____;_____________________t__l_________t____t_________________________r_____________________r_____________________________________t__r_r______t__r___________________________t___)__t_____________________r_______________________r________t____3__________________t__________________________r____________________(___________l_________________________r___l______t__________________tr__t_(_____________________________________________f______________________________________r_______________________r___________________________________________________________________________________t_____________________t________________________________t__________r____tr_______t________________________(________________________________________________t_rl___l_____________________________________________________________________l______r________________________________|__________________________________________t_____r_r_____________________________________r__l_____________________________rr______________________________t_____________________________________________l________________rt____)___________________________________________r________t_____l________________.__J___ _oi.n_Jma(_r , _C_ _ (X... -. l) x'_.3x___,_j _ , . : _ '_ _ , _ , _ . _ ''. . _ ,

___,/;'____f_!y\J!_5,x^'_'_.1\_-_ ;''! , _ '','" ',__'' ',:_'''_ --_'_'_!''_'__^)!''''-'-'_- -- __ ;---, ' -_ ',-_-' :- ''; _ _'; '' --', ' ;-_ -_ ' '_ r,'_ ,_ _., x' ,_. ' , . :. ' 'i :. !. ' ' , ' ' ' , : ' ' ' ,_'' __X__'_y_!'' _, _,_ ;',' ''_',.' ','

5._J_ __ ,_--x: _;'!-__'__!x_ 3?3_,______:';_?.,.__: :.,_':'; -,;::;::'-- ,: .'_ ;-=-'.:-'-.'_-=.:-__,_-:;,. . = .'- _ ___'__; --:=. ;'':-' -._:_:;'__'-- _ ' ;_.;

-,_-._s __' ,!.._x____.._J'_y_!_+; _.t_(_; .___ _.__;____'__ _.,_;_\__.!__.; ,_:__.__.v___;',-t_;??:_ ;__(_. ;,x_;:_; _.)-_''__,_x ,____:,_-'_'_:____,__. __x_.:__ .?_ ( ;_=_:':'=: ,._: , -",..= _ ,: '. _ ''_'';'_

__ .__So_Y.?._!_,G___?r_._v,?_ :',c_._'r.__ .. __ _.._'_ ' _ ' _ _ _ ; ' " : ' ' _ ' ; ; _ ; i '._,_, '.S'.a_/?,e.._;_,,,J___.:_..J{ .__.; .____.____?____.:___' __J;r..-_ _3_,j' _.__,!_a;,__, __; _; __'___; __;_,__._: -.;_____ : ' ' . _,__:.'_.__; _;__ ._

S__ t ,;_._ ____c_' ___'.J_? ,___3.,_' ;.,_.______.___ _ ._!_. _ ; _ .:'i __, _ ' _ _.,.. __. ..'_ _;. _ _i,,____:,;.._._;'___;_ _; . ;__ _; ___ __ ._ _ ,_ _,____; _:__ _ ;__. ; __ ___ , __ .;___

_, ' ._ _______._' _ _ _^_....____ ._!__/Jt___t. t_._,. ' )_'' .,__ ,_ __ ,_ ._.__,_ ' __'...._____' _ _._ __ _! _ _ _ __.. _ _ . . '_. . ' _ _ _ _

' i ,_ ' I ; _i ' '' ''_ _''-s--__-_.s--_/_!___;__, _-;ì;' '_d-- ,t-'-!__-�'- -_'^ _!-__-'__;-_-_-;_''___!'_'_0- ;-'!"' __- '--'_'-'' '! -!, ' - ,_ '- -;'_ ''' -; _ ,'.__'__i___,;..____.__!_..___..!__.. _____.'.___;'.___ __ ; " I_-_ :'A?,,' s_ .;'_,.__ -__- ,_.__ .!____.__ __3_' _:'! _t__ _ .--_:, _._;._____. ._ _-., -_. '. ___ i_ .:; _ _. _ _ , _ _ " __.__ _ _._._. !_ _ _ ' ._ _.__.. __ ' __ _ ..__ '; _ _: _; _ _. _ ' _ _ ... _ __. _ - _ __. ____ -

-'_-_-Y_---__'___-_! ' '_-_--_'_--_-__ '' _-,___'_ -_,-_,- _!__-__----; -;_ _-__- _ -_ ______, _,hp;/,'__' r _ t _ _ _ ; _ _ '_-___;_-._ .'__-____;,__.?; ____!_. ;',_:";._. :.: ;' _-;_ __''_x, .._.= ____:___ _.:. ;:-=_ ;___,, _._ __'_ _._' _._- :: _ _: "_ _: _ -" __' _ '.T.._ _ ;, - ' ' _ __ ' ... _. '. ='_J,''!?_-_. _ ,_'_a'.;;_';_)' ,_x _ _'-;- /,Mx_________-_.__''__'''. /-''_____/---"_'__ ___' _' _!__.___::x' ' _:_ ___;.!_x,____;_._____ ,..:__1___,_._,__.,_.__. ______. .____ .. , _'"__. _'____.__, ' ' ;____ :,...:?

. (w J S_. ?,,,_. ' _D _, ?_ __ ;..__ =_ _, ! __ _.,,_ ;__. , ; : ;_ ,__.__ _ i _ ___ ; , :..__ , ' ' __ ; ._. _ :.. ' _ ,_: _ ' - , _ _ _,: _'_ _ _ - _ _. : ' _ ' ' ' _ ' ' _ ,

T_,__J,__! _-___-; __- ,- _-'-,,,-_; --;--_, '_, _-_',.-'; _' - ; -, _;, .._;'!_- , :_ .' -_, - _ ___-_, _._- ,- _ _-; - ,_ ,., _ ; ^--' , ''' :- ;_- '_ ,-'"

_ '_-yc_'______._______,____..r__q_ct_',____ _ _ _'__ . __ ___ _ _ _i . _, , ; _ ' ; _. ' ' _ ' ! '_____ ._ .__v__/___�.,r _ __,_.__' _ ''_3_ \ _! ' , __ ; ' ; ' ' ' ' ' ; ' ' '', ' ,_L J , i _J ,r ,I_ ; _ . ; !''_'' '- -';-_';--"-__--_ -'' _- , \__'-' _-- ._ __h_'\\_-'_'' - _ !___'- '-'' ___-! __ -' _-- -_-, _i- . !_-_ _, , !_ , ;, _ _ _ '_ _ q __ --'-. _; _' __' -_,?,, J- ?,- _ ?; __- _:__J,_, _ -- ,'__h;_-_:' . .; _--__ ?- ;-- _,.3, _-; _ - ' ._

, '- /\J ,n7 _?' ;;,.;, . _ ,':. ' _ _ _,L J___ _, ' c.,; . u_. J + ___ __.__ ; !,__._ ; _ , . _0 _ _l' ,_ _,-' ' , ' - -- ' - _ '

l_______________________________________(___r_________________________________r___t_______________________________l____l_(_________________________l__>____l_______________________________r___________r_____c_______________________________________________________)_________+_Q__t____r____________________________r_________________________/_____________________l_t________________________________lJ_______t_____________9____________________________________________________________r____)__T______________________________________\__r__l_______________________________________________________________________________t_______________________________r__t__________________________________t___________________________________________________________________________________________________________________________________________________________r________________________________T___t_____________________________________________________________________________________l_____r_r_________________________l_________________________t_____________________________________________________________________________________t_________t__________________l____________l__________________tt________t_________________________r_r__________________r______r__________________r____t_______t___________+_______t________________l_________________________rt__________________tt__________l___l______________

_ __.___-J, _ _ ____.'a^_ _; ..Cos_____ _, v_J . _ _ _. ._ _ _ __ . _. __ ' ; ' '' ' -

__ _'__,__-_.__ ;__ __!,___. _ ,'___ __?_ __ ?_. __, _ _ __ _. _, _ _._ __ '. _ ' ' _ ' _ ' _ '

___ _____J_u_ _ur_' ' ' ' _ '(._-__(__c,o,___ ____4.._. __ __ __'__._ ._._ _ _. _ '_ _ =_ __,__:__ __ __.-- ._'-. _. . '- ' '' ' ''

_. '_ Cd ) ó_. _. _e_ _ _ !_ _ __ _ u ' ' _ ' _ ' , ' ' ' i ' _ ' ' 'r\e.__ = __, ;'? _ __ ' . , ' __.,_ç,_____._ .o___ __. _ :_ __ __.__ _ __ :-: '_.. '__ _ - - ' ' '' -' ' _ '_ - -' - ' _ ' - -'' - ' ' - -

'_ _ '_. _.__.___C_____ =_______ .._. '_ _ __ _ _'. ":-._' _ _ __ '. ,=-'__ _ : ' '' !'"'-''--'' '_ ' - ' '- _ '_- "'- ' _ - " _ ' = "'\ -" '\___' -_ - - _ _ _ - - _-__-.- ._- _ . '. _.' _' _ _ , _ _ ___ _5..Q _-- ' _ "-î-'/ _J_ '' _'___ -" ''c__ ' ' ': ' ' ' : ,'-"'-"_;^ ' ' '_'t"- ' _. .___'__. '____ i____ _c_o;___e-!__;-__.___,.__: _:: ;_= _- ''-' _: __ ;_'_ ' ' _'_ -_':-:.,_='-_:'-_'-_; ,_: ;_'_'' __- ,,: :__: '_' '-'_ _-; -';''; :_i-_: _

J ' rTT! _'' -- '"" _''-M__;/i_-' ',_- -_'" -''_'"'- -''_ "-'- - - 1'_' '_'_'__ "__ _ ___._..___ ! _ __,_ _4. i__._I_?_-__ cJ__= __'_?_!.,._"-- ______.'~i_r _. '_ _ _ _ _ '

. t ' i __ _,'. !_-_?__.._;: ___,3_ __c- _c,,__ ____-___J_=_ __= _._ '_^_:' _' _: _"'_'-- _ __ '_ -'_ -_ _''_'-- '_''--_"" ; "'; " -_ "" -_ ,"' _: '-__ ': _ r_,___ ! ' rt____-_- !-" - _- "-^ '- -'-";- '- " _ ' ' _-'' -_'-' "___ - ..__5__ _ _ __,__ ,,/ _' _;____?i_i_ ___('. '__'__?___/,;, __ '__. ?,_.. _ ._ _ ' _ __' _

r_e , ' ' ''' ;_'''-'-_'___ _ _ _ _ _. ___ r ___3_.J______;____X_t_ __V__?_/___h_.+__.4. _____'_.'__,_ ' _ __ _: __'._ _' , __= : ;:";- ;_:'. _:'_- ;--'_ ;'_ _

?,oJ!_ .\__v _, ___-,_x _- 4 = __ ,! , ' '_ ' ' ' i -"!_'''''''--'"'-""t_--^^-_'''-___ ._., _'__ ___ ?_ U__ _'_,_ ' ' : rT_,_ _j_ !, T_:4 __ _ ' i , _ _ ' ' - --;'-' ^-1-_- --"''-_____'_'- "_r'^_'. "_ _ _- -_'" -'_x-- -'_ ' "---_'__'__ ____ __ -___ __,-_ -- -_,_ ____, - _,-- _-._ __ - _ -_ __ v '- +_ _ _ _ _ __ _N i - _-_- _._ .._ _ ' _ _i I ___0_ _ i r ' _ ' ' ; ' ._ .___I__. -_ __.____ _ r_ _ _ __'____,__ _'_ _ __ __t__ __, '_;-_'_-. ;______ __-____X._-,____,_?;_!,_-___ __ __._ __ _ _.__;__ ._'__.__ _'_ _ __ _ _ : -_. ''-' __'

J-_,____;a_?x-_._"____s_X, .,___/ ,___;_. _.'_'__"._ _'_ .__i_'_'_ ,__._'__ _: '_;_ .,_.,=' __:.

_ _ ; '' ''''. ; +.--'_''"''_'_'''I_'-'--'"-_ _ ; __An__s_.;__ _ ;_c_ __n:_;___,_ '_J ___+..._''__?______-__r'___\,,c__;)_ _- __;-" - '_)__=-_ _ ' -_ ' , ":-__i - ''"- '_ ''' -'' "-'"_ '--

:=,=._-__=:-__'-____.,____s__ ___i;____= __/__.__._.__:'_- "'."-_' - '- - - _ --' ' -' ' '__ ' -' '-

___.__. ________ ' r_. '"' ' '' ' ' ' _ _,! rvI'/ _!_!._-.'__ ^-' - ^- "-'-' '-;- ' ,_''_''i '-'' -_--____ ' )__ C_?\' _ '-_--_ ' _' ' 'J,"- -_'_' _'_'_- -' ''_- '' v _- --"- '- _ ' ' '_ ''_' ____" -

__r_?_xr_t_________________________________________________)_______rl_____lt_______________________________tr___________,___________________l________l____t_|__l__________________5_________r________r________________________________________tr______________________r__r_____t____________________________0_______0___tt__tr___________________________t_____t__t____________________________l______t_l___________t_______________________________l________________(_________0_t____ll___t__r______________________u______________tt__l_______t____t_______________________________r______t________________t__________r___c____l_______________________r___________t__r_____________________________________r_____________________r_________________l____l_ll_________________r__________________t_lt____trlr____tlr_______________t___l_____l____________________rttt_r______________________t_______l__tr__rr_______________)_____l___________r__________________l_r___t__r__lr______________________________________________________________________________________________________________t_________________r________________________t_____________t____t_________r__l_______r_________________r_l________lr____t___r_________________r_t_______________r___r________________)_____l__t_________________tr_____________t__t_l____________________t______r_______- _ -' _.__J__,!_____,__.._c,_J -_0__'i'_--_5--_ '- -_'' ' - - : - - - ' "-' '-, '' -, - -- -; ' ' ; -' '. 7-7,): C__ _?.__ , ._'__, _q.__r_J. _�____ _'__?__ J__;r_ _ _ . _ _ _ ', , : _ , _ ; ' _ ' '-- - ''' ' ' _- '- _'

' _6../.,__.._ ;_____ __o.__,.r__4,_d_,'ni_.:_/_ ___J__/,.___'t__ '__ ,. __ ; ' ' : , ' ' - -'

. _ _.. __;,_ ;__;__!__00,,J_' _,___-;____'____'' ____ .:; --__._ _ ;. _,___ -_="..._.;,.--'' ____ _._. , ', :-;,___,,.-,__ ;, :': ' _._ - . _ ' . :_.,_

, : ;. _, _,_q _',_.,_,n_,_? !;___ _.____! _-._1o;_ __._..;! :_ '_.;, _,; ; ' _! : : ' _.; .:!___ -__ !;:-,_-:!-_-_,_'''" '':-_ : ':.-'- ''- ';- ' '- --; '

_,__ w_,._,,,;_,Jc,_-_':._.._sL/?d;_.'-,__;__;.,.__;__;-�,_,'_.;--___, ; _,--,_-=':_ ;.-' , ,_ ,, '',, '-; ,_: :_ - ,,

__?. J___.__;3._, .,__;J,__?__ _ _. __ _ . ''_ : _ ' .__ . ' ' ' _ !; ''' ' -_' ''.- _ ' ' _ -- - ,

_'._'___!'':; --''--_!-','!' ; ',''.-'_ '--' ;_- ':--_-'--- ';-' ' '''-'-,-';'-''' ' ' '-';"'"'' ';__ , Tr___(___,_Jh__n_.__!_.? _c..rc._'__ . . ' ' ; , , _ ; '' !!. ' ; : ' ,, : : _' ,'_I) '1(_7L_ _-s _y!-_ ;Cx____!r__.r_?___J'_-a'y _;_\'?_ --, !, ' ' , _ -; ' ! , ; ! - ' '' ,- ;-_ ',' l i;,_; i;_ _';_' ,''; ','_..;m'?5,"'_lir.____J_it-__J__.__!u?_r_ ' ____t!4'__s'_Li; ! _ ' ' _ ' ' ' _ , ' ' _ ' ' '" _'--'',-- __ __,_;', __';,'' _ ' !);'!' ' i !,,''':---',_'i"', ' ;- --",_'i'-'-_-''-'"'!,'-' ';_ ,!-,-'' -;!__-'-_ '_ _ _' -_- _- _ -, _ -,_ ; -, :--';-__ '_--;_ ' i_ ; __ ' '-\;''-' _'_,rx-_ _'3 ___o !"_'' _''_,-_ , '_,-- ''-J_J_--''- ',_/_ !!__-'''c'x'! _____--'' ' --_ ' !__ '- -! ! _ _ - ___ ---;'-' ,__'-l- U'; ;''_,,_-' ''-__,--"'-'-!, '--,----_ _' _,' ? - I.i'';-!'T--;'' _'"';--_-- _ i__ _ !._- _ '_ ,, '--_.--_ _ _, _6.,_______C_'..___!'___"..__d_; .,v_!__/_t'____.'_;._.h.__'...c_,,__I_ rpt, _i,__'1^_i__. _,' _ ' , , ' _ ,, ''

.__ 0_ ?, U___'_'UJ__,____, __u___ orc)_'rr___(__,,t_ t _',_,)__,_t _,.'._.,,' ' ' ; ' _ , !!_'J/ ,.__.,__,:_____ _ '_'_____:_;_---''",:-_=.:;. _'-"''::,-..='-:,:__,._,___,_:_.'.__' ! ', - -;- t, ;, ;_- ' ; -_ i ' ' ": ,'' '

' __c., i ;;__ :'.__ ___.,__ '._._. _5___ __%.__'_. ,!___:, _ __ ___;-. ;_ ____ ',_!_k__,'__?,_ _;___:=_i__._____ ____,_ _,,__..___'____ ''o.,? '',6. _! _.___! _ __'___.__ c_ -:o-J "._ '_ _ ;_ - '_ ' '._; '_. ' ' - ; '_

''.;--___.)_._._._}',;_!',/____';' _;.''_''.-'__'_;_:'__'. _____; -:'!.--__.;--;_',_:''__;,__;',..;,.-'',. .,' _',_-.''..;:_'_'_:__..'. _' -; ;' '-';'_'''-; _ ;

! ! ,o ,' ' r-�ú_a,''-_- ; '-''-'', ' ;-' '-'' -' ' -'-_ !'' _ , , _ --__.. ,-- ,_mf,_,. _; __,, _, ___..__ ___ _ ___ ._ ; __._ _ _ _ . ...___'__ _.__ _ ' __ _ ' . , '

_ . _ __C_,__:'.rJ_/'___;_.._.J_c_>__n__,,'_u__!,_'j''_,'__/c; ' '' _ '' -' -; ' ''' ;-, - ' -' ; , _ _ ' '__)_ ___n!.__c'__ _' oJn.t_ _ ' ' , ! ' ' ' ''' "_'''_ ''-- '''" ' '_' -' --,-- '-_''-- " '"-'" ' -'_ '--- '' '' -'' ' - '' -'--_ ;l _ _.I_, '' ;', ,' .'' -'-;i'

__,__ ; ?_ J ' L _i_; fo 'u_J !o_ ?-_e qn 'a l_ _____( ' - ' _ _ __! __' s _ _' - - -;, - _ _, - _m? _ - ;?L ?_, �n_t-; - i_' __ /9 _a_ _, _ ' ! - '' " ,! ' T ! i_ ; ; --' '!U !--_ '' ;' _ -!_-'_!_'_ -. _'''_' -' ' --'' - ' , -'-' -, ; "''' '_ "^__,_,_______. :'__ _ _,.._.. ___' _____'' ; ;, _ ___ .' , , ;, '_ , ' ;' ' _ ' -' ' ' '- : , _ '

. '. ' !. __, ', - ' ' '_, , ' ' g ',, ; _, ;J,.a _ _ ' __ '_ -T' __ !,, _ __ i, ) ' ' ' ' -, " - ' ' ',. ' '

; ;:-' '_'-_' -'' ''''_. :!.'_ _ '__;__ '' ''_ ' ; : '_, ;_: ;

_____l__)|t____________________________________________t_|_t_t____l_________________________________________?____t_lr_r___t()_____m0_________________________________________________h_a__tr_t_rt_rt|___________________________________________l___t_J__t_|___t_|_________________________________________t___________________________r_______1___________________________t_____________________________________0______________________________l_________________________________________J_________|_t__________________________________________rt_t______________________________t_____t__(__|l_||__________________________________________T___|__tl|______________________________________________c__________t)t_r_______________________________________________ltrl|__|_r___________________________________________________|r_ll_tr_______________________________________Jt|_____|________________________________________r__r|_______________________________________________l____J_______________________________________________________l__|__________________________________________Jl____________________________________________________________r_ttr|___t__________________________________________r_____t_______tl_________________________________________rl_t___|_____________________________________rl____________l_r____________________________1__t___________________________________________________r|_||________________________________________________xtt|____t___________________________________rv_ttl_tt________________________________t_t_r_l|__t___r___________________________JJ__|_______________________tl___r|_t_________________________)tl__|________________r_l_rt___r___r____________________r__t_____________________|)|r_________________________________l_r_________________l_______________,t____________t____________t________________l____l______,r?_,h (y_J_ ' ___- Y.,___ = , _._,

ii_s . ' : J _;,a i .

-_'___-.'..__.__-_'___:s;!____' _____'s.__.__.-_.___,__.__....__.C_.___?,_:.f._?!__?J__n_ '__'__' _____ _ _ . _,_-. :!_A,__. __!!____ _.,-c_; ___._c_!_._J____,;__._ __ct.___._ - _(___;._J'_(, _/'__,c__. _/?._.; _ ___ _ , __:. ,;_. _'.. _;?

. _,. __ ''-___.___. ' :m. _,,__._.L.___ __ _; _-_ '-_! 'u._ ;_... _!__ ;c. C_,_c_ ____,_ i_ __.J __ ___,___ ._.._ '___. ;_.._._.. _ ' '_ , ' !....._. '_ _ ; _, ..,.____J !_ .__ :_ ;'_...,.._... _._.._,___!__._ ._,!__..l .,.__ ___.i__,..., _____1__' _ _,._ __'_.___.__;__''.__'__._.... ._ '_.'_ ,__,__ ._ _, .._, _ ,.., ;______ __?__;. _j' ____c_J_1?_,_._c__ _. .,, ___ l_._' ,.._. ' '__: ,.._:. _ ._ '._...' ' ._ _._ . .i_ ' .!.. _ _ _ ;.' .I' ,: _ . ,. J ,,i_ __ . ' !,___ _ __,___.,Jg?t._i,_ I !_ t , , ': ' _ ' ' . ' _. !!_ .___)_!s;_____?-v.!' ! s' _!___\' ! ! ' _ " '_ ' ' '--_,:._ ;_:___, _,'' '' )-S_h _'' , ;_ ' , ,1

' 5_!_;' _ s','__y_ ' ' _!! ! ____x' ' _ ; ' : ' ' ' ;- ' t; ,, 'l_-S-'_^x__;' co___'x J :' _, _ ' ! ':'_ '' ì! '_--_! -- '-''_'__'''-' _ -!- -_' - --^!i _-!--'i- i -' ''-''.- -- i 'i -'"--- "_-!--_J -' -! !! _ __ _-- ' -!_ ! ' ',';' S__? __'__F_ _, _S_''n'x_o_X ' _ , ' '_ ' '' ' _._.___' ;,,, , _._;,,. ' ; ___ ! 'I'ì ',_ _.._.,_ ' _2' _ __'_\?_co___x _. __i_,X ____..2_!/xX ! '... _' _:__' _ __ __ _, __....'._ ' fy! _x _ '_,_J' x' ' co__.x ' _,,.....;_ _ .. _ ._ _. . _ '. , , .,_. , _.._. __ a

, _ .. ___._u, !__, _ ' ' _ _! ,b ' ' _ , __ _. _'_ ______-_ ' _. _ _. ',._... ' ..-___.-_,. _---' .. ._ '.__ '_ - . . ;._ ;__ ' ; - ;, ' ' . __ : _- _

_ _ _' - ' _ __ - ;_. _ =_- '; ____ ' _ _...._ ;_- __ ; �_ :.c __ _- _ -: :_6 __ ' '..Ki !__ __ __ - __ :.___._,__,__ '_._... ;...._,,___., ' ' ' ' -. ' -.. ;..-! ;,...__s:_:'.;.'_ 0 :.' ;,_.'.--:'=-=;..___,,' =__- _; ____;; ;-'__=_ , - :-;.;._='''.:-__=;_;__;;-;_'_ '-:'=�_=;;-__: - .--' : - _ ., _ _';:_';-_ ;'!,;';-J0_.!) .C__,__c._. fcx__ _____ ,. _ C1\.___ __X_ Jq_.? _C _, _-_,X; _.,..._.. ,_,;,_J' ,__._, ._?- ______ _ _C..3._ = _ .v? (; _ _,._____�_,_, __,rf_:. _/ _C__),___,?