mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle‚ the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship
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CENTRAL LIMIT THEOREM There are many situations in business where populations are distributed normally; however‚ this is not always the case. Some examples of distributions that aren’t normal are incomes in a region that are skewed to one side and if you need to are looking at people’s ages but need to break them down to for men and women. We need a way to look at the frequency distributions of these examples. We can find them by using the Central Limit Theorem. The Central Limit Theorem states that
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In mathematics‚ the Pythagorean Theorem — or Pythagoras’ theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas‚ it states: In any right-angled triangle‚ the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths
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4.14 TRIANGLES Triangles are three-sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180º. Triangles can be classified according to the size of its angles. Some examples are : Acute Triangles An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below‚ a‚ b and c are all acute angles. Sample Problem 1: A triangle has angles 46º‚ 63º and 71º. What type of triangle is this? Answer:
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HYDROLOGY & HYDRAULIC ENGINEERING I LABORATORY REPORT 3 TITLE : BERNOULLI’S THEOREM APPARATUS NAME : ID. NO. : SECTION : 02 EXPERIMENT DATE : 10th December 2009 SUBMISSION DATE : 17th December 2009 GROUP NO. : 2 GROUP MEMBERS : LECTURER : LAB INSTRUCTOR : TABLE OF CONTENT Content | Page | Summary | 2 | Objective | 2 | Theory | 3 - 5 | Equipment/ description of experimental apparatus | 6 | Procedure | 6 | Data and observation | 6a | Analysis | 7‚8
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The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal‚ Neeraj Kayal‚ and Nitin Saxena‚ computer scientists at the Indian Institute of Technology Kanpur‚ on August 6‚ 2002‚ in a paper titled "PRIMES is in P".[1] The authors received many accolades‚ including the 2006 Gödel Prize and the 2006 Fulkerson Prize‚ for this work. The algorithm determines whether a number
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Climate is a measure of the average pattern of variation in temperature‚ humidity‚ atmospheric pressure‚ wind‚ precipitation‚ atmospheric particle count and other meteorological variables in a given region over long periods of time. Climate is different from weather‚ in that weather only describes the short-term conditions of these variables in a given region. A region’s climate is generated by the climate system‚ which has five components: atmosphere‚ hydrosphere‚ cryosphere‚ land surface‚ and biosphere
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variety of international activities to advance climate change science‚ monitor our environment‚ and promote activities that reduce greenhouse gas emissions. EPA establishes partnerships‚ provides leadership‚ and shares technical expertise to support these activities. conducts research to understand the environmental and health impacts of climate change and to provide sustainable solutions for adapting to and reducing the impact from a changing climate. EPA’s partners reduced over 345 million metric
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
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