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Exam 5
Exam 5

... Thus with the simplex method we are evaluating z at some but not all of the corner points. The simplex method is designed so that the value of z increases on each step and stops when we reach a maximum. Note that the simplex method gives us only one solution even if the problem to which it is applie ...
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... 11). Which Properties of Inequality differ from the corresponding Properties of Equality? Explain and include examples. 12). Why do the graphs of some inequalities include open circles, while others do not? Explain. 13). Describe two kinds of compound inequalities. ...
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... number 536, it would be nicer if there were 4 more ones. So we just rewrite 176 to make it easier. [If the sum is quick, just do the sum.] 536  176  536  4  172  536  4  172  540  172 . Step 2: Now consider the new value, 540. It would be nicer if there were 6 more tens. So we just re ...
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On Triangular and Trapezoidal Numbers

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... This solution can also be derived from Theorem 1 since the characteristic polynomial has the decomposition (5). Since the DIFS of order (r^r) is the r-fold convolution of DIFS of order ...
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2007 KS3 SATs Maths Level 4-6 (Paper 1)

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Law of large numbers



In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)
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