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

Research Concepts and Terminologies

• Element: The basic unit of the population.
• Population: The entire group of interest.
• Study Population: The specific subset being studied.
• Sample: A subset of the population.
• Sampling Unit: The individual entity selected.
• Sampling Frame: The list of all units in the population.
• Observation Units: The units from which data is collected.
• Variable: A characteristic that varies.
• Parameter: A numerical characteristic of a population.
• Statistics: Numerical characteristics of a sample.
• Sampling Error: The difference between sample and population values.

Sampling Procedures

Non-Probability Sampling

• Accidental Sampling
• Quota Sampling
• Convenience Sampling
• Purposive Sampling

Probability Sampling

• Random Sampling
• Systematic Sampling
• Stratified

) Hypotheses, Type I and Type II Errors, and Statistical Tests

For each of the following tests, state the hypotheses, identify if it is a right-, left-, or two-tailed test and write Type I Error and Type II Error pertaining to the problem.

1. a) A professor of statistics states that the average student spends 3 hours studying for the midterm exam. Ho: μ = 3 vs. Ha: μ ≠ 3 Two-tailed test Type I Error: Concluding the average student doesn’t study 3 hours for midterm when in fact that is false. Type II Error: Not concluding the average student doesn’t study 3 hours for midterm when in fact that is true.
2. b) A spouse stated that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. Ho: μ = 1200 (or

Accounting Principles and Financial Analysis Practice

1. The accounting equation can be expressed in all of the following ways except: LIABILITIES = ASSETS + OWNER’S EQUITY

2. The financial statements, in the order in which they are prepared, are: INCOME STATEMENT, RETAINED EARNINGS, BALANCE SHEET, AND CASH FLOW.

3. An account, in its simple form, is made up of which parts? A TITLE, A DEBIT SIDE, AND A CREDIT SIDE

4. Every transaction affects at least two accounts. The purchase of land in exchange for cash is recorded with which of the following entries? DEBIT TO LAND AND CREDIT TO CASH

5. A credit may represent a: INCREASE IN LIABILITY ACCOUNT

6. A prepaid expense, such as the purchase of insurance for an upcoming period, is initially recorded in the accounting

Linear Programming

Linear Programming is an optimization technique useful for allocating scarce resources among competing demands.

Examples of LP Applications

• Selecting the product mix in a factory to make the best use of machine and labor hours available while maximizing the firm’s profit.
• Scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor.
• Determining food ingredient combinations that satisfy stated nutritional requirements at a minimum cost level.

Basic Concepts

• A single objective function states mathematically what is being maximized or minimized.
• Decision variables represent choices that the decision maker can control.
• Constraints are limitations that restrict the decision variables.

Planes in 3D Space

Equations for planes parallel to coordinate planes:

• x = a (parallel to yz-plane)
• y = b (parallel to xz-plane)
• z = c (parallel to xy-plane)

Example: Plane Through a Point

Find the equation of the plane passing through (3, -1, 7) and perpendicular to the vector n = <4, 2, -3>:

4(x - 3) + 2(y + 1) - 3(z - 7) = 0

Example: Plane Through Three Points

Find the equation of the plane through P₁(1, 2, -1), P₂(2, 3, 1), and P₃(3, -1, 2):

P₁P₂ = <1, 1, 2>; P₁P₃ = <2, -3, 3>

n = P₁P₂ × P₁P₃ = <9, 1, -5>

Equation: 9(x - 1) + 1(y - 2) - 5(z + 1) = 0

Example: Line and Plane Parallelism

Determine if the line x = 3 + 8t, y = 4 + 5t, z = -3 - t is parallel to the plane x - 3y + 5z = 12.

The line is parallel to the plane if it is perpendicular... Continue reading "Mastering Planes, Quadratic Surfaces, and 3D Coordinates" »

Golden circle:

This relates to the innovation. If a company is able to attract those who share its beliefs, it is also able to connect easier with innovators.

This is a graph made up of three circles, each inside the other. Each circle has a meaning and a way to apply it to our business efficiently.

We can explain the operation of the Golden Circle in such a way that while most companies ask themselves the answers to the question 'what' as their starting point, they are fully aware of the 'how', but very few companies are clear about the 'why'.

The 'what' responds to what we do and what we want to do. The 'how' responds to the processes through which we carry out our actions, and the 'why' would respond to the reason why we develop our business.... Continue reading "The Golden Circle: Driving Innovation and Quality Management" »

Essential Aspects of Corporate Liquidity Analysis

There are two essential aspects in the analysis of the liquidity of a company. On one hand, there is the quality of the coverage of current debts with the most liquid assets; on the other hand, there is the temporal aspect—that is, the agility of current assets to become cash, as well as the agility of current debts to expire.

Evaluating Debt Coverage and Working Capital

In order to analyze the quality of the coverage of current debts, we start by calculating the working capital and its complementary ratios. The positive value of the working capital serves as an indicator (though never definitive evidence) of a good liquidity situation.

Liquidity Ratios: Acid Test and Cash Ratio

Due to the limitations... Continue reading "Analyzing Corporate Liquidity and Financial Health" »

Market Value Performance Measures

• Market Value Added (MVA): Market Capitalization (Number of shares × Price per share) - Equity.
• Market-to-Book Ratio: Measures value added per dollar invested by shareholders. Calculated as: Market Value of Equity / Book Value of Equity (Total Shareholders' Equity).

Measuring Profitability

• Economic Value Added (EVA): Profit after deducting all costs, including the cost of capital. Formula: [After-tax operating income] - [Cost of Capital × Total Capitalization at start of year (Long-term debt + Total equity)].
• Return on Equity (ROE): Net Income / Equity (start of year).
• Return on Assets (ROA): [(1 - Tax Rate) × Interest Expense + Net Income] / Total Assets (start of year).
• Return on Capital (ROC): [(1 - Tax Rate)