fv^ ` Kdxpr MTHU^Grphbj "` K currentpoint " ` K,Times .` K` K(` S(`a(`m(``p(`l)e(`  )P(` `r)o(` b(`Pl)e(`pm(` )1(`4(`-)3(` )p(`0a(`g(`e(` P )4(`"3(`$9( `0a( `)) )W( `h( `a( `t) )i)s( ` P )t)h( ``e( ` )f)r)e( `e( `z( `@i)n( `g( ` )p( `Po( `i)n( `! t) )d( `$0e( `%p( `'r)e( `)@s( `*`s( `+i)o( `-n( `/P )o( `1f) )w( `5`a( `6t)e( `8r) )i)n( `< )a( `> )s( `@o( `B@l)u( `Dt)i)o( `Gn( `I0 (0o(f) )1(7(`.)1( )g(  )o( f) )s(u(pc(r)o(0s(Pe(,) )C (1)2 (H (F2)2 (!O (#81)1 (%,) )a('n()cd(* )2(-#0(.0(0#.) )g(3# )o(5cf) )w(93a(:t)e(<r)?(> (`0b(`)) )W(`0h(`a(` t) )i)s(`  )t)h(`e(` )a(`c(`@t)u(`a(`l) )f)r)e(`e(`z(`@i)n(`!g(`# )p(`%Po(`&i)n(`) t) )o(`,0f) )t)h(`00e(`1 )s(`3`o(`4l)u(`70t)i)o(`:Pn(`;?( G(@i)v(e(n(`:) )C ( 1)2 ( H (2)2 (O (1)1 (`1(`p7(`.)1(`0 )g(!02(!0(!00(!.) )g(! )w(! a(! t)e(!r, Symbol(&`@D(&`t (' Lf, Symbol (&`=(&`E?(-@K(-@f(-@=(- (+ -)1(+ }.)8(+ 6 (*Iao (+VC(/ m& ,,S(30a(3)(3m(3`o(3l)a(3 r) )m(3 a(3Ps(3ps(3 )o(3f) )s(3u(3 g(3a(3r) )i)s(3 )3(34(3!P2(3".)3(3%4(3&g(3( )s(3)o(3+p )o(3-u(3/0r(:0c(:o(:n(:v(:e(:Pr)s(: `i)o(: n(: 0 )f)a(:0c(:t)o(:r) )i)s(:p (83(8m4(82(8m.)3(84(8!-g(o(B$l(B&ns(B'u(B)g(B*a(B,r(H 0(H.)0(H5(HM0(H0(H m(H -o(H l(Lm2(L0(Lm0(L.(L-g(L]w(L ]a(L t)e(L r I@IJ(JZX(H1(H0(H0(H0(Hg(Hw(Ha(Hwt)e(H!r(L1(Lk(Lg II"(J#=(H&a0(H'.)2(H*!5(H+0(H-m(H0o(H1l(H31s(H4Qu(H5g(H7Qa(H8r(L+k(L,ag(L.w(L0a(L2t)e(L41r I&4I:(J:=(J=^0(J>.)2(JA5(JB0(JDm(S@D(St (TLf (S=(SU((SrK (T f (S )(S]((Szm(S)(SW=(Q-)1(QT.)8(Q6 (P8o (Q-C(VXm RR*(S :X(Q#'0(Q$.)2(Q&5(Q(g0(Q*m(V'?1 R"R,(S-=(S0$-(S2d0(S3.)4(S6$6(S75 (Rs9Ho (S:pC(Y b(Y)(YMf)r)e(Y}e(Yz(Y i)n(Y mg(Y  )p(Y-o(Yi)n(Yt) )o(Y f) )t)h(Y e(Y] )s(Y=o(Yl)n(Y!  )=(Y#} )f)p(Y& )o(Y(f) )s(Y+o(Y-=l)v(Y/e(Y0n(Y2]t(Y3+(Y6]D(Y8-t (Z9if (_0f)r)e(_`e(_z(_i)n(_Pg(_  )p(_ o(_ i)n(_t) )o(_f) )t)h(_e(_@ )s(_ o(_l)n(_ )=(_!0(_".)0(_$0(_&@0 (]'o (_) C(_++(_.,((_/9-(_00(_2Y.)4(_46(_65 (]7o (_8C(_;")(_<=(_?-(_AR0(_B.)4(_E6(_F5 (]H6o (_I^C/MTsave save def 50 dict begin /bdef {bind def} bind def /xdef {exch def} bdef /rndpos { transform round exch round exch itransform } bdef /rndvec { dtransform round exch round exch idtransform } bdef /rnddist { 0 rndvec pop } bdef /rndmvto { rndpos moveto } bdef /rndlnto { rndpos lineto } bdef currentpoint 3 -1 roll sub neg 3 1 roll sub 19392 div 24608 3 -1 roll exch div scale currentpoint translate 64 32 translate 0 setgray /fs 0 def /sf {exch dup /fs xdef dup neg matrix scale makefont setfont} bdef /f1 {findfont dup /cf xdef sf} bdef /ns {cf sf} bdef 768 /Times-Roman f1 -32 576 rndmvto /gs {{glyphshow} forall} bdef [/S] gs 384 576 rndmvto [/a] gs 720 576 rndmvto [/m] gs 1312 576 rndmvto [/p] gs 1696 576 rndmvto [/l] gs 1904 576 rndmvto [/e] gs 2240 576 rndmvto [/space] gs 2432 576 rndmvto [/P] gs 2848 576 rndmvto [/r] gs 3088 576 rndmvto [/o] gs 3472 576 rndmvto [/b] gs 3856 576 rndmvto [/l] gs 4064 576 rndmvto [/e] gs 4400 576 rndmvto [/m] gs 4992 576 rndmvto [/space] gs 5184 576 rndmvto [/one] gs 5568 576 rndmvto [/four] gs 5952 576 rndmvto [/hyphen] gs 6192 576 rndmvto [/three] gs 6576 576 rndmvto [/space] gs 6768 576 rndmvto [/p] gs 7152 576 rndmvto [/a] gs 7488 576 rndmvto [/g] gs 7872 576 rndmvto [/e] gs 8208 576 rndmvto [/space] gs 8400 576 rndmvto [/four] gs 8784 576 rndmvto [/three] gs 9168 576 rndmvto [/nine] gs -16 2880 rndmvto [/a] gs 320 2880 rndmvto [/parenright] gs 560 2880 rndmvto [/space] gs 752 2880 rndmvto [/W] gs 1472 2880 rndmvto [/h] gs 1856 2880 rndmvto [/a] gs 2192 2880 rndmvto [/t] gs 2400 2880 rndmvto [/space] gs 2592 2880 rndmvto [/i] gs 2800 2880 rndmvto [/s] gs 3088 2880 rndmvto [/space] gs 3280 2880 rndmvto [/t] gs 3488 2880 rndmvto [/h] gs 3872 2880 rndmvto [/e] gs 4208 2880 rndmvto [/space] gs 4400 2880 rndmvto [/f] gs 4400 2880 rndmvto [/f] gs 4640 2880 rndmvto [/r] gs 4880 2880 rndmvto [/e] gs 5216 2880 rndmvto [/e] gs 5552 2880 rndmvto [/z] gs 5888 2880 rndmvto [/i] gs 6096 2880 rndmvto [/n] gs 6480 2880 rndmvto [/g] gs 6864 2880 rndmvto [/space] gs 7056 2880 rndmvto [/p] gs 7440 2880 rndmvto [/o] gs 7824 2880 rndmvto [/i] gs 8032 2880 rndmvto [/n] gs 8416 2880 rndmvto [/t] gs 8624 2880 rndmvto [/space] gs 8816 2880 rndmvto [/d] gs 9200 2880 rndmvto [/e] gs 9536 2880 rndmvto [/p] gs 9920 2880 rndmvto [/r] gs 10160 2880 rndmvto [/e] gs 10496 2880 rndmvto [/s] gs 10784 2880 rndmvto [/s] gs 11072 2880 rndmvto [/i] gs 11280 2880 rndmvto [/o] gs 11664 2880 rndmvto [/n] gs 12048 2880 rndmvto [/space] gs 12240 2880 rndmvto [/o] gs 12624 2880 rndmvto [/f] gs 12864 2880 rndmvto [/space] gs 13056 2880 rndmvto [/w] gs 13600 2880 rndmvto [/a] gs 13936 2880 rndmvto [/t] gs 14144 2880 rndmvto [/e] gs 14480 2880 rndmvto [/r] gs 14720 2880 rndmvto [/space] gs 14912 2880 rndmvto [/i] gs 15120 2880 rndmvto [/n] gs 15504 2880 rndmvto [/space] gs 15696 2880 rndmvto [/a] gs 16032 2880 rndmvto [/space] gs 16224 2880 rndmvto [/s] gs 16512 2880 rndmvto [/o] gs 16896 2880 rndmvto [/l] gs 16896 2880 rndmvto [/l] gs 17104 2880 rndmvto [/u] gs 17488 2880 rndmvto [/t] gs 17696 2880 rndmvto [/i] gs 17904 2880 rndmvto [/o] gs 18288 2880 rndmvto [/n] gs 18672 2880 rndmvto [/space] gs -16 4032 rndmvto [/o] gs 368 4032 rndmvto [/f] gs 608 4032 rndmvto [/space] gs 800 4032 rndmvto [/one] gs 1184 4032 rndmvto [/seven] gs 1568 4032 rndmvto [/period] gs 1760 4032 rndmvto [/one] gs 2144 4032 rndmvto [/space] gs 2336 4032 rndmvto [/g] gs 2720 4032 rndmvto [/space] gs 2912 4032 rndmvto [/o] gs 3296 4032 rndmvto [/f] gs 3536 4032 rndmvto [/space] gs 3728 4032 rndmvto [/s] gs 4016 4032 rndmvto [/u] gs 4400 4032 rndmvto [/c] gs 4736 4032 rndmvto [/r] gs 4976 4032 rndmvto [/o] gs 5360 4032 rndmvto [/s] gs 5648 4032 rndmvto [/e] gs 5984 4032 rndmvto [/comma] gs 6176 4032 rndmvto [/space] gs 6368 4032 rndmvto [/C] gs 7346 4032 rndmvto [/H] gs 8409 4032 rndmvto [/O] gs 9427 4032 rndmvto [/comma] gs 9619 4032 rndmvto [/space] gs 9811 4032 rndmvto [/a] gs 10147 4032 rndmvto [/n] gs 445 ns 6863 4224 rndmvto [/one] gs 7085 4224 rndmvto [/two] gs 7942 4224 rndmvto [/two] gs 8164 4224 rndmvto [/two] gs 8952 4224 rndmvto [/one] gs 9174 4224 rndmvto [/one] gs 768 ns 10531 4032 rndmvto [/d] gs 10531 4032 rndmvto [/d] gs 10915 4032 rndmvto [/space] gs 11107 4032 rndmvto [/two] gs 11491 4032 rndmvto [/zero] gs 11875 4032 rndmvto [/zero] gs 12259 4032 rndmvto [/period] gs 12451 4032 rndmvto [/space] gs 12643 4032 rndmvto [/g] gs 13027 4032 rndmvto [/space] gs 13219 4032 rndmvto [/o] gs 13603 4032 rndmvto [/f] gs 13843 4032 rndmvto [/space] gs 14035 4032 rndmvto [/w] gs 14579 4032 rndmvto [/a] gs 14915 4032 rndmvto [/t] gs 15123 4032 rndmvto [/e] gs 15459 4032 rndmvto [/r] gs 15699 4032 rndmvto [/question] gs 16035 4032 rndmvto [/space] gs -16 5184 rndmvto [/b] gs 368 5184 rndmvto [/parenright] gs 608 5184 rndmvto [/space] gs 800 5184 rndmvto [/W] gs 1520 5184 rndmvto [/h] gs 1904 5184 rndmvto [/a] gs 2240 5184 rndmvto [/t] gs 2448 5184 rndmvto [/space] gs 2640 5184 rndmvto [/i] gs 2848 5184 rndmvto [/s] gs 3136 5184 rndmvto [/space] gs 3328 5184 rndmvto [/t] gs 3536 5184 rndmvto [/h] gs 3920 5184 rndmvto [/e] gs 4256 5184 rndmvto [/space] gs 4448 5184 rndmvto [/a] gs 4784 5184 rndmvto [/c] gs 5120 5184 rndmvto [/t] gs 5328 5184 rndmvto [/u] gs 5712 5184 rndmvto [/a] gs 6048 5184 rndmvto [/l] gs 6256 5184 rndmvto [/space] gs 6448 5184 rndmvto [/f] gs 6688 5184 rndmvto [/r] gs 6688 5184 rndmvto [/r] gs 6928 5184 rndmvto [/e] gs 7264 5184 rndmvto [/e] gs 7600 5184 rndmvto [/z] gs 7936 5184 rndmvto [/i] gs 8144 5184 rndmvto [/n] gs 8528 5184 rndmvto [/g] gs 8912 5184 rndmvto [/space] gs 9104 5184 rndmvto [/p] gs 9488 5184 rndmvto [/o] gs 9872 5184 rndmvto [/i] gs 10080 5184 rndmvto [/n] gs 10464 5184 rndmvto [/t] gs 10672 5184 rndmvto [/space] gs 10864 5184 rndmvto [/o] gs 11248 5184 rndmvto [/f] gs 11488 5184 rndmvto [/space] gs 11680 5184 rndmvto [/t] gs 11888 5184 rndmvto [/h] gs 12272 5184 rndmvto [/e] gs 12608 5184 rndmvto [/space] gs 12800 5184 rndmvto [/s] gs 13088 5184 rndmvto [/o] gs 13472 5184 rndmvto [/l] gs 13680 5184 rndmvto [/u] gs 14064 5184 rndmvto [/t] gs 14272 5184 rndmvto [/i] gs 14480 5184 rndmvto [/o] gs 14864 5184 rndmvto [/n] gs 15248 5184 rndmvto [/question] gs -32 6336 rndmvto [/G] gs 512 6336 rndmvto [/i] gs 720 6336 rndmvto [/v] gs 1104 6336 rndmvto [/e] gs 1440 6336 rndmvto [/n] gs 1824 6336 rndmvto [/colon] gs 2032 6336 rndmvto [/space] gs 2224 6336 rndmvto [/C] gs 3202 6336 rndmvto [/H] gs 445 ns 2719 6528 rndmvto [/one] gs 2941 6528 rndmvto [/two] gs 3798 6528 rndmvto [/two] gs /thick 0 def /th { dup setlinewidth /thick xdef } bdef 38 th /sol { [] 0 setdash } bdef /dsh { [ exch 3 div dup .6 mul ] 0 setdash } bdef /dot { [ thick 3 -1 roll 5 div ] 0 setdash } bdef sol 1968 11430 rndmvto 2435 0 rlineto stroke 4020 6528 rndmvto [/two] gs 4020 6528 rndmvto [/two] gs 4808 6528 rndmvto [/one] gs 5030 6528 rndmvto [/one] gs 3617 10793 rndmvto [/o] gs 768 ns 4265 6336 rndmvto [/O] gs -80 7488 rndmvto [/one] gs 304 7488 rndmvto [/seven] gs 688 7488 rndmvto [/period] gs 880 7488 rndmvto [/one] gs 1264 7488 rndmvto [/space] gs 1456 7488 rndmvto [/g] gs -16 8640 rndmvto [/two] gs 368 8640 rndmvto [/zero] gs 752 8640 rndmvto [/zero] gs 1136 8640 rndmvto [/period] gs 1328 8640 rndmvto [/space] gs 1520 8640 rndmvto [/g] gs 1904 8640 rndmvto [/space] gs 2096 8640 rndmvto [/w] gs 2640 8640 rndmvto [/a] gs 2976 8640 rndmvto [/t] gs 3184 8640 rndmvto [/e] gs 3520 8640 rndmvto [/r] gs 1648 11638 rndmvto [/space] gs 1997 11138 rndmvto [/hyphen] gs 2237 11138 rndmvto [/one] gs 2621 11138 rndmvto [/period] gs 2813 11138 rndmvto [/eight] gs 3197 11138 rndmvto [/six] gs 3862 11138 rndmvto [/C] gs 2881 12222 rndmvto [/m] gs -16 13182 rndmvto [/a] gs 320 13182 rndmvto [/parenright] gs 720 13182 rndmvto [/m] gs 768 /Symbol f1 0 9792 rndmvto [/Delta] gs 768 /Times-Italic f1 464 9792 rndmvto [/t] gs 0 11638 rndmvto [/K] gs 512 11638 rndmvto [/f] gs 445 ns 780 9984 rndmvto [/f] gs 768 /Symbol f1 1221 9792 rndmvto [/equal] gs 1024 11638 rndmvto [/equal] gs 768 /Times-Roman f1 1797 9792 rndmvto [/question] gs 1312 13182 rndmvto [/o] gs 1312 13182 rndmvto [/o] gs 1696 13182 rndmvto [/l] gs 1904 13182 rndmvto [/a] gs 2240 13182 rndmvto [/r] gs 2480 13182 rndmvto [/space] gs 2672 13182 rndmvto [/m] gs 3264 13182 rndmvto [/a] gs 3600 13182 rndmvto [/s] gs 3888 13182 rndmvto [/s] gs 4176 13182 rndmvto [/space] gs 4368 13182 rndmvto [/o] gs 4752 13182 rndmvto [/f] gs 4992 13182 rndmvto [/space] gs 5184 13182 rndmvto [/s] gs 5472 13182 rndmvto [/u] gs 5856 13182 rndmvto [/g] gs 6240 13182 rndmvto [/a] gs 6576 13182 rndmvto [/r] gs 6816 13182 rndmvto [/space] gs 7008 13182 rndmvto [/i] gs 7216 13182 rndmvto [/s] gs 7504 13182 rndmvto [/space] gs 7696 13182 rndmvto [/three] gs 8080 13182 rndmvto [/four] gs 8464 13182 rndmvto [/two] gs 8848 13182 rndmvto [/period] gs 9040 13182 rndmvto [/three] gs 9424 13182 rndmvto [/four] gs 9808 13182 rndmvto [/g] gs 10192 13182 rndmvto [/space] gs 10384 13182 rndmvto [/s] gs 10672 13182 rndmvto [/o] gs 11056 13182 rndmvto [/space] gs 11248 13182 rndmvto [/o] gs 11632 13182 rndmvto [/u] gs 12016 13182 rndmvto [/r] gs -16 14834 rndmvto [/c] gs 320 14834 rndmvto [/o] gs 704 14834 rndmvto [/n] gs 1088 14834 rndmvto [/v] gs 1472 14834 rndmvto [/e] gs 1808 14834 rndmvto [/r] gs 6256 14626 rndmvto 2602 0 rlineto stroke 0 16670 rndmvto 1703 0 rlineto stroke 2048 14834 rndmvto [/s] gs 2048 14834 rndmvto [/s] gs 2336 14834 rndmvto [/i] gs 2544 14834 rndmvto [/o] gs 2928 14834 rndmvto [/n] gs 3312 14834 rndmvto [/space] gs 3504 14834 rndmvto [/f] gs 3744 14834 rndmvto [/a] gs 4080 14834 rndmvto [/c] gs 4416 14834 rndmvto [/t] gs 4624 14834 rndmvto [/o] gs 5008 14834 rndmvto [/r] gs 5248 14834 rndmvto [/space] gs 5440 14834 rndmvto [/i] gs 5648 14834 rndmvto [/s] gs 5936 14834 rndmvto [/space] gs 6317 14334 rndmvto [/three] gs 6701 14334 rndmvto [/four] gs 7085 14334 rndmvto [/two] gs 7469 14334 rndmvto [/period] gs 7661 14334 rndmvto [/three] gs 8045 14334 rndmvto [/four] gs 8429 14334 rndmvto [/g] gs 6973 15418 rndmvto [/m] gs 7565 15418 rndmvto [/o] gs 7949 15418 rndmvto [/l] gs 1274 16378 rndmvto [/g] gs 659 17462 rndmvto [/one] gs -19 16378 rndmvto [/one] gs 365 16378 rndmvto [/seven] gs 941 16378 rndmvto [/one] gs 2708 17462 rndmvto [/three] gs 3092 17462 rndmvto [/four] gs 3476 17462 rndmvto [/two] gs 4052 17462 rndmvto [/three] gs 4436 17462 rndmvto [/four] gs 749 16378 rndmvto [/period] gs 3860 17462 rndmvto [/period] gs 768 /Symbol f1 1378 16522 rndmvto [/slash] gs 768 /Times-Italic f1 1943 16878 rndmvto [/X] gs 3402 16378 rndmvto [/m] gs 3946 16378 rndmvto [/o] gs 4330 16378 rndmvto [/l] gs 2647 16670 rndmvto 2663 0 rlineto stroke 0 18874 rndmvto 3882 0 rlineto stroke 768 /Symbol f1 4969 17606 rndmvto [/slash] gs 4969 17606 rndmvto [/slash] gs 5502 16878 rndmvto [/equal] gs 768 /Times-Italic f1 4881 17462 rndmvto [/g] gs 8414 16878 rndmvto [/m] gs 8958 16878 rndmvto [/o] gs 9342 16878 rndmvto [/l] gs 9774 16878 rndmvto [/s] gs 10062 16878 rndmvto [/u] gs 10446 16878 rndmvto [/g] gs 10830 16878 rndmvto [/a] gs 11214 16878 rndmvto [/r] gs 2509 18582 rndmvto [/m] gs 3053 18582 rndmvto [/o] gs 3437 18582 rndmvto [/l] gs 1517 19666 rndmvto [/g] gs 2077 19666 rndmvto [/w] gs 2589 19666 rndmvto [/a] gs 2973 19666 rndmvto [/t] gs 3181 19666 rndmvto [/e] gs 3517 19666 rndmvto [/r] gs 4122 19082 rndmvto [/X] gs 6535 18582 rndmvto [/g] gs 768 /Times-Roman f1 6110 16878 rndmvto [/zero] gs 6686 16878 rndmvto [/zero] gs 7070 16878 rndmvto [/five] gs 7454 16878 rndmvto [/zero] gs 7838 16878 rndmvto [/zero] gs 205 18582 rndmvto [/zero] gs 781 18582 rndmvto [/zero] gs 1165 18582 rndmvto [/five] gs 1549 18582 rndmvto [/zero] gs 1933 18582 rndmvto [/zero] gs 45 19666 rndmvto [/two] gs 429 19666 rndmvto [/zero] gs 813 19666 rndmvto [/zero] gs 4807 18582 rndmvto [/one] gs 5191 18582 rndmvto [/zero] gs 5575 18582 rndmvto [/zero] gs 5959 18582 rndmvto [/zero] gs 6494 16878 rndmvto [/period] gs 589 18582 rndmvto [/period] gs 1197 19666 rndmvto [/period] gs 4826 18874 rndmvto 4074 0 rlineto stroke 9716 18874 rndmvto 5130 0 rlineto stroke 768 /Times-Italic f1 7095 18582 rndmvto [/w] gs 7095 18582 rndmvto [/w] gs 7607 18582 rndmvto [/a] gs 7991 18582 rndmvto [/t] gs 8199 18582 rndmvto [/e] gs 8535 18582 rndmvto [/r] gs 6727 19666 rndmvto [/k] gs 7063 19666 rndmvto [/g] gs 11681 18582 rndmvto [/m] gs 12225 18582 rndmvto [/o] gs 12609 18582 rndmvto [/l] gs 13041 18582 rndmvto [/s] gs 13329 18582 rndmvto [/u] gs 13713 18582 rndmvto [/g] gs 14097 18582 rndmvto [/a] gs 14481 18582 rndmvto [/r] gs 10961 19666 rndmvto [/k] gs 11297 19666 rndmvto [/g] gs 11857 19666 rndmvto [/w] gs 12369 19666 rndmvto [/a] gs 12753 19666 rndmvto [/t] gs 12961 19666 rndmvto [/e] gs 13297 19666 rndmvto [/r] gs 17566 19082 rndmvto [/m] gs 464 21420 rndmvto [/t] gs 2098 21420 rndmvto [/K] gs 445 ns 780 21612 rndmvto [/f] gs 768 /Times-Roman f1 6215 19666 rndmvto [/one] gs 9761 18582 rndmvto [/zero] gs 10337 18582 rndmvto [/two] gs 10721 18582 rndmvto [/five] gs 11105 18582 rndmvto [/zero] gs 15646 19082 rndmvto [/zero] gs 16222 19082 rndmvto [/two] gs 16606 19082 rndmvto [/five] gs 16990 19082 rndmvto [/zero] gs 768 /Symbol f1 9092 19082 rndmvto [/equal] gs 15038 19082 rndmvto [/equal] gs 1221 21420 rndmvto [/equal] gs 768 /Times-Roman f1 10145 18582 rndmvto [/period] gs 16030 19082 rndmvto [/period] gs 1813 21420 rndmvto [/parenleft] gs 768 /Symbol f1 0 21420 rndmvto [/Delta] gs 5511 21212 rndmvto 2435 0 rlineto stroke 8890 21212 rndmvto 2570 0 rlineto stroke 445 /Times-Italic f1 2727 21612 rndmvto [/f] gs 2727 21612 rndmvto [/f] gs 14600 21075 rndmvto [/o] gs 768 ns 3898 21420 rndmvto [/m] gs 8186 21420 rndmvto [/X] gs 10855 20920 rndmvto [/m] gs 14896 21420 rndmvto [/C] gs -32 22964 rndmvto [/b] gs 768 /Times-Roman f1 3021 21420 rndmvto [/parenright] gs 3613 21420 rndmvto [/parenleft] gs 4487 21420 rndmvto [/parenright] gs 9319 20920 rndmvto [/period] gs 13220 21420 rndmvto [/period] gs 381 22964 rndmvto [/parenright] gs 768 /Symbol f1 4887 21420 rndmvto [/equal] gs 11652 21420 rndmvto [/equal] gs 12260 21420 rndmvto [/minus] gs 768 /Times-Roman f1 5540 20920 rndmvto [/hyphen] gs 5780 20920 rndmvto [/one] gs 6164 20920 rndmvto [/period] gs 6356 20920 rndmvto [/eight] gs 6740 20920 rndmvto [/six] gs 7405 20920 rndmvto [/C] gs 6424 22004 rndmvto [/m] gs 781 22964 rndmvto [/f] gs 1021 22964 rndmvto [/r] gs 1261 22964 rndmvto [/e] gs 1597 22964 rndmvto [/e] gs 1933 22964 rndmvto [/z] gs 2269 22964 rndmvto [/i] gs 2477 22964 rndmvto [/n] gs 2861 22964 rndmvto [/g] gs 3245 22964 rndmvto [/space] gs 445 ns 7160 20575 rndmvto [/o] gs 768 ns 8935 20920 rndmvto [/zero] gs 9511 20920 rndmvto [/two] gs 9895 20920 rndmvto [/five] gs 10279 20920 rndmvto [/zero] gs 9983 22004 rndmvto [/one] gs 12836 21420 rndmvto [/zero] gs 13412 21420 rndmvto [/four] gs 13796 21420 rndmvto [/six] gs 14180 21420 rndmvto [/five] gs 3437 22964 rndmvto [/p] gs 3437 22964 rndmvto [/p] gs 3821 22964 rndmvto [/o] gs 4205 22964 rndmvto [/i] gs 4413 22964 rndmvto [/n] gs 4797 22964 rndmvto [/t] gs 5005 22964 rndmvto [/space] gs 5197 22964 rndmvto [/o] gs 5581 22964 rndmvto [/f] gs 5821 22964 rndmvto [/space] gs 6013 22964 rndmvto [/t] gs 6221 22964 rndmvto [/h] gs 6605 22964 rndmvto [/e] gs 6941 22964 rndmvto [/space] gs 7133 22964 rndmvto [/s] gs 7421 22964 rndmvto [/o] gs 7805 22964 rndmvto [/l] gs 8013 22964 rndmvto [/n] gs 8397 22964 rndmvto [/space] gs 8589 22964 rndmvto [/equal] gs 9021 22964 rndmvto [/space] gs 9213 22964 rndmvto [/f] gs 9453 22964 rndmvto [/p] gs 9837 22964 rndmvto [/space] gs 10029 22964 rndmvto [/o] gs 10413 22964 rndmvto [/f] gs 10653 22964 rndmvto [/space] gs 10845 22964 rndmvto [/s] gs 11133 22964 rndmvto [/o] gs 11517 22964 rndmvto [/l] gs 11725 22964 rndmvto [/v] gs 12109 22964 rndmvto [/e] gs 12445 22964 rndmvto [/n] gs 12829 22964 rndmvto [/t] gs -16 24310 rndmvto [/f] gs 224 24310 rndmvto [/r] gs 464 24310 rndmvto [/e] gs 800 24310 rndmvto [/e] gs 1136 24310 rndmvto [/z] gs 768 /Symbol f1 13229 22964 rndmvto [/plus] gs 13853 22964 rndmvto [/Delta] gs 768 /Times-Italic f1 14317 22964 rndmvto [/t] gs 445 ns 14633 23156 rndmvto [/f] gs 768 /Times-Roman f1 1472 24310 rndmvto [/i] gs 1472 24310 rndmvto [/i] gs 1680 24310 rndmvto [/n] gs 2064 24310 rndmvto [/g] gs 2448 24310 rndmvto [/space] gs 2640 24310 rndmvto [/p] gs 3024 24310 rndmvto [/o] gs 3408 24310 rndmvto [/i] gs 3616 24310 rndmvto [/n] gs 4000 24310 rndmvto [/t] gs 4208 24310 rndmvto [/space] gs 4400 24310 rndmvto [/o] gs 4784 24310 rndmvto [/f] gs 5024 24310 rndmvto [/space] gs 5216 24310 rndmvto [/t] gs 5424 24310 rndmvto [/h] gs 5808 24310 rndmvto [/e] gs 6144 24310 rndmvto [/space] gs 6336 24310 rndmvto [/s] gs 6624 24310 rndmvto [/o] gs 7008 24310 rndmvto [/l] gs 7216 24310 rndmvto [/n] gs 7600 24310 rndmvto [/space] gs 7792 24310 rndmvto [/equal] gs 8384 24310 rndmvto [/zero] gs 8960 24310 rndmvto [/zero] gs 9344 24310 rndmvto [/zero] gs 9728 24310 rndmvto [/zero] gs 12441 24310 rndmvto [/zero] gs 13017 24310 rndmvto [/four] gs 13401 24310 rndmvto [/six] gs 13785 24310 rndmvto [/five] gs 8768 24310 rndmvto [/period] gs 11756 24310 rndmvto [/parenleft] gs 12825 24310 rndmvto [/period] gs 15074 24310 rndmvto [/parenright] gs 445 /Times-Italic f1 10148 23965 rndmvto [/o] gs 14205 23965 rndmvto [/o] gs 768 ns 10444 24310 rndmvto [/C] gs 14501 24310 rndmvto [/C] gs 768 /Symbol f1 11164 24310 rndmvto [/plus] gs 12025 24310 rndmvto [/minus] gs 15474 24310 rndmvto [/equal] gs 16082 24310 rndmvto [/minus] gs 16082 24310 rndmvto [/minus] gs 768 /Times-Roman f1 16658 24310 rndmvto [/zero] gs 17234 24310 rndmvto [/four] gs 17618 24310 rndmvto [/six] gs 18002 24310 rndmvto [/five] gs 17042 24310 rndmvto [/period] gs 445 /Times-Italic f1 18422 23965 rndmvto [/o] gs 768 ns 18718 24310 rndmvto [/C] gs end MTsave restore d MATH D@DSMT5MacRomanTimesSymbolCourierMT Extra"OED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Sample Problem 14-3 page 439a) What is the freezing point depression of water in a solution of 17.1 g of sucrose, C 12 H 22 O 11 , and 200. g of water? b) What is the actual freezing point of the solution?Given: C 12 H 22 O 11 17.1 g200. g waterDt f ==?Kf==  -1.86 o Cma)molar mass of sugar is 342.34g so ourconversion factor is  342.34gmol 17.1g 1X mol342.34g ==0.0500molsugar 0.0500mol200.gwaterX 1000gwater1kg== 0.250molsugarkgwater==0.250mDt f ==(K f )(m)== -1.86 o CmX 0.250m1=="-0.465 o Cb)freezing point of the soln = fp of solvent++Dt f freezing point of the soln =0.000 o C++("-0.465 o C)=="-0.465 o C