cahtt proportion

7/27/2019 Cahtt Proportion

1/12

96


2/12

97

5.

APPLIED PROPORTION

!"#$%&'()*#+)(,-.%,#/(001,2

3'4#52465.,422#16#7)171)8%1,#%,#()&'%84&85)(.

*42%9,#%2#615,*4*#571,#8'4#7)40%24#8'(8#1!:4&82#()4

!4(58%65.#*54#81#&4)8(%,#7'"2%&(.#7)174)8%42#8'(8#()4

04(25)(!.4#(,*#8'4)461)4#(!.4#81#!4#)47)1*5&4*;#3'%2

%*5(.#1)#&5.85)4;

@,#A11-#@=# B'(784)# @@=# /4&8%1,# C# 16#D4

4."#74)&4%>4*M

(,*#0(8'40(8%&(.#1)*4)#LN'%&'#0("#1)#,18#!4#>%25K

(.."#74)&478%!.4#1)#)4.(84*#81#8'4#8')44K*%04,2%1,(.4O74)%4,&4#16#()&'%84&85)4M;#E%25(.#1)*4)#%2#8'4)461)4

7'4,104,1.19%&(.=#)(8'4)#8'(,#0(8'40(8%&(.=#%,#,(K

85)4;

%4N%,9#8'4#1!:4&82#6)10

*%664)4,8#(,9.42;#3'4#71N4)#16#)4&19,%TK

%,9#2%0%.()#2'(742#%2#(&?5%)4*#>4)"#4()."

%,#.%64=#(,*#%2#1,4#1,#N'%&'#N4#.()94."

*474,*#%,#6%,*%,9#15)#N("#(!158;#3'4#24&K

1,*#)4.(8%1,2'%7#R4(2%."#)4&19,%T4*#!"#8'4

4"4S#%2#8'(8#16#1!:4&82#'(>%,9#8'4#2(04#2%T4

(2#N4..#(2#8'4#2(04#2'(74=#!58#8'4#)4&19K

,%8%1,# 16# 8'%2#*40(,*2#&107()(8%>4."

6(>15)(!.4# &1,*%8%1,2;#U4# &(,# 244# (8# (

9.(,&4#8'(8#8'4#25,#(,*#011,#()4#16#8'4

2(04#2'(74=#!58#6)10#8'4#4>%*4,&4#16#15)

4"42#(.1,4#N4#0%9'8#!4#840784*#81#8'%,-

8'(8#8'4"#N4)4#16#8'4#2(04#2%T4#(2#N4..V#%,

.11-%,9#(8#!5%.*%,92=#'1N4>4)=#8'4#4"4#&(,

)4&19,%T4# 8'%2#)4.(8%1,2'%7# 6(%)."#4(2%."

L/&'1.6%4.*=#WM;

3'424#8N1#*%664)%,9#&1,*%8%1,2Q#*%664)4,8#2%T4X

2(04#2'(74#(2#177124*#81#2(04#2%T4X2(04#2'(74#()4

8'4#815&'281,42#16#&10712%8%1,#8'(8#95%*4#(,#4664&K

8%>4#524#16#7)171)8%1,;

3'4#524#16#1!:4&82#'(>%,9#8'4#2(04#2%T4#(,*2'(74# )425.82#%,# 2"0048)";#4)8'4.422=

2"0048)"#%2#4224,8%(.#81#*42%9,#!4&(524#%8#7)1>%*42#(

6)(04N1)-#571,#N'%&'#8'4#()&'%84&8#&(,#!5%.*;#@,

1,4#24,24=#8'4#&1,*%8%1,2#16#4?5(.%8"#L1)#*5(.%8"M#&)4K

(84*#!"#2"0048)"#()4#(,(.19152#81#8'4#0484)#16#(

052%&(.#&10712%8%1,Q#28(8%(,*#4>4,#!1)%,9#N'4,

8(-4,#(.1,4=#!58# &)4(8%,9# (#,4&&422()"#615,*(8%1,61)#8'4#&10712%8%1,;

@,#&1,8)(28#81#1!:4&82#'(>%,9#8'4#2(04#2%T4#(,*

2'(74=#/&'1.6%4.*#*42&)%!42#1!:4&82#16#*%664)4,8#2%T4

(,*#2(04#2'(74#L84)04*#2%0%.()M#%,#8'4#61..1N%,9

0(,,4)Q


3/12

98

3PH#@B%2%!.4#1)*4)

!"# 8'4# )4748%8%1,# 16# 2%0%.()# 2'(742

L/&'1.6%4.*=#\M;@6#2"0048)"#%,>1.>42#8'4#28(8%&=#4?5(.#*%>%2%1,

16#(#9%>4,#1!:4&8=#45)"8'0"#%2#&'()(&84)%T4*#!"#(2"0K

048)%&(.#*%>%2%1,2#)425.8%,9# %,#8'4#01>404,8#(,*

24,24#16#(&8%1,#615,*#%,#8'4#!428#N1)-2#16#()8#(,*

()&'%84&85)4;#U%8'%,#8'4#052%&(.#(,(.19"=#45)"8'0"

%2#8'4#)'"8'0#8'(8#%2#.("4)4*#1>4)#8'4#0484)#L2"0K

048)"M#%,#1)*4)#81#!)%,9#052%Q#.%64;#3'4#7175.()

52(94#16# 8'4# 84)0#F7)171)8%1,J# 525(.."# )464)2# 81

45)"8'0"#)(8'4)#8'(,#2"0048)";

@8#%2#%071)8(,8#81#5,*4)28(,*#8'(8#7)171)8%1,

(.1,4#N%..#,18#7)1*5&4#!4884)=#01)4#!4(58%65.=#1)

01)4#5,%6%4*#!5%.*%,92;#P1N4>4)=#N'4,#58%.%T4*#(2#(

'()01,%T%,9#(94,8#61)#*%27()(84#4.404,82=#7)171)K

8%1,#*)(0(8%&(.."#%,&)4(242#8'4#&'(,&42#16#(#*42%9,4)

&)4(8%,9#(,#4O&4..4,8#!5%.*%,9;

]@YH4)%8"#(,*#72"&'1.19%&(.#*%2&1061)8#%,'4)4,8

%,#&1,*%8%1,2#16#*5(.%8";#B1,2%*4)4*#1,4K*%04,2%1,K

(.."=#%8#%07.%42#*%>%*%,9#(#.%,4#25&'#8'(8#1,4#7%4&4#'(2

&.4()#*10%,(,&4#1>4)#8'4#18'4)#!58#*142#,18#1>4)K

N'4.0#%8=#8'52#428(!.%2'%,9#(#)4.(8%1,2'%7#16#'()01,"

!48N44,#8'4#8N1;

Y1N#8'(8#8'4#8')44#*%664)4,8#N("2#16#*%>%*%,9

.%,42#'(>4#!44,#%,8)1*5&4*=#%8#)40(%,2#81#!4#*4&%*4*

4O(&8."#N'4)4#(.1,9#8'4#.4,98'#16#8'424#.%,42#8'4

*%>%2%1,2#()4#81#!4#7.(&4*;#$474(84*#)(8%12#N%8'%,

(,#()&'%84&85)(.#&10712%8%1,#%2#8'4#4224,&4#16#(,"

7)171)8%1,(.#2"2840;#3'4#&'1%&4#16#(#7()8%&5.()#7)1K

71)8%1,(.#2"2840#N%..#248#8'4#)(8%1#16#1,4#24904,8#1

8'4#.%,4#81#8'4#18'4)#61)#!18'#75,&85(8%1,#(,*#*%6K

64)4,8%(8%1,;# @8# %2# 24.6K4>%*4,8# 8'(8# 8'4# )(8%1# 1

2"0048)"#%2#CQC;#4#!44,

407.1"4*#8')159'158#8'4#N1).*#(8#>()%152#8%042#(,*

N%8'#>()"%,9#*49)442#16# 25&&422;#3'4# 25&&422#16# (

7)171)8%1,(.#2"2840#'(2#05&'#81#N%8'#%82#(!%.%8"#81


4/12

99

%*4)2

+@bc$H#W;`


5/12

100

3PH#@B%&4;#@8#&(,#(.21#!4#248#81#*%>%*4#.%,42#(,*#&%)&.42#%,81

24904,82#1)#()&2;

BBBBB%4N

8'%2#(2#(#01*4),#!5%.*%,9=#8'4#*401,28)(!.4#7)42K

4,&4#16#&.(22%&(.#7)171)8%1,%,9#%2#5,4O74&84*;

@,#8'4#*42%9,#16#8'4#I(.(&4#16#+%,4#


6/12

101

4#94,%52#2500()%T4*#!"#'%2#!4.%46#8'(8

8'4#()8%28#0528#F&())"#'%2#&107(2242#%,#'%2#4"42J#)(8'4)

8'(,#%,#'%2#'(,*2;

3'4#&1.50,2#16#!18'#8'4#0(:1)#(,*#0%,1)#1)K

*4)2#()4#75,&85(84*#!"#4,8(!.(85)42#16#)4.(84*#)(8%12;

@,#8'4#0(:1)#1)*4)=# 8'%2#75,&85(8%1,#%,&.5*42#8'4

74*428(.=#(,*#(,#(**%8%1,(.#75,&85(8%1,#247()(842#8'4&1.50,#6)10#8'4#74*428(.;

1.>%,9

+@bc$H#W;f a%&'4.(,94.1Q#B(7%81.%,4#I(.(&4=#$104#L*42%9,4*#CW_gM


7/12

102

3PH#@B4)K)5,J#524*

81#)47)424,8#2.174;#3'%2#'%9'.%9'82#8'4#(!%.%8"#16#(,"

*%(91,(.#.%,4#81#*42&)%!4#(#)4&8(,9.4;#3'4)461)4=#!18'

8'4#2.174#16#8'4#*%(91,(.#(,*#%82#(,9.4#6)10#8'4#'1K

)%T1,#&(,#!4#524*#81#4O7)422#(#7()8%&5.()#)4&8(,9.4

L+%95)4#W;eM;

$HB@I$$HB@I$$HB@I$$HB@I$$HB@I$GBGBGBGBGB4,

)4&8(,9.4#)47)424,82#8'4#250#16#%82#9,101,#(,*#%82

)4&%7)1&(.;

D%2&1>4)%,9#8'4#)4&%7)1&(.#(,*#8'4#9,101,#1

(,"#9%>4,#)4&8(,9.4#(..1N2#8')44#)4.(84*#)4&8(,9.42

81#!4#%*4,8%6%4*#(.1,9#8'4#274&8)50=#7)1*5&%,9#(

)5*%04,8()"#2&(.4#16#)4&8(,9.42#,18#5,.%-4#8'4#-4"2

16#(#7%(,1#L+%95)4#W;CCM;

+@bc$H#W;g /74&8)50#16#)4&8(,9.42


8/12

103

4#%82

28(8%&'()(&84)%28%(2#(#*42%9,#811.;#G,."#8'4#b1.*4,

/4&8%1,#'(2#(#2?5()4#9,101,#L+%95)4#W;C^M;

+5)8'4)01)4=# 8'4# 6(&8# 8'(8#(..# )4&8(,9.42#()4

&107124*#16#)4&%7)1&(.2#(,*#9,101,2#04(,2#8'(8

8'4"#&(,#!4#(99)49(84*#%,81#(**%8%>4#7)19)422%1,2;

H(&'#)4&8(,9.4#&(,#!4#4%8'4)#*%>%*4*#%,81#(#9,101,

(,*#(#)4&%7)1&(.=#1)#>%4N4*#(2#(#9,101,#1)#)4&%7)1K

&(.#16# 8'4#(*:(&4,8# )4&8(,9.4# %,# 8'4#7)19)422%1,;

+@bc$H#W;e D%(91,(.#16#(#)4&8(,9.4

+@bc$H# W;Ch< $4&%7)1&(.#16#(#)4&8(,9.4 +@bc$H#W;ChA b,101,#16#(#)4&8(,9.4

+@bc$H#W;CC /74&8)50#16#)4&8(,9.42#N%8'#)4&%7)1&(.#(,*#9,101,#16#(#7()8%&5.()#)4&8(,9.4#%*4,8%6%4*


9/12

104

3PH#@B4#16#8'4#&1,K

&478#16#4?5(.%8"X*5(.%8"#L+%95)4#W;C`M;

$485),%,9#81#8'4#,18%1,#16#%*4,8%6"%,9#(#F2&(.4J

16#)4.(84*#)4&8(,9.42#81#N1)-#N%8'=#8'4#(**%8%1,#1

8'4##)4&8(,9.4#81#8'4#)474)81%)4#16#(..1N2#61)#8'4

&)4(8%1,#16#(#L1)#b1.*4,#/4&8%1,M#24)%42#16#)4&8K

(,9.42;#Y184#8'(8#4>4)"#18'4)#)4&8(,9.4#%,#8'4#24)%42

7()8%&%7(842# %,# 8'4# (**%8%>4# 7)19)422%1,# L+%95)4

W;CWM;

4#7)19)422%1,


10/12

105


11/12

106

3PH#@B(8%1,#7)1:4&8%1,2#&(,

)425.8#%,#'()01,%152# (,*#%,*44*#!4(58%65.# 8')44K

*%04,2%1,(.#1!:4&82#(,*#27(&42;

+@bc$H#W;Cf b1.*4,#24&8%1,#(**%8%>4#7)19)422%1,

A@A]@Gb$%52=#*4#


12/12

107

cahtt proportion

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