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Sharp EL-5250 50Ç6= 15890700, 15890700. 35∏5= 38955840, The state lottery, Example, Result

Models: EL-5230 EL-5250

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Chapter 8: Application Examples

The state lottery

Example

The state you live in has two different numbers lotteries. In the first, you must pick 6 numbers between 1 and 50 in any order. In the second, you have to pick 5 numbers between 1 and 35, but you must pick them in the correct order. Which lottery gives you the better chance of winning?

In the first lottery, your chances of winning with one ticket are one in 50C6:

1. Press b 0 50 @ N 6 e.

50Ç6=

15890700.

Your chances of winning the second lottery with one ticket are one in

35P5:

2.Press 35 @ e 5 e.

Result

■Your chances are better in the first lottery.

15890700. 35∏5=

38955840.

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Page 116

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Sharp EL-5250, EL-5230 operation manual 50Ç6= 15890700, 15890700. 35∏5= 38955840, The state lottery, Example, Result

Contents

OPERATION MANUAL EL-5230 EL-5250PROGRAMMABLE SCIENTIFIC CALCULATOR Page Programmable Scientific Calculator IntroductionBefore You Get Started General InformationContents IntroductionChapter 1 Before You Get Started Chapter 2 General InformationChapter 3 Scientific Calculations Binary, Pental, Octal, Decimal and Hexadecimal Operations N-baseChapter 4 Statistical Calculations Chapter 5 Equation SolversChapter 6 Complex Number Calculations Chapter 7 ProgrammingChapter 8 Application Examples Purchasing with payment in n-month installmentsSome like it hot Celsius-Fahrenheit conversion How many digits can you remember?Appendix Introduction Operational Notes NORMAL MODE Key Notation in This ManualπRŒ˚-10 ExamplePage Resetting the calculator Before You Get StartedChapter Preparing to Use the CalculatorThe Hard Case Calculator Layout and Display Symbols Calculator layoutDisplay BUSY2ndF xy /r θSelecting a mode What you can do in each modeOperating Modes MODE-1 ƒNORMAL ⁄STAT ¤PROG ‹EQNA Quick Tour 8Œ‰3-7˚-10.5Turning the calculator on and off Entering and solving an expression110.4504172 Editing an expression8Œ‰3-7˚-10.5= 110.4504172 8Œ‰3-7˚-10.5 8Œ‰3-7˚-10.5 =NORMAL MODE 0. π NORMAL MODE 0. πRŒ Using variables0. 2„ÒR NORMAL MODENORMAL MODE Using simulation calculations ALGBπRŒ= 201.0619298 1ı3πRŒH1ı3πRŒH H=8 1ı3πRŒH= 670.20643281ı3πRŒH R=z 1ı3πRŒH= 678.5840132 Using the solver function AnsÒV 678.5840132 AnsÒV 678.5840132 V=1ı3πRŒHV=1ı3πRŒH H=z V=1ı3πRŒH V=z678.5840132 V=1ı3πRŒH H=z ExampleR¬ 678.5840132 L¬ Other features10.125 ¤STAT ‹RESET General InformationClearing the Entry and Memories Memory clear keyOverwrite mode and insert mode Editing and Correcting an Equation123456 Cursor keys3˚5+3˚2= 21. 3˚5+3˚2 3˚5+3˚2= 21. 3˚5+2 3˚5+3˚2= 35+23˚5+3˚2= Delete keyThe SET UP menu SET UP ƒDRG ⁄FSE ¤Setting the floating point numbers system in scientific notation Determination of the angular unitUsing Memories Using alphabetic charactersUsing global variables 0. 6ÒAUsing local variables 6. A=¬ƒA¡ 1.25E-5ÒA1 0.0000125Using variables in an equation or a program 0.0000125 A1=1ıA¡-1000A= ¬ƒA¡Using the last answer memory 3Œπ= 28.274333885Ans= 141.3716694 Global variable MA-L, N-Z Using memory in each modeMode z ALL DATA z z CLEARED! z z z Resetting the calculatorNORMAL MODE zALL DATA CL?z z YES¬DEL z z NO¬ENTERzNORMAL mode Scientific CalculationsArithmetic operations ChapterFunctions Constant calculationsjH$1.5 + Math menu Functions ƒabs⁄ipart ¤intFunction Key operationsResult 24∂ΩsecDifferential/Integral Functions Differential functionIntegral function ExampleKey operations ResultWhen performing integral calculations Random Function Random numbersRandom dice Random coinAngular Unit Conversions Chain CalculationsExample Key operationsFraction Calculations 4.8333333334.641588834 0∂31∂1.5∂Binary, Pental, Octal, Decimal, and Hexadecimal Operations N-base 11001.b Time, Decimal and Sexagesimal Calculations Coordinate Conversions r =x = y =Calculations Using Physical Constants Key operations Resultλc, p λc, nCalculations Using Engineering Prefixes 100 @j6k10 @j5e PrefixModify Function Solver Function TŒ=4πGMREntering and solving an equation Changing the value of variables and editing an equationA˚B=C˚D A˚B=C˚D D=zA˚B=C˚D A˚B=C˚DERROR Important notesCALCULATION A˚B=C˚DSimulation Calculation ALGB Entering an expression for simulation calculationChanging a value of variables and editing an expression πRŒH= 785.3981634BCsinA2 BCsinA2 B=z BCsinA2 C=5 BCsinA2= 7.5Simulate an equation for different values BCsinA22BCsinA2 B=z BCsinA2= 7.071067812BCsinA2= Chapter 3 Scientific CalculationsFiling Equations EQTN FILE ƒLOAD ⁄SAVE ¤DEL SAVETITLE?SAVERING Saving an equationTITLERING DELETE¬DEL QUIT¬ENTER Loading and deleting an equationDEL ¬º⁄RING º¤AREA-3 º‹CIRCUIT Page Inverse regression calculation Statistical CalculationsChapter Single-variable statistical calculation Linear regression calculationData Entry and Correction Quadratic regression calculationData entry Data correction30 d d d ExampleStatistical Calculation Formulas σx =Σx 2 - nx sx =Normal Probability Calculations Values for Pt, Qt, and Rt are given to six decimal placesStandardization conversion formula Chapter 4 Statistical CalculationsStatistical Calculations Examples ⋅10+50=x = 60 →Pt ? t = -0.5 →Rt ?x=3 → y=? Key operationsResult Equation Solvers Simultaneous Linear Equationsa1x + b1y = c1 a2x + b2y = c2 D = D =Z= D= x= 3.238095238 y=-1.638095238x+ y- z = x = ?Example Quadratic and Cubic Equation SolversX¤-6.333333333 X⁄-1.233600307 X¤ 0.216800153 +1.043018296i ExampleChapter Complex Number CalculationsComplex Number Entry +5.i PROG mode PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DELEntering the PROG mode Selecting the NORMAL program mode or the NBASE program modeCreating a NEW Program MODETITLE? NORMAL ƒNORMAL ⁄NBASEExample Use of variablesSLOPE NORMAL Y=M¡X+5 SLOPE NORMAL M¡=? 2. Entering the program Input and display commands Programming CommandsCOMMAND-1 ƒPrint ⁄Print ¤Input ‹Wait Indicates the line is a remark Flow control GosubEqualities and inequalities Statistical Commands STATSTAT xy DataEditing a Program Error Messages ERROR LBL DUPLICATE BREAKDEL ¬º⁄AREA º¤TEMP º‹STAT TITLEAREA DELETE¬DEL QUIT¬ENTER PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DELDeleting Programs Application Examples Programming ExamplesSome like it hot Celsius-Fahrenheit conversion TEMP NORMAL PROGRAM?PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DEL Running the programThe Heron Formula A + B + C T =SIDE LENGTHS HERON NORMALExample ResultNBASE NBASE PROGRAM? 2B or not 2B N-base conversionRunning the program Program codeKey operations Example T testx - m t = sx2 Program code Key operationsRunning the program ResultA circle that passes through 3 points X 1 2+Y 1 2-X 2 2-Y 2 2Y 2-Y 3 - X 2 2+Y 2 2-X 3 2-Y 3 2Y 1-Y2X 1-X 2Y 2-Y 3 - X 2-X 3Y 1-Y X 1 2+Y 1 2-X 2 2-Y 2 2X 2-X 3 - X 2 2+Y 2 2-X 3 2-Y 3 2X 1-XProgram code Key operationsExample ResultExample Radioactive decayDECAY NORMAL PROGRAM? DECAY NORMAL ORIGINAL MASSMº=? T= YEARSDelta-Y impedance circuit transformation Program code Key operations1DELTA TO Y 2Y TO DELTAProgram code Key operationsObtaining tensions of strings = -- =sin A + B A, B angles that strings make from perpendicular lines DMS21.966 23.761 T=Results ExamplePurchasing with payment in n-month installments n n-month installment1 - 1 + i -n P price of the productPRICE PAYBYMNNORMALPrint S i 0 S eDigital dice Program codeKey operations Running the programHow many digits can you remember? Program code Key operationsRunning the program Program codeKey operations Calculation Examples 23∂56∂4.09∂Ωse86164.09 86164.09 AnsÒT 8.616 Geosynchronous orbits4.217 7.424Twinkle, twinkle, little star Apparent magnitude of stars TŒ=4πŒGM˚ R„ R=z1Î0.4˚4.8-2. 89= 4.8-log0.0003 0.4=Example ResultDATA SET= 3. 7.95,108DATA DATA SET= DATA SET= 4. Í≈= 13254.15 Memory calculationsExample Result50Ç6= 15890700 15890700. 35∏5= 38955840The state lottery ExampleBattery Replacement Notes on battery replacementWhen to replace the batteries AppendixReplacement procedure CautionsAutomatic power off function zALL DATA CL?zz YES¬DEL z z NO¬ENTERzThe OPTION menu ¤DELETE LCD CONTRAST + DARK ¬LIGHTOPTION ƒCTRST ⁄M.CHK The OPTION displayDELETE ƒEQTN ⁄PROG If an Abnormal Condition OccursDeleting equation files and programs Error Messages Error noError message SolutionUsing the Solver Function Effectively Newton’s method‘Dead end’ approximations Range of expected valuesChanging the range of expected values RANGEabCalculation accuracy Solving y = x3 - 3x2 + x + 5 for y = Equations that are difficult to solveSolving y = sin x for y = Technical Data Calculation rangesx, y → r, θ Memory usage FunctionDynamic range VariablesPriority levels in calculations Filing Equation functionsSpecifications For More Information about Scientific Calculators In EuropePRINTED IN CHINA / IMPRIMÉ EN CHINE / IMPRESO EN CHINA SHARP CORPORATION04LGK TINSE0796EHZZ