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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
HOW MUCH WILL A NEW CAR COST? THE AVERAGE COST OF A NEW CAR IN 1990 WAS $14371. IN 2003 THE AVERAGE COST HAD RISEN TO $22360. WHAT IS THE AMOUNT OF THE MONTHLY PAYMENT? THE AMOUNT
Exponential smoothing It is a weighted moving average technique, this is described by: New forecast = Old forecast + a (Latest Observation - Old forecast) Whereas a = Sm
(a) The generating function G(z) for a sequence g n is given by G(z) = 1 - 2z/(1 + 3z)3 Give an explicit formula for g n . (b) For the sequence gn in the previous part co
sin2A+cos2A
GENERAL RULE A general rule is to subtract the probabilities with an even number of components inside the parentheses and add those with an odd number of components (one or th
Levels of significance A level of significance is a probability value which is utilized when conducting tests of hypothesis. A level of significance is mostly the probability
Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.
A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx
Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to
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