Notes, summaries, assignments, exams, and problems for Mathematics

Key Terms in Linear Programming & Optimization

Constraint

An equation or inequality that rules out certain combinations of decision variables as feasible solutions.

Problem Formulation

The process of translating a verbal statement of a problem into a mathematical statement called the mathematical model.

Mathematical Model

A representation of a problem where the objective and all constraint conditions are described by mathematical expressions.

Decision Variable

A controllable input for a linear programming model.

Objective Function

The expression that defines the quantity to be maximized or minimized in a linear programming model.

Nonnegativity Constraints

A set of constraints that requires all variables to be nonnegative.

Linear Program

A mathematical... Continue reading "Linear Programming Terminology: Core Concepts Defined" »

Sensitivity Analysis: The study of how changes in the coefficients of a linear programming problem affect the optimal solution.

Objective Function Coefficient Allowable Increase (Decrease): The allowable increase (decrease) of an objective function coefficient is the amount the coefficient may increase (decrease) without causing any change in the values of the decision variables in the optimal solution. The allowable increase/decrease for the objective function coefficients can be used to calculate the range of optimality.

Objective Coefficient Range (Range of Optimality): The range of values over which an objective function coefficient may vary without causing any change in the values of the decision variables in the optimal solution.

Shadow

1. The t-test is never valid if the sample size is small, say less than 30. (TRUE OR FALSE)

It can be valid if the sample is approximately normal.

2. The results of an observational study indicate that people who use vitamin supplements get fewer colds than people who don't. However, we can't conclude that vitamin supplements prevent colds because this type of study does not allow us to infer causation. (TRUE OR FALSE)

Only experimental designs can infer causation because it allows us to create treatment groups that are very similar.

3. A survey was administered to a random sample of college students. Both males and females were surveyed, and one question asked was "How much are you willing to spend on a stereo system (in dollars)?" An analysis

Polygon Interior Angles Theorem

The sum of the measures of interior angles of an n-gon is (n-2)x180

Interior angles of a quadrilateral:

The sum of the measures of the interior angles of a quadrilateral is 360^o

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Angles have to measure up to 360. 360/n (n=#of sides)

Theorems

If a quadrilateral is a parallelogram, then its opposite sides are congruent

If a quadrilateral is a parallelogram, then its opposite angles are congruent

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

If a quadrilateral is a parallelogram, then its diagonal bisects each other

If both pairs of opposite sides of a quadrilateral

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Accounting Fundamentals: Key Concepts & Transactions

What is Statistics?

Statistics is a set of tools designed to analyze data and deduce information about a population from a given sample.

The Three-Step Process of Statistics

1. Sampling and Design of the Experiment: Take a sample (or many) from the population, make observations about the sample, and turn them into numerical data.
2. Descriptive Statistics: Analyze the data to get information about the sample.
3. Statistical Inference: From the data, deduce information about the whole population.

Context is Crucial

The context of a statistical study is crucial in interpreting the results. A population is a set of individuals (people, cases, etc.) that we want to analyze. A sample is a subset of the population. A variable is an aspect or characteristic of the... Continue reading "Statistics: A Guide to Data Analysis and Population Inference" »

MONEY

Budgeting and Expenses

• Budget: A plan for how to spend money.
• Grant: Money given by the government for a particular purpose, often education.
• Loan: Money borrowed from a bank or other lender, usually with interest.
• Fee: Money paid for a professional service (e.g., lawyer, consultant).
• Fare: Money paid to travel by bus, train, taxi, etc.

Savings and Investments

• Savings: Money set aside for future use.
• Donation: Money given to a charity or other organization.
• Deposit: A portion of a larger payment made upfront.
• Will: A legal document that specifies how a person's assets will be distributed after their death.
• Lump sum: A single payment of a large amount of money.

Financial Terms

• Fine: Money paid as a penalty for breaking a rule or law.
• Installment: A

Decision Making and Problem Solving

Defining the Process

Problem Solving: Identifying the difference between the actual and desired state of affairs, and taking action to resolve the difference.

Decision Making: Defining the problem, identifying alternatives, determining criteria, evaluating alternatives, and choosing an alternative.

Types of Decision Problems

Single-Criterion Decision Problem: Finding the best solution based on one criterion.

Multicriteria Decision Problem: Finding the best solution considering multiple criteria.

Key Concepts in Decision Making

Decision: The selected alternative.

Model: A representation of a real object or situation.

• Iconic Model: A physical replica of a real object.
• Analog Model: A physical representation, but doesn'

Probability Distributions

Discrete Random Variables

1. If the outcomes of a discrete random variable follow a Poisson distribution, then which of the following is true?
   • (A) The mean equals the variance.
2. Which of the following is not a characteristic of a binomial probability distribution?
   • (A) Each trial has a finite number of possible outcomes.
3. If the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a binomial distribution and round the answer to four places.)
   • (C) 0.1800
4. The number of arrivals of delivery trucks per hour at a loading station is an example of which of the following processes?
   • (C) Poisson
5. When sampling without replacement