Top 10k strings from Maths (1986)(Hill MacGibbon)(Tape 2 of 2 Side B).tzx in <root> / bin / z80 / software / Sinclair Spectrum Collection TOSEC.exe / Sinclair ZX Spectrum - Utilities & Educational / Sinclair ZX Spectrum - Utilities & Educational - [TZX] (TOSEC-v2007-01-01) /
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4 hint=hint+1 4 <8<<8D @<D 4 ,"e. Is the","transformation a","ROTATION"," (press 1)","or a REFLECTION?"," (press 2)",1 4 ( )"," ( )",1 3 ;"maps P into P 3 ;"The"'"image"'"of,"; 3 ;"Multiplying 3 ;" Answer the following questions,giving all answers to 3 sf. where necessary.": 3 ,"e."," BC=",3 3 ,"d."," Angle BCX,"," <BCX= 3 ,"b."," AX=",2 3 ,"a."," BX=",3 3 ,"Pr(1st is French)"," =7/20" 3 ,"Pr(1st a toffee)"," =5/12" 3 ,"7/20","",1 3 ,"5/12","",1 3 ,"1/5","",7 3 ,"1/3","",7 3 ,"1","",11 3 ,"-3","",8 3 ," Swap a and d.",1 3 ," Change signs.",1 3 ," BC=BX/ 2 | DD <TTxD 2 vctt=vctt+1 2 press key when ready 2 horizontal 2 hint=attmpts-1 2 hint=attmpts 2 h$+v$=g$+u$ 2 b$=" ": 2 a,qi1,qi2,qi3,qi4,qi5,qi6,qi7,qi8,qi9,qi10,qi11,qi12,qi13,qi14,qi15,qi16,qi17,qi18,qi19: 2 Programmed by Tony Topliss. 2 BCX=BX/XC"," = 2 BCX=BX/BC",3 2 BCX"," = 2 @ D< DTT@D 2 ;r;" out of ";a: 2 ;"enter units of answer: "; 2 ;"enter answer: "; 2 ;"UNITS!": 2 ;"Then change the 2 ;"QUESTIONS"; 2 ;"MATHEMATICS"; 2 ;"MATHEMATICS LEARNING MODULES"; 2 ;"Finally divide by 2 ;"CORRECT";: 2 ;"5 4"; 2 ;"0 3": 2 ;" To find the 2 ;" Thus the angle between 2 ;" First interchange 2 ;" Draw on your diagram any perpendicular lines that you think you will need to calculatethe bearing of B from S."'" Then press key to check for theeasiest.": 2 ;" Draw a diagram and then press key to check it before answeringthe following questions.": 2 ;" Do you wish to work through thenotes before you attempt the questions? Press Y/N. ": 2 ;" ": 2 ;" ": 2 999999999999999999999999999999999:888888899999999999999999989:999:8::8:88999999999999999999899999:8::8:8899999999999999999989999999999999999999999999999999999999888888888888<<<<<<<8888888888899888888888888<<<<<<<888888888889988<<<<<<<<<<<<<<<<<<<<<<<<<<<89988<<<<<<<<<<<<<<<<<<<<<<<<<<<89988<<<<<<<<<<<<<<<<<<<<<<<<<<<89988<<<<<<<<<<<<<<<<<<<<<<<<<<<899888888888888888888888888888888998888888::::::::::::::::8888888998888888::::::::::::::::8888888998888888::::::::::::::::88888889988888888888888888888888888888899888888888888888888888888888888998888888888888888888888888888889988888888888888888888888888888899888888888888888888888888888888998888888888888888888888888888889999999999999999999999999999999998888888888888888888888888888888888888888888888888888888888888888 2 . A number is chosen at random from:-"'"1, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7": 2 ,(only 1 of 6 2 2 ,"d."," (-4 )"," 2 ,"d."," ( )"," 2 ,"c.","Pr(5 or 7)=","","ENTER fraction;","Eg. 5/9 .",2 2 ,"c."," XC=",2 2 ,"c."," ( 0 -1)"," ( )"," ( )",1 2 ,"c."," (1 )"," 2 ,"c."," ( )"," 2 ,"c. The image of"," (0) ( )"," ( )=( )"," (5) ( )",1 2 ,"b.","Pr(2 or 3)=","","ENTER fraction;","Eg. 5/9 .",2 2 ,"b."," ( 0 )"," ( )"," ( )",1 2 ,"b."," (4 )"," 2 ,"b."," ( )"," 2 ,"b. The image of"," (5) ( 4)"," ( )=( )"," (0) ( )",1 2 ,"a.","The bearing of","B from S= 2 ,"a.","Pr(3 or 5)=","","ENTER fraction;","Eg. 5/9 .",2 2 ,"a."," ( )"," ( )"," ( )",1 2 ,"a."," (8 )"," 2 ,"a."," ( )"," 2 ,"Pr(2nd is Italian)"," =5/19" 2 ,"Pr(1st is German)"," =8/20" 2 ,"Pr(1st a mint)"," =3/12" 2 ,"8/20","",1 2 ,"5/19","",6 2 ,"5/11","",11 2 ,"3/7","",11 2 ,"3/12","",1 2 ,"3","",10 2 ,"2","",11 2 ,"2","",10 2 ,"1/4","",7 2 ,"1","",10 2 ,"-4","",8 2 ,"-2","",6 2 ,"-1","",7 2 ," Rotation." 2 ," Reflection." 2 ," Pr(5 or 7)","=Pr(5)+Pr(7)",2 2 ," Pr(3 or 5)","=Pr(3)+Pr(5)",2 2 ," Pr(2 or 3)","=Pr(2)+Pr(3)",2 2 ( )"," 2( 1)",2 2 ( )"," 2( 1)",1 2 ( )"," 2( )",2 2 ( )"," 2( )",1 2 "mathcode6" 2 "mathcode5" 2 "MODULESF" 2 "MODULESE" 2 ","","","",8 2 " ": 2 and the 2 When you see the message below,press @ to leave the module. 2 In this module you got:- answers correct without a hint. 2 If you need more help, work through the following sections in the PAN STUDY AID. 2 ENTER the number of the module you wish to work through:- (0 if you have finished with these modules) 2 Do you wish to work through thenotes again before you attempt the questions? Press Y/N. 2 To use Module again, press R Press S to STOP 2 10 2 1 |=2x6-3x4= 1 |=2x5-3x4=": 1 |=2x5-(-3)x4=": 1 y,x;a$;v$: 1 vval,g$,u$,x,y,nlsq: 1 translation 1 right angle 1 reflections 1 reflection 1 possibility set 1 perpendicular 1 mathcode6 X 1 mathcode5 X 1 favourable 1 determinant 1 base ABCD 1 attmpts,vval,g$,u$,x,y,nlsq: 1 The "'"transformation"'"is a ROTATION "'"through the "'"angle shown. 1 The "'"transformation "'"is a REFLECTION"'"in the line "'"shown. 1 Pr(more than 5)=_ 1 Pr(even)=_ 1 Pr(A or B)=Pr(A) 1 Pr(A and B)=Pr(A).Pr(B) 1 Pr(2 or 3)=_ 1 Pr(1 or 3)=_ 1 Pr(1 and H)= 1 MODULESF ALMOST READY 1 MODULESF > 1 MODULESF 1 MODULESE ALMOST READY 1 MODULESE > 1 MODULESE 1 F 1 E 1 Created with Ramsoft MakeTZX 1 CBX=XC/BX"," XC=BXx 1 CBX=BX/BC",3 1 CBX"," = 1 =( )"," (0) ( )",1 1 ;'''"28. Determinant and Inverse of 2 x 2 Matrices"''"29. Transformation Matrices"''"30. Finding the Matrix to Describe a Transformation": 1 ;'"22. Probability-Definition"''"23. Probability-Addition Rule"''"24. Probability-Product Rule"''"25. Trigonometry"''"26. Bearings"''"27. Trigonometry,3-Dimensional": 1 ;"we call the expression 1 ;"the probability that it is an even number, 1 ;"the image under"; 1 ;"since,"; 1 ;"of 0 0.6 -0.8": 1 ;"of 0"; 1 ;"c d 0 c": 1 ;"b -a"'"describe 1 ;"and,"'" 1 ;"and maps into ."; 1 ;"and ,we can write down the"''"matrix of the transformation.": 1 ;"a b 1 a"; 1 ;"What is 5 0.8 0.6"; 1 ;"What is 5";'" the image under"; 1 ;"We can combine many of these transformations.For example the image (x 1 ;"The required 1 -1"''"matrix is, 1 1": 1 ;"The addition of matrix 2"; 1 ;"TRIGONOMETRY,3-DIMENSIONAL": 1 ;"TRIGONOMETRY": 1 ;"TRANSFORMATION MATRICES": 1 ;"TO DESCRIBE A TRANSFORMATION": 1 ;"T"'''"etc."''"The complete possibility set is written;"'"(1,H),(2,H),(3,H),(4,H),(5,H), (6,H),(1,T),(2,T),(3,T),(4,T), (5,T),(6,T)": 1 ;"Similarly;"'" 1 ;"PROBABILITY-PRODUCT RULE": 1 ;"PROBABILITY-DEFINITION": 1 ;"PROBABILITY-ADDITION RULE": 1 ;"Module ";qu+27 1 ;"Module ";qu+21 1 ;"MATRICES": 1 ;"FINDING THE MATRIX"; 1 ;"DETERMINANT AND INVERSE OF 2 X 2"; 1 ;"BEARINGS": 1 ;"5 -4": 1 ;"5 4": 1 ;"4"'"denotes the"'"position vector"'"of the point P"'"relative to the"'"origin.": 1 ;"2x5-3x4"; 1 ;"2x5-(-3)x4= 1 ;"2, 2, 2, 1 ;"2 0 3 6"; 1 ;"2 4 2 -4 -5 0 1"; 1 ;"1 0"; 1 ;"1 d": 1 ;"1 1"'" into and"'" 0 1"''" 0 -1"'" into"'" 1 1": 1 ;"0.8 -0.6"; 1 ;"0.6 0.8": 1 ;"0 2"'"maps P into P 1 ;"0 2 4 8"; 1 ;"0 1"; 1 ;"0 -3"; 1 ;"0 b"; 1 ;"0 3"; 1 ;"-b a"'"describe 1 ;"-5 -3 2 3 1 0"'" Here, 1 ;" Where two events,A and B,are mutually exclusive and independent,"'" 1 ;" What are the possible outcomes when we throw a fair die and toss a fair coin?": 1 ;" To find the angle between a line and the base,draw a perpendicular from a point on the line to the base. Thus the angle between 1 ;" The matrix maps into"; 1 ;" The complete possibility set iswritten;"'"(1,H),(2,H),(3,H),(4,H),(5,H), (6,H),(1,T),(2,T),(3,T),(4,T), (5,T),(6,T)"''" Of these 12 outcomes,in 1 ;" The Product Rule is that if A and B are independent events,"'" 1 ;" The PROBABILITY of an event is defined as:-"; 1 ;" Similarly,"'" 1 ;" Pages 154-156.": 1 ;" Page 179.": 1 ;" Page 111.": 1 ;" Matrices of the form a b"; 1 ;" Look at this"'"rectangular box."'"If the base is"'" 1 ;" If we know the images of"; 1 ;" If we have a triangle containing a 1 ;" Given a 2 x 2 matrix 1 ;" Exercise 21, page 186.": 1 ;" Exercise 18c, page 165.": 1 ;" Exercise 13b, page 115.": 1 ;" Exercise 13a, page 111.": 1 ;" Every line 1 ;" Draw careful diagrams to solve the questions which will be given below, about the transformation matrices.": 1 ;" Draw careful diagrams to answerthe following questions.": 1 ;" Chapter 21.": 1 ;" Chapter 17 page 149.": 1 ;" Always check that,"; 1 ;" All matrices whose determinantsare 1 ;" 3 0 1 3 3 3"; 1 ;" 2 1 0 2 1 1"; 1 ;" 2 0 1 2 3 4"; 1 ;" 1 1 0 1 1 3"; 1 ;" 0 1 0 0 1 4"; 1 ;" 0 0 1 0 3 5"; 1 ;" The tansformation is a 1 ;" Pr(2 and H)= 1 ;" Choose a number at random from:-"'" 1, 2, 2, 2, 3, 3, 4, 4, 4, 4": 1 ;" 12 1 2 and a rotation through +45 degrees. 1 1,2,3,3,3,3,4,5,5, 1 ."'''"and those of the form a b"; 1 ."'"Fill in the"'"missing letter"'"in each of the"'"following:-": 1 ."'" In the triangle"'"ABC,BX is"'"perpendicular"'"to AC,AB=8cm,"'"<XBC=25 1 ."'" In the triangle"'"ABC,BX is"'"perpendicular"'"to AC,AB=7.5cm,"'"AC=10cm and"'"<BAC=51.2 1 ."'" In the triangle"'"ABC,BX is"'"perpendicular"'"to AC,AB=4cm,"'"AC=6cm and"'"<BAC=40 1 ."'" Find the"'"tangent of each"'"of the following"'"angles."''"(Enter the tangents"'"as fractions like"'"this:- 3/4.)": 1 ."'" A boat,B is 5km"'"from a rock,R on"'"a bearing of 240 1 ."'" A boat,B is 3km"'"from a rock,R on"'"a bearing of"'"140 1 ."'" Find the matrix that maps"''" 1 0 0 -1"'" into and into"'" 0 1 1 0": 1 ."'" Find the matrix that maps"''" 1 0 0 -1"'" into and into"'" 0 -1 1 0": 1 . Work out the inverses of the following matrices:-"; 1 . Work out the determinant of the following matrices:-"; 1 . Sweets are chosen from 1 . Books are chosen without replacement from a shelf containing 1 . A number is chosen at random from:-"'" 1, 2, 3, 5, 5, 7, 9": 1 . A number is chosen at randomfrom:-"''" 1, 2, 2, 3, 4, 5, 7, 8, 8, 10": 1 . A number is chosen at randomfrom:-"'" 1, 1, 1, 2, 2, 3, 4, 5": 1 . 1 ,we may only need to use the definition of 1 ,all"'"lines in the base"'"are 1 ,4,5,5,7,8,9,"''"the probability that it is a '3',written 1 ,"h. If the angle","between SC and","the base is z,"," 1 ,"g. If the angle","between SB and","the base is y,"," 1 ,"f. This rotates","through,"," degrees"," anticlockwise.",1 1 ,"f. This reflects","in,","x-axis (press 1)","y-axis (press 2)","y-x=0 (press 3)","y+x=0 (press 4)",1 1 ,"f. If the angle","between SA and","the base is x,"," 1 ,"e.","Pr(1st is German","& 2nd is Italian)","=8/20X",1 1 ,"e.","Pr(1st is German","& 2nd is Italian)","= X .",1 1 ,"e.","Pr(1st a mint","& 2nd a toffee)","=3/12X",1 1 ,"e.","Pr(1st a mint","& 2nd a toffee)","= X .",1 1 ,"e."," Pr(>2)= /8",1 1 ,"e."," Pr(>2)= /10",1 1 ,"e. If the angle","between RD and","the base is z,"," 1 ,"d.","Pr(1st is German","& 2nd is French)","=8/20X",1 1 ,"d.","Pr(1st is German","& 2nd is French)","= X .",1 1 ,"d.","Pr(1st a mint","& 2nd a mint)","=3/12X",1 1 ,"d.","Pr(1st a mint","& 2nd a mint)","= X .",1 1 ,"d."," | 1 ,"d."," Pr(>5)= /8",1 1 ,"d."," Pr(>5)= /10",1 1 ,"d."," ( 0 -1)"," ( )"," (-1 )",1 1 ,"d."," ( 0 -1)"," ( )"," ( 1 )",1 1 ,"d."," (-4 3)"," 1 ,"d. The image of"," (0) (-3)"," ( )=( )"," (5) ( )",1 1 ,"d. The image of"," (0) ( 3)"," ( )=( )"," (5) ( )",1 1 ,"d. The angle","between QD and","the base ABCD is","angle QD .",1 1 ,"d. If the angle","between RB and","the base is y,"," 1 ,"c.","Pr(even)= /8",1 1 ,"c.","Pr(even)= /10",1 1 ,"c.","Pr(1st is French","& 2nd is German)","=7/20X",1 1 ,"c.","Pr(1st is French","& 2nd is German)","= X .",1 1 ,"c.","Pr(1st a toffee","& 2nd a toffee)","=5/12X",1 1 ,"c.","Pr(1st a toffee","& 2nd a toffee)","= X .",1 1 ,"c."," | 1 ,"c."," XC=",2 1 ,"c."," (1 -3)"," 1 ,"c. The angle","between RD and","the base ABCD is","angle RD .",1 1 ,"c. If the angle","between RA and","the base is x,"," 1 ,"b.","The bearing of","S from B= 1 ,"b.","The bearing of","S from B= 1 ,"b.","Pr(1st is French","& 2nd is Italian)","=7/20X",1 1 ,"b.","Pr(1st is French","& 2nd is Italian)","= X .",1 1 ,"b.","Pr(1st a toffee","& 2nd a mint)","=5/12X",1 1 ,"b.","Pr(1st a toffee","& 2nd a mint)","= X .",1 1 ,"b."," | 1 ,"b."," Pr(5)= /8",1 1 ,"b."," Pr(5)= /10",1 1 ,"b."," (4 2)"," 1 ,"b. The angle","between RA and","the base ABCD is","angle RA .",1 1 ,"b. If the angle","between QD and","the base is z,"," 1 ,"a.","Pr(1st is French","& 2nd is French)","=7/20X",1 1 ,"a.","Pr(1st is French","& 2nd is French)","= X .",1 1 ,"a.","Pr(1st a toffee)","=",1 1 ,"a."," | 1 ,"a."," Pr(2)= /8",1 1 ,"a."," Pr(2)= /10",1 1 ,"a."," (8 -2)"," 1 ,"a. The image of"," (5) ( )"," ( )=( )"," (0) ( )",1 1 ,"a. The image of"," (5) ( )"," ( ) 1 ,"a. The angle","between RB and","the base ABCD is","angle RB .",1 1 ,"a. If the angle","between QC and","the base is y,"," 1 ,"[Only 11 left]","Pr(2nd a mint)"," =3/11" 1 ,"[Only 11 left,of","which 5 are","toffees]","Pr(2nd a toffee)"," =5/11" 1 ,"[Only 11 left,of","which 4 are","toffees]","Pr(2nd a toffee)"," =4/11" 1 ,"[Only 11 left,of","which 2 are","mints]","Pr(2nd a mint)"," =2/11" 1 ,"Work through the","problem a step","at a time.","<BRS=40 1 ,"Work through the","problem a step","a time.","<BRS=60 1 ,"There is 1 '5'","in set E."," Pr(5)=1/8" 1 ,"There is 1 '5'","in set E."," Pr(5)=1/10" 1 ,"There are no","numbers greater","than 5 in set E."," Pr(>5)=0/8" 1 ,"There are 7","numbers greater","than 2 in set E."," Pr(>2)=7/10" 1 ,"There are 6 even","numbers in set E."," Pr(even)=6/10" 1 ,"There are 4","numbers greater","than 5 in set E."," Pr(>5)=4/10" 1 ,"There are 3","numbers greater","than 2 in set E."," Pr(>2)=3/8" 1 ,"There are 3 even","numbers in set E."," Pr(even)=3/8" 1 ,"There are 2 '2's","in set E."," Pr(2)=2/8" 1 ,"There are 2 '2's","in set E."," Pr(2)=2/10" 1 ,"Swap a and d.",1 1 ,"SP=PR-1=1.5"," 1 ,"SP=PR-0.5=1.798"," 1 ,"Reflection in","the line;"," y+x=0" 1 ,"Pr(2nd is German)"," =8/19" 1 ,"Pr(2nd is French)"," =7/19" 1 ,"Pr(2nd is French)"," =6/19" 1 ,"Change signs.",1 1 ,"BD=5(Pythagoras)",1 1 ,"Anticlockwise","rotation through"," 90 degrees." 1 ,"AX=4x0.7660"," =3.064"," =3.06 to 3 sf." 1 ,"=3/11 + 3/11","=6/11" 1 ,"=3/11 + 2/11","=5/11" 1 ,"=2/7 + 1/7","=3/7" 1 ,"=2/11 + 3/11","=5/11" 1 ,"=1/7 + 2/7","=3/7" 1 ,"=1/7 + 1/7","=2/7" 1 ,"<BCX=90-<XBC"," =65 1 ,"90","",1 1 ,"8/19","",6 1 ,"71","",9 1 ,"7/19","",6 1 ,"7.89","cm",6 1 ,"7","",10 1 ,"65","",6 1 ,"6/19","",6 1 ,"6/11","",11 1 ,"6.55","cm",6 1 ,"6","",10 1 ,"5/11","",6 1 ,"5.85","cm",6 1 ,"5.30","cm",6 1 ,"5.06","cm",6 1 ,"47.8","",6 1 ,"41.2","",6 1 ,"4/11","",6 1 ,"4.70","cm",6 1 ,"4.59","cm",6 1 ,"4","",10 1 ,"3x6-4x5"," =-2" 1 ,"3x6-(-4)x5"," =38" 1 ,"3x6-(-4)x(-5)"," =-2" 1 ,"3x(-6)-(-4)x5"," =2" 1 ,"38","",6 1 ,"313","",9 1 ,"3/11","",6 1 ,"3.90","cm",6 1 ,"3.06","cm",6 1 ,"3","",11 1 ,"2x1-3x(-2)"," =8" 1 ,"251","",9 1 ,"2/7","",11 1 ,"2/11","",6 1 ,"2.94","cm",6 1 ,"2.57","cm",6 1 ,"2.14","cm",6 1 ,"1x8-2x3"," =2" 1 ,"1x4-(-2)x3"," =10" 1 ,"1x(-4)-(-3)x2"," =2" 1 ,"133","",9 1 ,"10","",5 1 ,"0.8x5+0.6x0"," =4" 1 ,"0.8x5+(-0.6)x0"," =4" 1 ,"0.8x0+0.6x5"," =3" 1 ,"0.8x0+(-0.6)x5"," =-3" 1 ,"0.6x5+0.8x0"," =3" 1 ,"0.6x5+(-0.8)x0"," =3" 1 ,"0.6x0+0.8x5"," =4" 1 ,"0.6x0+(-0.8)x5"," =-4" 1 ,"0","",10 1 ,"-3","",10 1 ,"-2","",8 1 ,"-2","",10 1 ,"-1","",4 1 ,"","","","","","So,bearing of","B from S=180+71"," =251 1 ,"","","","","","<BSP=90-43=47 1 ," XC=AC-AX",3 1 ," XC=AC-AX",2 1 ," <BCX=47.8 1 ," <BCX=41.2 1 ," =8x0.5736"," =4.589"," =4.59 to 3 sf." 1 ," =7.5x0.7793"," =5.845"," =5.85 to 3 sf." 1 ," =6.55 to 3 sf." 1 ," =4x0.6428"," =2.5712"," =2.57 to 3 sf." 1 ," =4.6995"," =4.70 to 3 sf." 1 ," =6-3.064"," =2.936"," =2.94 to 3 sf." 1 ," =2.139"," =2.14 to 3 sf." 1 ," =10-4.699"," =5.30 to 3 sf." 1 ," =7.889"," =7.89 to 3 sf." 1 ," =5.062"," =5.06 to 3 sf." 1 ," =3.903","=3.90cm to 3 sf." 1 ," 313 1 , there is no inverse, so singular matrices have no inverse.": 1 , since there are 3 1 , since there are 2 1 , since there are 1 , 2, 2, 2,"; 1 , (3 of the 6 2 1 , (2 of the 6 2 1 , only one of 1 , followed by a 1 ) of a point (x,y) is given by the above transformation:-;": 1 (translation 2 units parallel tothe x-axis then 1 unit parallel to the y-axis in a negative direction) 1 (rotation about the origin through +90 degrees in an anti- clockwise sense) 1 (reflection in the y-axis) 1 (enlargement factor 2) 1 (6,8),"''"since,"; 1 (-4,3)"''" 1 (-3,4)"''" 1 ( )"," 10( 1)",2 1 ( )"," 10( 1)",1 1 ( )"," 10( )",2 1 ( )"," 10( )",1 1 ( )"," 8( 2)",2 1 ( )"," 8( 2)",1 1 ( )"," 8( )",2 1 ( )"," 8( )",1 1 ","So,bearing of","B from S=133 1 "," =4.330 to 4 sf","RP=5 1 "," =2.5",8 1 "," =2.298 to 4 sf",8 1 "," =1.928 to 4 sf","RP=3 1 "," 5.301"," =1.103",1 1 "," 2.936"," =0.8757",1 1 "," 1.928"," =0.9326"," <SBP=43 1 "," 1.5"," =2.887"," <BSP=71 1 "," 0.9063",2 1 "," 0.7409",2 1 "," 0.6587",2 1 "'"where;"'" f=the number of equiprobable 1 "'"from R."'" A swimmer,S is"'"1km due South of"'"R.": 1 "'"(since there are 4 '3's out of 12 numbers)": 1 to thebase is 1 to find the required sides and angles.": 1 outcomes."''"The set of all equiprobable out-comes is denoted by 1 outcomes"''"and t=the 1 of them the die shows 1 of them the coin shows 1 of all 1 of a 2 x 2 matrix 1 mintswithout replacement."'" (ENTER fractions; eg. 6/18).": 1 in the line 1 from R."'" A swimmer,S is"'"0.5km due South"'"of R." 1 chocolates and 1 by matrix 0 -1"; 1 by matrix -1 0"; 1 by matrix 2 0"; 1 are called 1 and"'"<BAC=35 1 and is called the 1 Italian"'" (ENTER fractions; eg. 6/18).": 1 If a number is selected at random from,"''" 1,2, 1 German and 1 French books, 1 Find the matrix"'"which maps"; 1 '2's out of 10 numbers."; 1 This is an enlargement by a factor of 1 5 '2's or '3's but no number is both a '2' and a '3'.": 1 1 0 y 1"; 1 0 1 x 3"; 1 (taking care with 1 the 12 out-comes meets both requirements.": 1 the 12) Pr(6 and T)= 1 matrices.": 1 toffees, 1 the 2)Pr(even and H)= 1 12)": 1 12) Pr(>4 and H)= 1 6 2 12 1 12 1