discret math, Mathematics

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Regression model, Consider the regression model  Y i = a + bX i + u i ,  ...

Consider the regression model  Y i = a + bX i + u i ,  where the  X i   are non-stochastic and the  u i   are independently and identically distributed with  E[u i ] = 0  and  va

Properties of definite integral, Properties 1.  ∫ b a f ( x ) dx = -∫ ...

Properties 1.  ∫ b a f ( x ) dx = -∫ b a f ( x ) dx .  We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral

Binomial theorem, use the expansion of (1-x)^7 to find the value of 1.998^7...

use the expansion of (1-x)^7 to find the value of 1.998^7 correct to five significant figures

Explain pie charts, Explain Pie Charts ? If the frequencies are writte...

Explain Pie Charts ? If the frequencies are written as percentages, they can be easily compared using a pie chart. The following is an example of a pie chart using the data fr

Area, area of r=asin3x

area of r=asin3x

Grouping-categories of situations requiring division , Grouping - situatio...

Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t

Find the curve on the surface - shortest arc lenght, (a) Find the curve on ...

(a) Find the curve on the surface z=x 3/2 joining the points(x,y,z)=(0,0,0) and (1,1,1) has the shortest arc lenght? (b) Use a computer to produce a plot showing the surface an

Modeling with first order differential equations, We here move to one of th...

We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a

Extreme value theorem, Extreme Value Theorem : Assume that f ( x ) is cont...

Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and

Vectors, A 10 m ladder of 150N is placed at an angle 30degrees to a smooth ...

A 10 m ladder of 150N is placed at an angle 30degrees to a smooth wall at point A and the other end (point B) on the ground. Assume that the weight of the ladder acts at its mid po

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