...what that path was, until Galileo. There was yet another brilliant insight that led Galileo to his most astounding conclusion about projectile motion. First of all, he reasoned that a projectile is not only influenced by one motion, but by two. The motion that acts vertically is the force of gravity, and this pulls an object towards the earth at 9.8 meters per second. But while gravity is pulling the object down, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to Galileo's principle of inertia. He was indeed able to show that a projectile is controlled by two independent motions, and these work together to create a precise mathematical curve(Galileo). He actually found that the curve has an exact mathematical shape. A shape that the Greeks had already studied and called the parabola(Webster).Galileo reached was that the path of any projectile is a parabola. For an object to be consider projectile it must be dropped from a height, thrown vertically upwards...
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...Parañaque City A Term Paper Presented to: Edmar Orata Probability by: Jirolyn Fabro Miguel Angelo Rosales March 15, 2012 I - Introduction II - Interpretations III - Etymology IV - History V - Applications 1. Weather Forecasting 2. Batting Average 3. Winning the Lottery 4. VI - Discussion VII - I-Introduction Probability is the ratio of the number of ways an event can occur to the number of possible outcomes. Probability is expressed as a fraction or decimal from 0 to 1. Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we are not certain.[1] The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1, we call probability. [2] The higher the probability of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the likeliness that a (random) event will occur. The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the likeliness of events. Probability is used to...
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...The Money or The Passion: Is Money in Professional Sport Ruining the Ethos of the Game? Ross Schreuder Supervisor: Mr. Werth English Teacher: Mrs. Schroeder Table of Contents 1. Introduction 3 2. History and Evolution of Sport 3 3. What is the Ethos of Sport? 4 4. Positive and Negative Influences of Money in Sport and an Evaluation of their Impact on its Ethos 5 4.1 Doping: 5 4.2 Throwing Matches/ Match Fixing: 6 4.3 Other Factors Contributing to Unethical Behaviour in Sport 7 4.4 Sportsmanship vs. Gamesmanship 8 4.5 The Money in Barclays Premier League 9 4.5.1 Stadium naming rights 10 4.5.2 Transfers and Individual Sponsorships 10 4.6 Philanthropy 11 5. Conclusion 11 Bibliography 12 1. Introduction Money is, undoubtedly, evident in every aspect of professional sport. Player sponsorships and contracts, team ownership, stadia, media - its everywhere. If sport was not about the game, then arguably, sport would be about the money. Each and every week, transfers of players are made, ticket offices receive income, and money is handed from one profiteering person to the next. Where sport is widely thought to be about fair play, professional sport is, in fact, like war. There can only be one winner and what one team or individual gains, the other loses. Many sportsmen and women around the world are caught up with winning, not just because of the prowess of a title but, also because professionalism is now about money and...
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...a story. The story concerned a small group of undervalued professional baseball players and executives, many of whom had been rejected as unfit for the big leagues, who had turned themselves into one of the most successful franchises in Major League Baseball. But the idea for the book came well before I had good reason to write it—before I had a story to fall in love with. It began, really, with an innocent question: how did one of the poorest teams in baseball, the Oakland Athletics, win so many games? For more than a decade the people who run professional baseball have argued that the game was ceasing to be an athletic competition and becoming a financial one. The gap between rich and poor in baseball was far greater than in any other professional sport, and widening rapidly. At the opening of the 2002 season, the richest team, the New York Yankees, had a payroll of $126 million while the two poorest teams, the Oakland A's and the Tampa Bay Devil Rays, had payrolls of less than a third of that, about $40 million. A decade before, the highest payroll team, the New York Mets, had spent about $44 million on baseball players and the lowest payroll team, the Cleveland Indians, a bit more than $8 million. The raw disparities meant that only the rich teams could afford the best players. A poor team could afford only the maimed and the inept, and was almost certain to fail. Or so argued the people who ran baseball. And I was inclined to...
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...Patterns of world records in sports (2 articles) . . . . . . . 1.1.2 Competition, rankings and betting in soccer (3 articles) . . 1.1.3 An investigation into some popular baseball myths (3 articles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Uncertainty of attendance at sports events (2 articles) . . . 1.1.5 Home advantage, myths in tennis, drafting in hockey pools, American football . . . . . . . . . . . . . . . . . . . . . 1.2 Website . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modelling the development of world records in running Gerard H. Kuper and Elmer Sterken 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 2.2 Modelling world records . . . . . . . . . . . . . . 2.2.1 Cross-sectional approach . . . . . . . . . . 2.2.2 Fitting the individual curves . . . . . . . . 2.3 Selection of the functional form . . . . . . . . . . 2.3.1 Candidate functions . . . . . . . . . . . . . 2.3.2 Theoretical selection of curves . . . . . . . 2.3.3 Fitting the models . . . . . . . . . . . . . . 2.3.4 The Gompertz curve in more detail . . . . 2.4 Running data . . . . . . . . . . . . . . . . . . . . 2.5 Results of fitting the Gompertz curves . . . . . . . 2.6 Limit values of time and distance . . . . . . . . . 2.7 Summary and conclusions . . . . . . . . . . . . . References . . . . . . . . . . . . . . . ...
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...resources? Technology 2 A nation's production possibilities curve can shift outward: As a result of specialization and trade. With an increase in the quality and quantity of resources. Through the use of improved production techniques. 3 Factories storage, transportation and distribution facilities, as well as tools and machinery are all examples of physical ________ goods. Capital 4 To economists, land includes all ______, or gifts of nature, used in the production process. Natural Resources 5 The pleasure, satisfaction, or happiness obtained from consuming a good or service is known as (One Word) Utility 6 The need to make choices because economic wants exceed economic means, most likely describes The Economizing Problem 7 _________ is the discipline of economics concerned with individual units such as households, firms and government Macroeconomics 8 The four general categories of economic resources are: Land, Capital, Labor, and Entrepreneurial Ability. 9 A ____ ____ ____ list the different combinations of two products that can be produced with a specific set of resources, assuming full employment Production Possibilities Table. 10 Due to scarce resources, every individual, whether rich or poor, is faced with an _______ cost when choosing to produce or consume more of one good over another Opportunity. 11 A production possibilities curve "Implies" the attainable combination: of many goods that can...
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...CHAPTER ONE LIMITS, ALTERNATIVES, AND CHOICES CHAPTER OVERVIEW This chapter begins with a discussion of the meaning and importance of economics. In this first chapter, however, we will not plunge into problems and issues; instead we consider some important preliminaries. We first look at the economic perspective—how economists think about problems. Next, we examine the specific methods economists use to examine economic behavior and the economy, including distinguishing between macroeconomics and microeconomics. We then look at the economizing problem from both an individual and societal perspective. For the individual we develop the budget line, for society the production possibilities model. In our discussion of production possibilities, the concepts of opportunity costs and increasing opportunity costs, unemployment, growth, and present vs. future possibilities are all demonstrated. Finally, in the Last Word, some of the problems, limitations, and pitfalls that hinder sound economic reasoning are examined. The Appendix to Chapter 1 provides an important introduction to graphical analysis. While this will be review material for most students, for some this may be new. Instructors are strongly urged to confirm that their students understand this section before proceeding. The software supplement can provide effective remedial help for those students who are not familiar with graphical analysis, or just need a refresher. WHAT’S NEW There is a new learning objective...
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...PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2 1.38310223 J/K 8.31 J/K # mol 5.6731028 W/m2 # K4 6.63310234 J # s 6.0231023 mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha ...
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...planning. Market Economy: Resource allocation determined by a competitive market. Opportunity Cost: The best alternative foregone in order to produce a good or service. Public Good: A good or service that, once purchased by anyone, can of necessity be enjoyed by many. Externality: A cost of goods or services that is borne by someone other than the recipient of those goods or services. Lorenz Curve: Graphs the percentage of households against the percentage of income received. Ceteris Paribus (cet. par.): When analyzing one variable, the convention that all other variables are held constant. Inferior Good: An inferior good is one for which the quantity purchased decreases when real income increases. Giffen Good: A good for which there is a range of prices for which quantity and price vary directly, not inversely. Dependent Variable: A variable whose value is determined by the model. Independent Variable: A variable whose value is fixed external to the model. Complementary Good: A good whose demand curve shifts along with that of another good. Substitute Good: A good whose demand curve shifts inversely with that of another good. Normal Profit: The amount of profit just sufficient to keep resources in the industry. Included as part of cost. Coase’s Theorem: The exchange solution to external costs. Ricardo’s Theorem: A proof that a a poor country can trade to mutual advantage with a rich one, despite having no absolute advantage in any area. Okun’s Law: An equation relating...
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...planning. Market Economy: Resource allocation determined by a competitive market. Opportunity Cost: The best alternative foregone in order to produce a good or service. Public Good: A good or service that, once purchased by anyone, can of necessity be enjoyed by many. Externality: A cost of goods or services that is borne by someone other than the recipient of those goods or services. Lorenz Curve: Graphs the percentage of households against the percentage of income received. Ceteris Paribus (cet. par.): When analyzing one variable, the convention that all other variables are held constant. Inferior Good: An inferior good is one for which the quantity purchased decreases when real income increases. Giffen Good: A good for which there is a range of prices for which quantity and price vary directly, not inversely. Dependent Variable: A variable whose value is determined by the model. Independent Variable: A variable whose value is fixed external to the model. Complementary Good: A good whose demand curve shifts along with that of another good. Substitute Good: A good whose demand curve shifts inversely with that of another good. Normal Profit: The amount of profit just sufficient to keep resources in the industry. Included as part of cost. Coase’s Theorem: The exchange solution to external costs. Ricardo’s Theorem: A proof that a a poor country can trade to mutual advantage with a rich one, despite having no absolute advantage in any area. Okun’s Law: An equation relating...
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...Introductory Physics I Elementary Mechanics by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 rgb@phy.duke.edu Copyright Notice Copyright Robert G. Brown 1993, 2007, 2013 Notice This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its entirety in a downloadable PDF form or to be read online at: http://www.phy.duke.edu/∼rgb/Class/intro physics 1.php It is also available in an inexpensive (really!) print version via Lulu press here: http://www.lulu.com/shop/product-21186588.html where readers/users can voluntarily help support or reward the author by purchasing either this paper copy or one of the even more inexpensive electronic copies. By making the book available in these various media at a cost ranging from free to cheap, I enable the text can be used by students all over the world where each student can pay (or not) according to their means. Nevertheless, I am hoping that students who truly find this work useful will purchase a copy through Lulu or a bookseller (when the latter option becomes available), if only to help subsidize me while I continue to write inexpensive textbooks in physics or other subjects. This textbook is organized for ease of presentation and ease of learning. In particular, they are...
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...A Painted House John Grisham Chapter 1 The hill people and the Mexicans arrived on the same day. It was a Wednesday, early in September 1952. The Cardinals were five games behind the Dodgers with three weeks to go, and the season looked hopeless. The cotton, however, was waist-high to my father, over my head, and he and my grandfather could be heard before supper whispering words that were seldom heard. It could be a "good crop." They were farmers, hardworking men who embraced pessimism only when discussing the weather and the crops. There was too much sun, or too much rain, or the threat of floods in the lowlands, or the rising prices of seed and fertilizer, or the uncertainties of the markets. On the most perfect of days, my mother would quietly say to me, "Don't worry. The men will find something to worry about." Pappy, my grandfather, was worried about the price for labor when we went searching for the hill people. They were paid for every hundred pounds of cotton they picked. The previous year, according to him, it was $1.50 per hundred. He'd already heard rumors that a farmer over in Lake City was offering $1.60. This played heavily on his mind as we rode to town. He never talked when he drove, and this was because, according to my mother, not much of a driver herself, he was afraid of motorized vehicles. His truck was a 1939 Ford, and with the exception of our old John Deere tractor, it was our sole means of transportation. This was no particular problem except when...
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...A Painted House John Grisham Chapter 1 The hill people and the Mexicans arrived on the same day. It was a Wednesday, early in September 1952. The Cardinals were five games behind the Dodgers with three weeks to go, and the season looked hopeless. The cotton, however, was waist-high to my father, over my head, and he and my grandfather could be heard before supper whispering words that were seldom heard. It could be a "good crop." They were farmers, hardworking men who embraced pessimism only when discussing the weather and the crops. There was too much sun, or too much rain, or the threat of floods in the lowlands, or the rising prices of seed and fertilizer, or the uncertainties of the markets. On the most perfect of days, my mother would quietly say to me, "Don't worry. The men will find something to worry about." Pappy, my grandfather, was worried about the price for labor when we went searching for the hill people. They were paid for every hundred pounds of cotton they picked. The previous year, according to him, it was $1.50 per hundred. He'd already heard rumors that a farmer over in Lake City was offering $1.60. This played heavily on his mind as we rode to town. He never talked when he drove, and this was because, according to my mother, not much of a driver herself, he was afraid of motorized vehicles. His truck was a 1939 Ford, and with the exception of our old John Deere tractor, it was our sole means of transportation. This was no particular problem except when...
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...Chapter 1 – Reasoning with Economics: Models and Information • Economists base much of our thinking on simplified models of reality that neglect many details o Models that apply to a broad range of situations must be simple, but they can help you think logically no matter what happens in your market. • Why be abstract when you have facts? o Reality is so complex and our mental capacities so limited that we must be selective in what we think about. • Economists are human and they have values and beliefs that might render their objectivity suspect o Positive economics describes and analyzes things as they are (or as objectively as they can be seen) o Normative economics is about how things “ought to be” – it explicitly acknowledges the researcher’s values. Whatever positive theory may say, an economist’s normative views on prostitution or the drug trade might lead her to recommend that these activities remain illegal. • Rationality o Economics studies the choices people make in the face of constraints that limit their options o Economics studies the allocation of scarce resources among competing goals. Underlying both definitions is an assumption that people act rationally, with an eye towards attaining objectives they have chosen. o Rationality does not mean that people are computers People may not perfectly understand their own preferences or do not know how best to overcome the obstacles that stand between them and their goals. o What rationality offers...
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...Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10, 2012 1 Contents Preface 4 Mathematics of Finance 1. Simple Interest . . . . . . . . . . . . . . . . . . . . . . . 2. Discrete and Continuous Compound Interest . . . . . . 3. Ordinay Annuity, Future Value and Sinking Fund . . . 4. Present Value of an Ordinay Annuity and Amortization . . . . Matrices and Systems of Linear Equations 5. Solving Linear Systems Using Augmented Matrices . . . . 6. Gauss-Jordan Elimination . . . . . . . . . . . . . . . . . . 7. The Algebra of Matrices . . . . . . . . . . . . . . . . . . 8. Inverse Matrices and their Applications to Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . Linear Programming 9. Solving Systems of Linear Inequalities . . . . . . . . . . . . . . 10. Geometric Method for Solving Linear Programming Problems 11. Simplex Method for Solving Linear Programming Problems . 12. The Dual Problem: Minimization with ≥ Constraints . . . . . Counting Principles, Permuations, and 13. Sets . . . . . . . . . . . . . . . . . . 14. Counting Principles . . . . . . . . . 15. Permutations and Combinations . . . . . . 5 5 12 19 26 . . . . 34 34 42 53 62 . . . . 69 69 77 86 97 Combinations 106 . . . . . . . . . ...
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