Properties Of Markov Chain

Team Summary Week Two

Brenda Rivera, Bukky Obashe, Alex Lee

MATH 212

June 17, 2012

Serhat Altunc

CH 1.1 Linear Equations and Graphs | | |
The standard form of an inequality equation with one variable is AX+B=0 so A ≠0 | 2X=4 | Ch1, pg 3 |
The solution of an inequality that involves a single variable is a number that when substituted for the variable it makes the equationtrue. | X/2=4/2X=2 | |
| | Ch1, Pg3 |
Linear Inequalities. Linear Inequalities are equations that solve for variables that are graphed along a linear line. | 3X-12>03X>12X>4 ----4< --------- or (4,∞) | Ch1, Pg 5Ch1, pg 6 |
CH 1.2 Graphs and Lines | | |
The equation form for solving for two variables is AX+BY=CThis equation is used to find the X and Y intercepts forgraphs. The standard form for a linear equation in two variables is Ax + By = C with A and B not both zero. The graph of this equation is a line, and every line in a Cartesian coordinate system is the graph of a linear equation. | 3X-4Y=12 -4Y=12-3X -4Y/4 = (12-3X)/4 so Y = (12-3x)/4Once you have found either X or Y you then substitute a number for the unsolved variable.Y = (12-3*2)/4 Y=1.5Once you have solved for one variable you substitute the number for that variable and redo the equation to solve for the other.3X-4*1.5=12 3X-6=12 3X=12+6 3X=18 3X/3 = 18/3 X=6The ordered pair would be (6,1.5). This would be your intercept point. | Ch1, pg 15 |
The equation for finding the slope of a line would beM= (Y2-Y1) / (X2-X1)The point-slope form of the equation of the line withslope m that passes through (x1, y1) is y - y1 = m(x - x1). | Given intercept points (0,300) , (100,4300)So M = (4300-300) / (100-0)So M = 40 | Ch 1, Pg 16Ch.1, pg 19 |
To find the Slope Intercept you use the formulaY=MX+BThe equation y = mx + b is the slope-intercept form of the equation of the line with slope m and y intercept b. | You substitute in the slope”M” and B for the Y intercept pointfrom a given pairY=40X+300You then substitute X and Y for an ordered pair. | Ch 1,pg 19 |
CH 1.3 LINEAR REGRESSIONA graph of the points in a data set is called a scatter plot. Linear regression is used to find the line that is the best fit for a data set. A regression model can be used to interpolate between points in a data set or to extrapolate or predict points outside the data set.If thevariables x and y are related by the equation y = mx + b then x and y are linearly related and the slope m is the rate of change of y with respect to x. In applications, ratio (1) is called the rate of change of y with respect to x. Since the slope of a line is unique, the rate of change of two linearly related variables is constant. | Example | Ch1, pg 28Ch.1, pg 28 |
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| | Ch.1 , pg 31|
Chapter 2 Functions and Graphs | Examples | Reference (Where is it in the text?) |
Equations in Two VariablesThe graph of an equation of the form AX+BY=C where A and B are not both zero, is a line. Because a line is determined by any two of its points, such an equation is easy to graph: Just plot any two points in its solution set and sketch the unique line through them. | | Ch 2, pg 44 |A function is a correspondence between two sets of elements such that to each element in the first set there corresponds to one and only one element in the second set. The first set is called the domain, and the set of corresponding elements in the second set is called the range. | | Ch. 2, pg 46 |
Functions Specified by EquationsIf in an equation in two variables, we get exactly one output(value for the dependent variable) for each input (value for the independent variable), then the equation specifies a function. The graph of such a function is just the graph of the specifying equation. If we get more than one output for a given input, the equation does not specify a function. | | Ch.2, pg 47 |
The graphs of six basic elementary functions (the identity function, the square and...