between 1 and 100. The teacher expected this task to take Guass several minutes to an hour to keep him busy but
|
|
- Brooke Day
- 5 years ago
- Views:
Transcription
1 Sec 5.8 Sec 6.2 Mathematical Modelig (Arithmetic & Geometric Series) Name: Carl Friedrich Gauss is probably oe of the most oted complete mathematicias i history. As the story goes, he was potetially recogiized for his mathematical brilliace at the age of 8 whe he was assiged busy work by his teacher for causig disruptios i class. He was told by the teacher to add all of the umbers betwee ad = The teacher expected this task to take Guass several miutes to a hour to keep him busy but Gauss did it i secods. So, the teacher thikig he had cheated told him to add the umbers betwee ad 200. This time Gauss did t eve move, he just repoded with the aswer. He had devised a trick to add cosecutive umbers by pairig them i a special way at the age of 8. How did he do it? = He determied that if you fid the sum of the most outer pair of umbers it sums to ad that the ext ier pair after that sums to ad so o. I short, there should be 50 pairs of umbers that sums to. So, this suggests: Usig the techiqe that Gauss may have developed, determie the sum of all the itegers from to pairs of It turs out that this strategy works for the partial sum of ay Arithmetic Series. Cosider writig it as a formula. The Sum of terms of a arithmetic series The represets the umber of pairs of the terms that form the special sum. The a represets the first term of the series. The a represets the last term of the series. Determie the sum of the followig partial arithmetic series usig the formula Fid the S 62 of the followig series: M. Wikig Uit 6 2 page 07
2 Determie the sum of the followig partial arithmetic series usig the formula Fid the S 42, give that a = 6 ad a 42 = Fid the S 39 give that a = 6 ad d = 6 6. Fid the S 34 give that a 34 = 73 ad d = Determie the value of Determie the value of Addiso decides to try to save moey i a jar at home. She decides to save $20 the first week of the year ad each week she will icrease the amout she saves by $5. So, o the secod week she will save $25 ad the o third week she will save a additioal $30. This process would repeat for the whole year of 52 weeks. How much moey should she have i the jar at the ed of the year? M. Wikig Uit 6 2 page 08
3 There are also formulas that ca be created to fid the sum of a Geometric Series. First cosider the followig series This could also be re writte as: st term 2 d term 3 rd term 4 th term 5 th term 6 th term 7 th term 8 th term 9 th term 0 th term th term So, ay geometric series could be writte as:.. Cosider multiplyig both sides by a.. Next, add the two series similar to how you use elimiatio i solvig a system of equatios This formula works for the partial sum of ay Geometric Series. The a represets the first term of the series. The Sum of terms of a arithmetic series The represets the umber of sequetial terms to be icluded i the sum. The r represets the commo ratio from oe term to the ext. a2 r a Arithmetic a a d da2a S a a 2 Geometric a a r a r S r Determie the sum of the followig partial geometric series usig the formula.. Fid the S 4 of the followig series: M. Wikig Uit 6 2 page 09
4 Determie the sum of the followig partial geometric series usig the formula. 3. Determie the sum of the first terms (S ) for a geometric series give the first term is 6 (a =6) ad the commo ratio is 5 (r=5). 4. Give the sum of the first 2 terms of a geometric sequeces sum to ad the commo ratio is 2 (r=3), determie the first term (a ). a2 r a Arithmetic a a d d a2 a S a a 2 Geometric a a r a r S r 5 7. Determie the value of Determie the value of Determie the value of Determie the value of M. Wikig Uit 6 2 page 0
5 Usig the Algebra or the Ifiite Geometric Series formulas determie the fractio for the followig repeatig decimals Kelly decides to start savig moey. O the first week of the year, she saves oe cet ($0.0). The, for each week that follows she cotiues to double the amout she saved the previous week. So, o the secod week she saved a additioal 2 cets ($0.02) ad the 3 rd week 4 cets ($0.04). If this process were able to be cotiued for the etire year of 52 weeks, how much moey would Kelly have saved by the ed of the year? 6. Sarah Pikski was creatig a patter usig triagle tiles. She wated to show each successive step to show how her patter grows. She has already used 40 triagular tiles to create the patter below. If she cotiued how may tiles would it take i total to create 0 steps of the desig? M. Wikig Uit 6 2 page
CHAPTER : ARITHMETIC PROGRESSION CONTENTS. Idetify characteristics of arithmetic progressio PAGE 2.2 Determie whether a give sequece is a arithmetic p
ADDITIONAL MATHEMATICS FORM 5 MODULE ARITHMETIC PROGRESSION CHAPTER : ARITHMETIC PROGRESSION CONTENTS. Idetify characteristics of arithmetic progressio PAGE 2.2 Determie whether a give sequece is a arithmetic
More informationChapter 5: Sequences and Series
Chapter 5: Sequeces ad Series 1. Sequeces 2. Arithmetic ad Geometric Sequeces 3. Summatio Notatio 4. Arithmetic Series 5. Geometric Series 6. Mortgage Paymets LESSON 1 SEQUENCES I Commo Core Algebra I,
More informationMA Lesson 11 Section 1.3. Solving Applied Problems with Linear Equations of one Variable
MA 15200 Lesso 11 Sectio 1. I Solvig Applied Problems with Liear Equatios of oe Variable 1. After readig the problem, let a variable represet the ukow (or oe of the ukows). Represet ay other ukow usig
More informationphysicsandmathstutor.com
physicsadmathstutor.com 9. (a) A geometric series has first term a ad commo ratio r. Prove that the sum of the first terms of the series is a(1 r ). 1 r (4) Mr. Kig will be paid a salary of 35 000 i the
More informationLESSON #66 - SEQUENCES COMMON CORE ALGEBRA II
LESSON #66 - SEQUENCES COMMON CORE ALGEBRA II I Commo Core Algebra I, you studied sequeces, which are ordered lists of umbers. Sequeces are extremely importat i mathematics, both theoretical ad applied.
More informationWhen you click on Unit V in your course, you will see a TO DO LIST to assist you in starting your course.
UNIT V STUDY GUIDE Percet Notatio Course Learig Outcomes for Uit V Upo completio of this uit, studets should be able to: 1. Write three kids of otatio for a percet. 2. Covert betwee percet otatio ad decimal
More informationWe learned: $100 cash today is preferred over $100 a year from now
Recap from Last Week Time Value of Moey We leared: $ cash today is preferred over $ a year from ow there is time value of moey i the form of willigess of baks, busiesses, ad people to pay iterest for its
More informationUsing Math to Understand Our World Project 5 Building Up Savings And Debt
Usig Math to Uderstad Our World Project 5 Buildig Up Savigs Ad Debt Note: You will have to had i aswers to all umbered questios i the Project Descriptio See the What to Had I sheet for additioal materials
More informationFurther Pure 1 Revision Topic 5: Sums of Series
The OCR syllabus says that cadidates should: Further Pure Revisio Topic 5: Sums of Series Cadidates should be able to: (a) use the stadard results for Σr, Σr, Σr to fid related sums; (b) use the method
More informationAPPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES
APPLICATION OF GEOMETRIC SEQUENCES AND SERIES: COMPOUND INTEREST AND ANNUITIES Example: Brado s Problem Brado, who is ow sixtee, would like to be a poker champio some day. At the age of twety-oe, he would
More informationChapter 3. Compound interest
Chapter 3 Compoud iterest 1 Simple iterest ad compoud amout formula Formula for compoud amout iterest is: S P ( 1 Where : S: the amout at compoud iterest P: the pricipal i: the rate per coversio period
More informationLimits of sequences. Contents 1. Introduction 2 2. Some notation for sequences The behaviour of infinite sequences 3
Limits of sequeces I this uit, we recall what is meat by a simple sequece, ad itroduce ifiite sequeces. We explai what it meas for two sequeces to be the same, ad what is meat by the -th term of a sequece.
More information43. A 000 par value 5-year bod with 8.0% semiaual coupos was bought to yield 7.5% covertible semiaually. Determie the amout of premium amortized i the 6 th coupo paymet. (A).00 (B).08 (C).5 (D).5 (E).34
More informationSTRAND: FINANCE. Unit 3 Loans and Mortgages TEXT. Contents. Section. 3.1 Annual Percentage Rate (APR) 3.2 APR for Repayment of Loans
CMM Subject Support Strad: FINANCE Uit 3 Loas ad Mortgages: Text m e p STRAND: FINANCE Uit 3 Loas ad Mortgages TEXT Cotets Sectio 3.1 Aual Percetage Rate (APR) 3.2 APR for Repaymet of Loas 3.3 Credit Purchases
More informationEXERCISE - BINOMIAL THEOREM
BINOMIAL THOEREM / EXERCISE - BINOMIAL THEOREM LEVEL I SUBJECTIVE QUESTIONS. Expad the followig expressios ad fid the umber of term i the expasio of the expressios. (a) (x + y) 99 (b) ( + a) 9 + ( a) 9
More informationMath of Finance Math 111: College Algebra Academic Systems
Math of Fiace Math 111: College Algebra Academic Systems Writte By Bria Hoga Mathematics Istructor Highlie Commuity College Edited ad Revised by Dusty Wilso Mathematics Istructor Highlie Commuity College
More informationDate: Practice Test 6: Compound Interest
: Compoud Iterest K: C: A: T: PART A: Multiple Choice Questios Istructios: Circle the Eglish letter of the best aswer. Circle oe ad ONLY oe aswer. Kowledge/Thikig: 1. Which formula is ot related to compoud
More informationMATH : EXAM 2 REVIEW. A = P 1 + AP R ) ny
MATH 1030-008: EXAM 2 REVIEW Origially, I was havig you all memorize the basic compoud iterest formula. I ow wat you to memorize the geeral compoud iterest formula. This formula, whe = 1, is the same as
More information0.07. i PV Qa Q Q i n. Chapter 3, Section 2
Chapter 3, Sectio 2 1. (S13HW) Calculate the preset value for a auity that pays 500 at the ed of each year for 20 years. You are give that the aual iterest rate is 7%. 20 1 v 1 1.07 PV Qa Q 500 5297.01
More informationCalculation of the Annual Equivalent Rate (AER)
Appedix to Code of Coduct for the Advertisig of Iterest Bearig Accouts. (31/1/0) Calculatio of the Aual Equivalet Rate (AER) a) The most geeral case of the calculatio is the rate of iterest which, if applied
More information1 The Power of Compounding
1 The Power of Compoudig 1.1 Simple vs Compoud Iterest You deposit $1,000 i a bak that pays 5% iterest each year. At the ed of the year you will have eared $50. The bak seds you a check for $50 dollars.
More informationSingle-Payment Factors (P/F, F/P) Single-Payment Factors (P/F, F/P) Single-Payment Factors (P/F, F/P)
Sigle-Paymet Factors (P/F, F/P) Example: Ivest $1000 for 3 years at 5% iterest. F =? i =.05 $1000 F 1 = 1000 + (1000)(.05) = 1000(1+.05) F 2 = F 1 + F 1 i = F 1 (1+ = 1000(1+.05)(1+.05) = 1000(1+.05) 2
More informationChapter Four Learning Objectives Valuing Monetary Payments Now and in the Future
Chapter Four Future Value, Preset Value, ad Iterest Rates Chapter 4 Learig Objectives Develop a uderstadig of 1. Time ad the value of paymets 2. Preset value versus future value 3. Nomial versus real iterest
More informationENGINEERING ECONOMICS
ENGINEERING ECONOMICS Ref. Grat, Ireso & Leaveworth, "Priciples of Egieerig Ecoomy'','- Roald Press, 6th ed., New York, 1976. INTRODUCTION Choice Amogst Alteratives 1) Why do it at all? 2) Why do it ow?
More informationClass Sessions 2, 3, and 4: The Time Value of Money
Class Sessios 2, 3, ad 4: The Time Value of Moey Associated Readig: Text Chapter 3 ad your calculator s maual. Summary Moey is a promise by a Bak to pay to the Bearer o demad a sum of well, moey! Oe risk
More information2.6 Rational Functions and Their Graphs
.6 Ratioal Fuctios ad Their Graphs Sectio.6 Notes Page Ratioal Fuctio: a fuctio with a variable i the deoiator. To fid the y-itercept for a ratioal fuctio, put i a zero for. To fid the -itercept for a
More informationCHAPTER 2 PRICING OF BONDS
CHAPTER 2 PRICING OF BONDS CHAPTER SUARY This chapter will focus o the time value of moey ad how to calculate the price of a bod. Whe pricig a bod it is ecessary to estimate the expected cash flows ad
More informationEstimating Proportions with Confidence
Aoucemets: Discussio today is review for midterm, o credit. You may atted more tha oe discussio sectio. Brig sheets of otes ad calculator to midterm. We will provide Scatro form. Homework: (Due Wed Chapter
More informationOverlapping Generations
Eco. 53a all 996 C. Sims. troductio Overlappig Geeratios We wat to study how asset markets allow idividuals, motivated by the eed to provide icome for their retiremet years, to fiace capital accumulatio
More informationMath 124: Lecture for Week 10 of 17
What we will do toight 1 Lecture for of 17 David Meredith Departmet of Mathematics Sa Fracisco State Uiversity 2 3 4 April 8, 2008 5 6 II Take the midterm. At the ed aswer the followig questio: To be revealed
More informationISBN Copyright 2015 The Continental Press, Inc.
TABLE OF CONTENTS Itroductio 3 Format of Books 4 Suggestios for Use 7 Aotated Aswer Key ad Extesio Activities 9 Reproducible Tool Set 183 ISBN 978-0-8454-7897-4 Copyright 2015 The Cotietal Press, Ic. Exceptig
More informationNotes on Expected Revenue from Auctions
Notes o Epected Reveue from Auctios Professor Bergstrom These otes spell out some of the mathematical details about first ad secod price sealed bid auctios that were discussed i Thursday s lecture You
More informationGame Theory. Lecture Notes By Y. Narahari. Department of Computer Science and Automation Indian Institute of Science Bangalore, India July 2012
Game Theory Lecture Notes By Y. Narahari Departmet of Computer Sciece ad Automatio Idia Istitute of Sciece Bagalore, Idia July 01 Chapter 4: Domiat Strategy Equilibria Note: This is a oly a draft versio,
More informationFixed Income Securities
Prof. Stefao Mazzotta Keesaw State Uiversity Fixed Icome Securities FIN4320. Fall 2006 Sample First Midterm Exam Last Name: First Name: Studet ID Number: Exam time is: 80 miutes. Total poits for this exam
More informationOutline. Plotting discrete-time signals. Sampling Process. Discrete-Time Signal Representations Important D-T Signals Digital Signals
Outlie Discrete-Time Sigals-Itroductio. Plottig discrete-time sigals. Samplig Process. Discrete-Time Sigal Represetatios Importat D-T Sigals Digital Sigals Discrete-Time Sigals-Itroductio The time variable
More informationName Date MATH REVIEW 2. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Name Date MATH 1332 - REVIEW 2 SHORT ANSWER. Write the word or phrase that best completes each stateme or aswers the questio. Express the fractio as a perce. 1) 3 8 Write the decimal as a perce. 2) 0.775
More informationSection 3.3 Exercises Part A Simplify the following. 1. (3m 2 ) 5 2. x 7 x 11
123 Sectio 3.3 Exercises Part A Simplify the followig. 1. (3m 2 ) 5 2. x 7 x 11 3. f 12 4. t 8 t 5 f 5 5. 3-4 6. 3x 7 4x 7. 3z 5 12z 3 8. 17 0 9. (g 8 ) -2 10. 14d 3 21d 7 11. (2m 2 5 g 8 ) 7 12. 5x 2
More informationT4032-MB, Payroll Deductions Tables CPP, EI, and income tax deductions Manitoba Effective January 1, 2016
T4032-MB, Payroll Deductios Tables CPP, EI, ad icome tax deductios Maitoba Effective Jauary 1, 2016 T4032-MB What s ew as of Jauary 1, 2016 The major chages made to this guide sice the last editio are
More information. (The calculated sample mean is symbolized by x.)
Stat 40, sectio 5.4 The Cetral Limit Theorem otes by Tim Pilachowski If you have t doe it yet, go to the Stat 40 page ad dowload the hadout 5.4 supplemet Cetral Limit Theorem. The homework (both practice
More informationStatistics for Economics & Business
Statistics for Ecoomics & Busiess Cofidece Iterval Estimatio Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for the mea ad the proportio How to determie
More information1 Random Variables and Key Statistics
Review of Statistics 1 Radom Variables ad Key Statistics Radom Variable: A radom variable is a variable that takes o differet umerical values from a sample space determied by chace (probability distributio,
More informationMath 312, Intro. to Real Analysis: Homework #4 Solutions
Math 3, Itro. to Real Aalysis: Homework #4 Solutios Stephe G. Simpso Moday, March, 009 The assigmet cosists of Exercises 0.6, 0.8, 0.0,.,.3,.6,.0,.,. i the Ross textbook. Each problem couts 0 poits. 0.6.
More informationChapter 11 Appendices: Review of Topics from Foundations in Finance and Tables
Chapter 11 Appedices: Review of Topics from Foudatios i Fiace ad Tables A: INTRODUCTION The expressio Time is moey certaily applies i fiace. People ad istitutios are impatiet; they wat moey ow ad are geerally
More informationT4032-ON, Payroll Deductions Tables CPP, EI, and income tax deductions Ontario Effective January 1, 2016
T4032-ON, Payroll Deductios Tables CPP, EI, ad icome tax deductios Otario Effective Jauary 1, 2016 T4032-ON What s ew as of Jauary 1, 2016 The major chages made to this guide sice the last editio are outlied.
More informationCAPITAL PROJECT SCREENING AND SELECTION
CAPITAL PROJECT SCREEIG AD SELECTIO Before studyig the three measures of ivestmet attractiveess, we will review a simple method that is commoly used to scree capital ivestmets. Oe of the primary cocers
More informationSequences and Series
Sequeces ad Series Matt Rosezweig Cotets Sequeces ad Series. Sequeces.................................................. Series....................................................3 Rudi Chapter 3 Exercises........................................
More informationChapter 8. Confidence Interval Estimation. Copyright 2015, 2012, 2009 Pearson Education, Inc. Chapter 8, Slide 1
Chapter 8 Cofidece Iterval Estimatio Copyright 2015, 2012, 2009 Pearso Educatio, Ic. Chapter 8, Slide 1 Learig Objectives I this chapter, you lear: To costruct ad iterpret cofidece iterval estimates for
More informationChapter Four 1/15/2018. Learning Objectives. The Meaning of Interest Rates Future Value, Present Value, and Interest Rates Chapter 4, Part 1.
Chapter Four The Meaig of Iterest Rates Future Value, Preset Value, ad Iterest Rates Chapter 4, Part 1 Preview Develop uderstadig of exactly what the phrase iterest rates meas. I this chapter, we see that
More information2. Find the annual percentage yield (APY), to the nearest hundredth of a %, for an account with an APR of 12% with daily compounding.
1. Suppose that you ivest $4,000 i a accout that ears iterest at a of 5%, compouded mothly, for 58 years. `Show the formula that you would use to determie the accumulated balace, ad determie the accumulated
More informationFixed Income Securities
Prof. Stefao Mazzotta Keesaw State Uiversity Fixed Icome Securities Sample First Midterm Exam Last Name: First Name: Studet ID Number: Exam time is: 80 miutes. Total poits for this exam is: 400 poits Prelimiaries
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationModels of Asset Pricing
APPENDIX 1 TO CHAPTER 4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More informationModels of Asset Pricing
APPENDIX 1 TO CHAPTER4 Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More informationBuilding a Dynamic Two Dimensional Heat Transfer Model part #1
Buildig a Dyamic Two Dimesioal Heat Trasfer Model part #1 - Tis is te first alf of a tutorial wic sows ow to build a basic dyamic eat coductio model of a square plate. Te same priciple could be used to
More informationDr. Maddah ENMG 400 Engineering Economy 06/24/09. Chapter 2 Factors: How time and interest affect money
Dr Maddah ENM 400 Egieerig Ecoomy 06/4/09 Chapter Factors: How time ad iterest affect moey Sigle Paymet Factors Recall that P dollars ow are equivalet to F dollars after time periods at a iterest rate
More informationA random variable is a variable whose value is a numerical outcome of a random phenomenon.
The Practice of Statistics, d ed ates, Moore, ad Stares Itroductio We are ofte more iterested i the umber of times a give outcome ca occur tha i the possible outcomes themselves For example, if we toss
More informationAUTOMATIC GENERATION OF FUZZY PAYOFF MATRIX IN GAME THEORY
AUTOMATIC GENERATION OF FUZZY PAYOFF MATRIX IN GAME THEORY Dr. Farha I. D. Al Ai * ad Dr. Muhaed Alfarras ** * College of Egieerig ** College of Coputer Egieerig ad scieces Gulf Uiversity * Dr.farha@gulfuiversity.et;
More informationChapter 4: Time Value of Money
FIN 301 Class Notes Chapter 4: Time Value of Moey The cocept of Time Value of Moey: A amout of moey received today is worth more tha the same dollar value received a year from ow. Why? Do you prefer a
More informationT4032-BC, Payroll Deductions Tables CPP, EI, and income tax deductions British Columbia Effective January 1, 2016
T4032-BC, Payroll Deductios Tables CPP, EI, ad icome tax deductios British Columbia Effective Jauary 1, 2016 T4032-BC What s ew as of Jauary 1, 2016 The major chages made to this guide, sice the last editio,
More informationRandom Sequences Using the Divisor Pairs Function
Radom Sequeces Usig the Divisor Pairs Fuctio Subhash Kak Abstract. This paper ivestigates the radomess properties of a fuctio of the divisor pairs of a atural umber. This fuctio, the atecedets of which
More informationModels of Asset Pricing
4 Appedix 1 to Chapter Models of Asset Pricig I this appedix, we first examie why diversificatio, the holdig of may risky assets i a portfolio, reduces the overall risk a ivestor faces. The we will see
More informationMS-E2114 Investment Science Exercise 2/2016, Solutions
MS-E24 Ivestmet Sciece Exercise 2/206, Solutios 26.2.205 Perpetual auity pays a xed sum periodically forever. Suppose a amout A is paid at the ed of each period, ad suppose the per-period iterest rate
More informationSection Mathematical Induction and Section Strong Induction and Well-Ordering
Sectio 4.1 - Mathematical Iductio ad Sectio 4. - Strog Iductio ad Well-Orderig A very special rule of iferece! Defiitio: A set S is well ordered if every subset has a least elemet. Note: [0, 1] is ot well
More information2. The Time Value of Money
2. The Time Value of Moey Problem 4 Suppose you deposit $100 i the bak today ad it ears iterest at a rate of 10% compouded aually. How much will be i the accout 50 years from today? I this case, $100 ivested
More informationCAPITAL ASSET PRICING MODEL
CAPITAL ASSET PRICING MODEL RETURN. Retur i respect of a observatio is give by the followig formula R = (P P 0 ) + D P 0 Where R = Retur from the ivestmet durig this period P 0 = Curret market price P
More informationToday: Finish Chapter 9 (Sections 9.6 to 9.8 and 9.9 Lesson 3)
Today: Fiish Chapter 9 (Sectios 9.6 to 9.8 ad 9.9 Lesso 3) ANNOUNCEMENTS: Quiz #7 begis after class today, eds Moday at 3pm. Quiz #8 will begi ext Friday ad ed at 10am Moday (day of fial). There will be
More informationClass Notes for Managerial Finance
Class Notes for Maagerial Fiace These otes are a compilatio from:. Class Notes Supplemet to Moder Corporate Fiace Theory ad Practice by Doald R. Chambers ad Nelso J. Lacy. I gratefully ackowledge the permissio
More informationChapter Six. Bond Prices 1/15/2018. Chapter 4, Part 2 Bonds, Bond Prices, Interest Rates and Holding Period Return.
Chapter Six Chapter 4, Part Bods, Bod Prices, Iterest Rates ad Holdig Period Retur Bod Prices 1. Zero-coupo or discout bod Promise a sigle paymet o a future date Example: Treasury bill. Coupo bod periodic
More informationCAUCHY'S FORMULA AND EIGENVAULES (PRINCIPAL STRESSES) IN 3-D
GG303 Lecture 19 11/5/0 1 CAUCHY'S FRMULA AN EIGENVAULES (PRINCIPAL STRESSES) IN 3- I II Mai Topics A Cauchy s formula Pricipal stresses (eigevectors ad eigevalues) Cauchy's formula A Relates tractio vector
More informationSolutions to Problem Sheet 1
Solutios to Problem Sheet ) Use Theorem.4 to prove that p log for all real x 3. This is a versio of Theorem.4 with the iteger N replaced by the real x. Hit Give x 3 let N = [x], the largest iteger x. The,
More informationThe material in this chapter is motivated by Experiment 9.
Chapter 5 Optimal Auctios The material i this chapter is motivated by Experimet 9. We wish to aalyze the decisio of a seller who sets a reserve price whe auctioig off a item to a group of bidders. We begi
More informationFinding the Sum of Consecutive Terms of a Sequence
Mathematics 451 Finding the Sum of Consecutive Terms of a Sequence In a previous handout we saw that an arithmetic sequence starts with an initial term b, and then each term is obtained by adding a common
More informationCAPITALIZATION (PREVENTION) OF PAYMENT PAYMENTS WITH PERIOD OF DIFFERENT MATURITY FROM THE PERIOD OF PAYMENTS
Iteratioal Joural of Ecoomics, Commerce ad Maagemet Uited Kigdom Vol. VI, Issue 9, September 2018 http://ijecm.co.uk/ ISSN 2348 0386 CAPITALIZATION (PREVENTION) OF PAYMENT PAYMENTS WITH PERIOD OF DIFFERENT
More information11.7 (TAYLOR SERIES) NAME: SOLUTIONS 31 July 2018
.7 (TAYLOR SERIES NAME: SOLUTIONS 3 July 08 TAYLOR SERIES ( The power series T(x f ( (c (x c is called the Taylor Series for f(x cetered at x c. If c 0, this is called a Maclauri series. ( The N-th partial
More informationBasic formula for confidence intervals. Formulas for estimating population variance Normal Uniform Proportion
Basic formula for the Chi-square test (Observed - Expected ) Expected Basic formula for cofidece itervals sˆ x ± Z ' Sample size adjustmet for fiite populatio (N * ) (N + - 1) Formulas for estimatig populatio
More informationThe Limit of a Sequence (Brief Summary) 1
The Limit of a Sequece (Brief Summary). Defiitio. A real umber L is a it of a sequece of real umbers if every ope iterval cotaiig L cotais all but a fiite umber of terms of the sequece. 2. Claim. A sequece
More informationii. Interval estimation:
1 Types of estimatio: i. Poit estimatio: Example (1) Cosider the sample observatios 17,3,5,1,18,6,16,10 X 8 X i i1 8 17 3 5 118 6 16 10 8 116 8 14.5 14.5 is a poit estimate for usig the estimator X ad
More informationDriver s. 1st Gear: Determine your asset allocation strategy.
Delaware North 401(k) PLAN The Driver s Guide The fial step o your road to erollig i the Delaware North 401(k) Pla. At this poit, you re ready to take the wheel ad set your 401(k) i motio. Now all that
More information1 Savings Plans and Investments
4C Lesso Usig ad Uderstadig Mathematics 6 1 Savigs las ad Ivestmets 1.1 The Savigs la Formula Lets put a $100 ito a accout at the ed of the moth. At the ed of the moth for 5 more moths, you deposit $100
More informationLecture 2. Tuesday Feb 3 rd. Time Value of Money 1
Lecture 2. Tuesday Feb 3 rd Time Value of Moey 1 What is Moey? Moey is a promise A Eglish Bakote says: I promise to pay the Bearer o demad the sum of twety pouds Ad it is siged by the Chief Cashier of
More informationChpt 5. Discrete Probability Distributions. 5-3 Mean, Variance, Standard Deviation, and Expectation
Chpt 5 Discrete Probability Distributios 5-3 Mea, Variace, Stadard Deviatio, ad Expectatio 1/23 Homework p252 Applyig the Cocepts Exercises p253 1-19 2/23 Objective Fid the mea, variace, stadard deviatio,
More informationGAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME MATHEMATICS GRADE 12 SESSION 3 (LEARNER NOTES)
MATHEMATICS GRADE SESSION 3 (LEARNER NOTES) TOPIC 1: FINANCIAL MATHEMATICS (A) Learer Note: Ths sesso o Facal Mathematcs wll deal wth future ad preset value autes. A future value auty s a savgs pla for
More informationJournal of Statistical Software
JSS Joural of Statistical Software Jue 2007, Volume 19, Issue 6. http://www.jstatsoft.org/ Ratioal Arithmetic Mathematica Fuctios to Evaluate the Oe-sided Oe-sample K-S Cumulative Samplig Distributio J.
More information1 + r. k=1. (1 + r) k = A r 1
Perpetual auity pays a fixed sum periodically forever. Suppose a amout A is paid at the ed of each period, ad suppose the per-period iterest rate is r. The the preset value of the perpetual auity is A
More informationLecture 5: Sampling Distribution
Lecture 5: Samplig Distributio Readigs: Sectios 5.5, 5.6 Itroductio Parameter: describes populatio Statistic: describes the sample; samplig variability Samplig distributio of a statistic: A probability
More informationDepreciation is the loss in value over time the property is being used.
Module Depreciatio Dr Tareq Albahri 206 Depreciatio is the loss i value over time the property is beig used. Cases of depreciatio:-. Actio of elemets 2. Wear ad tear from use القيمة الدفترية Book value
More informationBinomial Theorem. Combinations with repetition.
Biomial.. Permutatios ad combiatios Give a set with elemets. The umber of permutatios of the elemets the set: P() =! = ( 1) ( 2)... 1 The umber of r-permutatios of the set: P(, r) =! = ( 1) ( 2)... ( r
More informationA point estimate is the value of a statistic that estimates the value of a parameter.
Chapter 9 Estimatig the Value of a Parameter Chapter 9.1 Estimatig a Populatio Proportio Objective A : Poit Estimate A poit estimate is the value of a statistic that estimates the value of a parameter.
More informationc. Deaths are uniformly distributed between integer ages. d. The equivalence principle applies.
Chapter 6 1. A whole life policy for 50,000 is issued to (65). The death beefit is payable at the ed of the year of death. The level premiums are payable for the life of the isured. a. Mortality follows
More informationSummary of Benefits RRD
Summary of Beefits RRD All Eligible Employees Basic Term Life, Optioal Term Life, Optioal Depedet Term Life ad Optioal Accidetal Death & Dismembermet Issued by The Prudetial Isurace Compay of America Effective:
More information1. Suppose X is a variable that follows the normal distribution with known standard deviation σ = 0.3 but unknown mean µ.
Chapter 9 Exercises Suppose X is a variable that follows the ormal distributio with kow stadard deviatio σ = 03 but ukow mea µ (a) Costruct a 95% cofidece iterval for µ if a radom sample of = 6 observatios
More informationFOR TEACHERS ONLY. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING/PHYSICS
PS P FOR TEACHERS ONLY The Uiersity of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICAL SETTING/PHYSICS Wedesday, Jue, 005 :5 to 4:5 p.m., oly SCORING KEY AND RATING GUIDE Directios to the
More informationOsborne Books Update. Financial Statements of Limited Companies Tutorial
Osbore Books Update Fiacial Statemets of Limited Compaies Tutorial Website update otes September 2018 2 f i a c i a l s t a t e m e t s o f l i m i t e d c o m p a i e s I N T R O D U C T I O N The followig
More informationAPPLIED STATISTICS Complementary Course of BSc Mathematics - IV Semester CUCBCSS Admn onwards Question Bank
Prepared by: Prof (Dr) K.X. Joseph Multiple Choice Questios 1. Statistical populatio may cosists of (a) a ifiite umber of items (b) a fiite umber of items (c) either of (a) or (b) Module - I (d) oe of
More informationAppendix 1 to Chapter 5
Appedix 1 to Chapter 5 Models of Asset Pricig I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy a asset, we are
More informationr i = a i + b i f b i = Cov[r i, f] The only parameters to be estimated for this model are a i 's, b i 's, σe 2 i
The iformatio required by the mea-variace approach is substatial whe the umber of assets is large; there are mea values, variaces, ad )/2 covariaces - a total of 2 + )/2 parameters. Sigle-factor model:
More informationFinancial Analysis. Lecture 4 (4/12/2017)
Fiacial Aalysis Lecture 4 (4/12/217) Fiacial Aalysis Evaluates maagemet alteratives based o fiacial profitability; Evaluates the opportuity costs of alteratives; Cash flows of costs ad reveues; The timig
More informationguaranteed universal life
guarateed uiversal life Uited of Omaha Life Isurace Compay A Mutual of Omaha Compay product guide L8416_0314 For Producer use oly. Not for use with the geeral public. 1 Guaratee your cliets future. Guarateed
More informationof Asset Pricing R e = expected return
Appedix 1 to Chapter 5 Models of Asset Pricig EXPECTED RETURN I Chapter 4, we saw that the retur o a asset (such as a bod) measures how much we gai from holdig that asset. Whe we make a decisio to buy
More informationSubject CT1 Financial Mathematics Core Technical Syllabus
Subject CT1 Fiacial Mathematics Core Techical Syllabus for the 2018 exams 1 Jue 2017 Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig
More information