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Functions | |

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Real Numbers, Inequalities, and Lines | |

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Real Numbers and Inequalities | |

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Sets and Intervals | |

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The Cartesian Plane | |

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Lines and Slopes | |

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Equations of Lines | |

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General Linear Equation | |

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Exponents | |

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Positive Integer Exponents | |

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Properties of Exponents | |

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Zero and Negative Exponents | |

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Roots and Fractional Exponents | |

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Fractional Exponents | |

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Avoiding Pitfalls in Simplifying | |

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Learning Curves in Airplane Production | |

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Functions | |

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Functions | |

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Solving Quadratic Equations | |

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Derivation of the Vertex Formula | |

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Derivation of the Quadratic Formula | |

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More About Functions | |

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Polynomial Functions | |

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Rational Functions | |

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Piecewise Linear Functions | |

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Composite Functions | |

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Shifts of Graphs | |

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Exponential Functions | |

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Exponential Functions | |

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Compound IntereSt. Depreciation by a Fixed Percentage | |

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The Number e | |

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Continuous Compounding of IntereSt | |

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Intuitive Meaning of Continuous Compounding | |

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The Function y = ex | |

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Exponential Growth | |

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Justification of the Formula for Continuous Compounding | |

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Logarithmic Functions | |

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Common Logarithms | |

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Properties of Common Logarithms | |

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Graphs of Logarithmic and Exponential Functions | |

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Logarithms to Other Bases | |

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Natural Logarithms | |

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Carbon-14 Dating | |

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Mathematics Of Finance | |

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Simple IntereSt | |

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Simple Interest Formula | |

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Total Amount Due on a Loan | |

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Discounted Loans and Effective Interest Rates | |

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Compound IntereSt | |

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Compound Interest Formula | |

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Growth Times | |

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Rule of | |

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Effective Rates | |

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Recap | |

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Annuities | |

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A First Example | |

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Geometric Series | |

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Accumulated Account Formula | |

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Sinking Funds | |

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How Long Will It Take? | |

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Amortization | |

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Present Value of an Annuity | |

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Amortization | |

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Unpaid Balance | |

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Equity | |

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Systems Of Equations And Matrices | |

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Systems of Two Linear Equations in Two Variables | |

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Systems of Equations | |

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Graphical Representations of Equations | |

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Equivalent Systems of Equations | |

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Elimination Method | |

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Matrices and Linear Equations in Two Variables | |

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Matrices | |

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Augmented Matrices from Systems of Equations | |

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Row Operations | |

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Solving Equations by Row Reduction | |

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Systems of Linear Equations and the Gauss-Jordan Method | |

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Names for Many Variables | |

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Row-Reduced Form | |

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Matrix Arithmetic | |

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Equality of Matrices | |

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Transpose of a Matrix | |

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Identity Matrix | |

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Scalar Multiplication | |

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Matrix Addition and Subtraction | |

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Matrix Multiplication as Evaluation | |

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Identity Matrices | |

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Matrix Multiplication with Systems of Equations | |

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Matrix Multiplication and Row Operations | |

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Inverse Matrices and Systems of Linear Equations | |

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Inverse Matrices | |

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How to Find Inverse Matrices | |

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Solving AX = B Using A-1 | |

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Introduction to Modeling: Leontief Models | |

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Linear Programming | |

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Linear Inequalities | |

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Inequalities in Two Variables | |

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Vertices of Feasible Regions | |

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Bounded and Unbounded Regions | |

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Applications | |

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Two-Variable Linear Programming Problems | |

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Linear Programming Problems | |

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Fundamental Theorem of Linear Programming | |

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Extensions to Larger Problems | |

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The Simplex Method for Standard Maximum Problems | |

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Standard Maximum Problems | |

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Matrix Form of a Standard Maximum Problem | |

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The Initial Simplex Tableau | |

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Basic and Nonbasic Variables | |

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The Pivot Element | |

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The Pivot Operation | |

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The Simplex Method | |

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Standard Minimum Problems and Duality | |

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Standard Minimum Problems | |

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The Dual of a Standard Minimum Problem | |

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Matrix Form | |

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Mixed Constraints: A Transportation Problem | |

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Probability | |

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Sets, Counting, and Venn Diagrams | |

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Sets and Set Operations | |

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Addition Principle for Counting | |

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The Multiplication Principle for Counting | |

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The Number of Subsets of a Set | |

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Permutations and Combinations | |

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Factorials | |

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Permutations | |

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Combinations | |

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Probability Spaces | |

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Random Experiments and Sample Spaces | |

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Events | |

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Probabilities of Possible Outcomes | |

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Probabilities of Events | |

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Probability That an Event Does Not Occur | |

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Probability Space | |

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Addition Rule for Probability | |

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Conditional Probability and Independence | |

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Conditional Probability | |

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The Product Rule for Probability | |

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Independent Events | |

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Bayes' Formula | |

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Bayes' Formula | |

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Random Variables and Distributions | |

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Random Variables | |

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Expected Value | |

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Binomial Distribution | |

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Statistics | |

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Random Samples and Data Organization | |

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Random Samples | |

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Bar Chart | |

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Histogram | |

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Measures of Central Tendency | |

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Mode | |

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Median | |

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Mean | |

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Mean, Median, and Mode | |

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Measures of Variation | |

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Range | |

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Box-and-Whisker Plot | |

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Interpreting Box-and-Whisker Plots | |

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Sample Standard Deviation | |

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Normal Distributions and Binomial Approximation | |

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Discrete and Continuous Random Variables | |

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Normal Distribution | |

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z-Scores | |

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The Normal and Binomial Distributions | |

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Markov Chains | |

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States and Transitions | |

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States and Transitions | |

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Markov Chains | |

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Types of Transition Matrices | |

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State Distribution Vectors | |

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The kth State Distribution Vector | |

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Duration in a Given State | |

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Regular Markov Chains | |

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Regular Markov Chains | |

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The Fundamental Theorem of Regular Markov Chains | |

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How to Solve D ? T = D | |

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Absorbing Markov Chains | |

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Absorbing Markov Chains | |

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Standard Form | |

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Transition Times and Absorption Probabilities | |

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Game Theory | |

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Two-Person Games and Saddle Points | |

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Payoff Matrix | |

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Optimal Strategy | |

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Finding Saddle Points | |

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Mixed Strategies | |

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Mixed Strategies and Expected Values | |

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Optimal Mixed Strategies for 2 ? 2 Games | |

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Other Interpretations of Mixed Strategies | |

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Games and Linear Programming | |

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Games as Linear Programming Problems | |

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Every Game Has a Solution | |

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Index | |