a NOR gate. DeMorgan’s theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs De Morgan’s theorem is used to simplify a lot expression of complicated logic gates. For example‚ (A + (BC)’)’. The parentheses symbol is used in the example. _ The answer is A BC. Let’s apply the principles of DeMorgan’s theorems to the simplification of
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A Brief History of the Pythagorean Theorem Just Who Was This Pythagoras‚ Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece‚ and did much traveling through Egypt‚ learning‚ among other things‚ mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group‚ the Brotherhood of Pythagoreans‚ which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols‚ rituals and prayers. In addition
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Describe the role of courts in the criminal justice process. The courts serve as the venue where disputes are then settled and justice is administered. In Australian courts the adversarial system of trial is used to determine guilt‚ this is two sides‚ one representing the accused the other the state‚ debate over the guilt of the accused; this is mediated by a neutral third party‚ the judge or magistrate. Guilt is determined by the judge‚ magistrate or a jury. Punishment for the accused if found
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Binomial‚ Bernoulli and Poisson Distributions The Binomial‚ Bernoulli and Poisson distributions are discrete probability distributions in which the values that might be observed are restricted to being within a pre-defined list of possible values. This list has either a finite number of members‚ or at most is countable. * Binomial distribution In many cases‚ it is appropriate to summarize a group of independent observations by the number of observations in the group that represent one of
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option is written on this stock with a $12 strike price and 8 months to expiry. a) b) c) d) Use the delta-hedging approach to price this call option. Use the risk-neutral valuation method to price this call option. Work recursively back through the Binomial tree‚ calculating the call option price at each node. Check that the option price at each node matches that calculated in part a. Again use the risk-neutral method to value this call option‚ but this time do not work back recursively. Rather‚ focus
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THE WIZARD OF OZ 2 The Wizard of Oz Scarecrow’s Speech on Pythagorean Theorem The Pythagorean theorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher‚ Pythagoras. In the Wizard of Oz‚ after the Scarecrow gets a brain‚ he states the Pythagorean theorem. However‚ he mistakenly says it applies to an isosceles triangle when it applies to a right triangle. He not only says the wrong triangle
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central The Central Limit Theorem A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve‚ Liapounov and Markov and they came up with the central limit theorem. The central limit theorem allows you to measure the variability in your sample results by taking only one sample and it gives a pretty nice way to calculate the probabilities for the total ‚ the average and the proportion
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Application There are some applications of Thevenin’s Theorem in our daily lives. Thevenin’s Theorem is very useful to reduce a network with several voltage sources and resistors to an equivalent circuit composed a single voltage source and a single resistance connected to a load only. It is used in simplifying and analysing complex linear networks power systems and circuits where one particular where a particular load resistor‚ RL in the circuit is subject to change‚ and recalculation of the circuit
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Bernoulli’s theorem i Bernoulli’s theorem‚ in fluid dynamics‚ relation among the pressure‚ velocity‚ and elevation in a moving fluid (liquid or gas)‚ the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady‚ or laminar. First derived (1738) by the Swiss mathematicianDaniel Bernoulli‚ the theorem states‚ in effect‚ that the total mechanical energy of the flowing fluid‚ comprising the energy associated with fluid pressure‚ the gravitational potential
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diagonally or from one tip to the opposite tip‚ we create two surfaces in the shape of triangles. Mathematicians’ related origami to a theorem called the Kawasaki theorem. The Kawasaki theorem states that if we add up the angle measurements of every angle around a point‚ the sum will be 180. It is a theorem giving a decision for an origami construction to be flat. Kawasaki theorem also states that a given crease pattern can be folded to a flat origami if all the sequences of angles ‚ ...‚ are surrounding
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