Alligation
Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity. Alligation medial is merely a matter of finding a weighted mean. Alligation alternate is more complicated and involves organizing the ingredients into high and low pairs which are then traded off. Alligation alternate provides answers when an algebraic solution (e.g., using simultaneous equations) is not possible (e.g., you have three variables but only two equations). Note that in this class of problem, there may be multiple feasible answers. Two further variations on Alligation occur : Alligation Partial and Alligation Total (see John King's Arithmetic Book 1795 which includes worked examples.) The technique is not used in s ...
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Arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today. History The prehistory of arithmetic is limited to a small number of artifacts, which may indicate the conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 20,000 and 18,000 BC, although its interpretation is disputed. The earliest written records indicate the Egyptians and Babylonians used all the elementary arithmetic operations: addition, subtraction, multiplication, and division, as early as 2000 BC. These artifacts do not always reveal the specific process used for solving problems, but t ...
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Weighted Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. Examples Basic example Given two school with 20 students, one with 30 test grades in each class as follows: :Morning class = :Afternoon class = The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in number of ...
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Coca-Cola
Coca-Cola, or Coke, is a carbonated soft drink manufactured by the Coca-Cola Company. Originally marketed as a temperance drink and intended as a patent medicine, it was invented in the late 19th century by John Stith Pemberton in Atlanta, Georgia. In 1888, Pemberton sold Coca-Cola's ownership rights to Asa Griggs Candler, a businessman, whose marketing tactics led Coca-Cola to its dominance of the global soft-drink market throughout the 20th and 21st century. The drink's name refers to two of its original ingredients: coca leaves and kola nuts (a source of caffeine). The current formula of Coca-Cola remains a closely guarded trade secret; however, a variety of reported recipes and experimental recreations have been published. The secrecy around the formula has been used by Coca-Cola in its marketing as only a handful of anonymous employees know the formula. The drink has inspired imitators and created a whole classification of soft drink: colas. The Coca-Cola Company p ...
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Sprite (soft Drink)
Sprite is an American-owned brand of clear, Lemon-lime drink, lemon and lime-flavored soft drink created by the Coca-Cola Company. Sprite comes in multiple flavors, including cranberry, cherry, grape, Orange (fruit), orange, tropical, ginger, and vanilla. Ice, peach, Berryclear remix, and newer versions of the drinks are Sugar substitute, artificially sweetened. Sprite was created to compete primarily against Keurig Dr Pepper's 7 Up. History The Sprite brand name was created by T. C. "Bud" Evans, a Houston-based bottler who also distributed Coca-Cola products, circa 1955 for a line of drinks with flavors such as strawberry and orange; the rights to the name were acquired by the Coca-Cola Company in 1960. The lemon-lime drink known today as Sprite was developed in West Germany in 1959 as Fanta Klare Zitrone ("Fanta Clear Lemon" in English) and was introduced in the United States under the Sprite name in 1961 as a competitor to 7 Up. Marketing Sprite advertisements often make ...
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Frederick V
Frederick V or Friedrich V may refer to: *Frederick V, Duke of Swabia (1164–1170) *Frederick V, Count of Zollern (d.1289) *Frederick V, Burgrave of Nuremberg (c. 1333–1398), German noble *Frederick V of Austria (1415–1493), or Frederick III, Holy Roman Emperor *Frederick I, Margrave of Brandenburg-Ansbach (1460–1536), or Friedrich V, Margrave von Brandenburg-Ansbach-Bayreuth *Frederick V, Margrave of Baden-Durlach (1594–1659) *Frederick V, Elector Palatine (1596–1632), or Friedrich V von der Pfalz *Frederick V of Denmark (1723–1766), king of Denmark and Norway *Frederick V, Landgrave of Hesse-Homburg Frederick V Louis William Christian, Landgrave of Hesse-Homburg (30 January 1748, Bad Homburg vor der Höhe – 20 January 1820, Bad Homburg vor der Höhe) was from 1751 to his death landgrave of Hesse-Homburg. He was born under Europe's Ancie ...