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

Part I: Complete the Following Table

Part II: Complete the Following Sentences

1. She is from the United States. She is American.
2. She is from Nigeria. She is Nigerian.
3. She is from Germany. She is German.
4. They are from Egypt. They are Egyptian.
5. We are from Canada. We are Canadian.

Part III: Select the Correct Sentence

1. Select the correct sentence.
   • a) She lives with Carlos, and she works on Saturdays.
2. Select the correct sentence.
   • c) They are running in the park.
3. Select the correct sentence.
   • b) She is 20 years old.
4. Select the correct sentence.
   • a) We always

Fundamental Accounting Principles and Practices

Core Accounting Definitions

Assets = Liabilities + Owner’s Equity: This is the fundamental accounting equation, representing the balance of a company's financial position.

Double-Entry Accounting

The recording of both debit and credit parts of every transaction, ensuring the accounting equation remains balanced.

Objective Evidence Principle

Requires that a source document (e.g., invoice, receipt) be prepared for every entry in a journal, providing verifiable proof of a transaction.

File Maintenance

The process of arranging accounts in a general ledger, assigning account numbers, and keeping records current.

Opening an Account

Writing an account title and number on the heading of an account in the ledger.... Continue reading "Essential Accounting Concepts and Financial Reporting" »

Chapter 1: Core Accounting Fundamentals

Key Financial Statements Equations

• Balance Sheet (BS) Equation: Assets = Liabilities + Stockholders' Equity (SHE)
• Income Statement (IS) Equation: Revenues - Expenses = Net Income (NI)
• Retained Earnings (RE) Equation: Beginning RE + Net Income - Dividends = Ending RE

Debit and Credit Rules

• A Debit increases: Expenses, Assets, Dividends (DEAD)
• A Credit increases: Liabilities, Revenues, Equity (CLEAR)

Objective of Financial Reporting

1. Provide information useful to equity investors and creditors.
2. Maintain the Entity Perspective (separating the company from its owners/people).
3. Ensure Decision Usefulness.

Adjusting Entries: Deferrals and Accruals

Deferrals (Cash Paid/Received Before Recognition)

Prepaid Expenses

Meaning: Paid... Continue reading "Core Financial Accounting Concepts and Principles" »

Math Reference Cheat Sheet

Rules for Multiplying and Dividing Integers

Special Rules for Integers

• Even amount of negative integers: Product/quotient is positive.
• Odd amount of negative integers: Product/quotient is negative.

Classifying Decimals

• Terminating decimals: Have a remainder of zero; the decimal stops.
• Non-terminating decimals: Continue infinitely.
  • Repeating: Continues infinitely and repeats a pattern (denoted by bar notation). Examples: 0.333..., 0.49090..., 0.166...
  • Non-repeating: Continues infinitely but does not repeat a pattern. Examples: Pi (π) and Euler's number (e).

Calculating Percent Error

% Error = [(Estimated Value... Continue reading "Essential Math Cheat Sheet: Integers, Decimals, and Properties" »

Metallurgical sample preparation for microscopy is a crucial step in analyzing the microstructure and properties of metallic materials. Proper sample preparation is essential to obtain accurate and meaningful results. The process involves several key steps:

1. Sample Selection for Microscopy

Choose a representative portion of the material to be analyzed. Ensure that the sample is free from external contaminants and has a flat surface for preparation.

2. Precision Cutting Techniques

Use a precision cutting method to obtain a small section of the material for analysis. Common cutting techniques include abrasive cutting (using a saw with abrasive blades), wire cutting, or electrical discharge machining (EDM) for hard materials.

3. Sample Mounting for

Bond Characteristics

• Coupon: The interest payment made by the bond issuer, usually expressed as an annual percentage of the bond's face value.
• Par (Face Value): The amount the bondholder receives when the bond matures, typically $1,000.
• Term to Maturity: The time remaining until the bond's maturity date when the issuer must repay the bond's par value.
• Denomination: The face value of the bond, usually in increments of $1,000.
• Quotation: Bonds are quoted as a percentage of their face value (e.g., a bond quoted at 95 is selling for 95% of $1,000, or $950).

Bond Prices, Yield to Maturity (YTM), Current Yield, and Rate of Return (HPR)

• Bond Prices: The market price of a bond depends on interest rates. Prices and interest rates have an inverse relationship.

Essential Financial Statement Formulas

• Stockholder Equity: Total Assets – Total Liabilities
• Retained Earnings: Net Income – Dividends Declared
• Net Income: Sales Revenue – Expenses
• Gross Profit: Sales Revenue – Cost of Goods Sold (COGS)
• Cost of Goods Sold (COGS) based on Rate: (1 – Gross Profit Rate) × Net Sales

Inventory Accounting Adjustments (LIFO and FIFO)

• Calculating LIFO Reserve: FIFO Ending Inventory Cost – LIFO Ending Inventory Cost
• Adjusting Balance Sheet from LIFO to FIFO Inventory: LIFO Reserve + LIFO Inventory

Accounting Estimates and Depreciation

Changing Accounting Estimates

• Book Value at Date of Change: Costs – Accumulated Depreciation
• New Remaining Useful Life: Original Life – Years Depreciated + Additional Years
• Depreciation

Discrete Random Variables

Discrete random variables are variables that can take on a finite number of distinct values. In simpler terms, a discrete random variable is a set of possible outcomes that is countable.

Continuous Random Variables

Continuous random variables are random variables that take an infinitely uncountable number of potential values, typically measurable amounts.

Example

1. List the sample space in the given experiment. How many outcomes are possible?

The sample space is: S = {NNN, NND, NDN, NDD, DNN, DND, DDN, DDD}

2. Count the number of defective keyboards in each outcome in the sample space and assign this number to the outcome. For instance, if you list NND, then the number of defective keyboards is 1.

The possible values of X are 0,... Continue reading "Introduction to Statistics: Discrete and Continuous Random Variables, Probability Distributions, and Sampling Techniques" »

Why Reinforcement Learning?

Reinforcement Learning (RL) is important because it enables machines to learn optimal behaviors through interaction with their environment, without needing labeled input/output pairs. It is especially useful in scenarios where the best actions are not immediately known, such as game playing, robotics, or dynamic pricing.

In RL, the agent gradually learns to take actions that maximize cumulative future rewards. Unlike supervised learning, RL focuses on long-term outcomes, rather than just immediate correctness.

Main Elements of Reinforcement Learning

• Agent: The learner or decision-maker.
• Environment: Everything the agent interacts with.
• State (S): The current situation of the environment.
• Action (A): Choices available to

Inventory Fundamentals

One use of inventory is to provide a hedge against inflation. ABC analysis divides an organization's on-hand inventory into three classes based upon annual dollar volume. Cycle counting is a process by which inventory records are verified. The difference(s) between the basic EOQ model and the production order quantity model is that the production order quantity model does not require the assumption of instantaneous delivery. Extra units that are held in inventory to reduce stockouts are called safety stock. Inventory record accuracy would be decreased by increasing stockroom accessibility. The two most important inventory-based questions answered by the typical inventory model are when to place an order and how many of