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

Business Documents

Commercial documents, also called "proof," constitute the evidence of any business operation conducted by a company. Thus, each proof tests a type of transaction. It is known that any operation involves at least two parts. For each of them, it will have a different meaning (as discussed later: buyer or seller, debtor or creditor, or collector payer, etc.).

Leases: VAT vs. TPO Taxation

It is important to note the demarcation between Value Added Tax (VAT) and Transfer Tax (Impuesto sobre Transmisiones Patrimoniales Onerosas - TPO). Residential leases and land leases are generally subject to TPO, while leases of business premises are subject to VAT.

Lease Taxation Details (TPO)

• Taxable Event: The constitution of the lease agreement.
• Contributor (Taxpayer): The tenant.
• Taxable Amount: The total rent payable throughout the entire duration of the contract.

Example: If a contract has a duration of one year and the monthly rent is €1,000, what is the tax base for this lease? It is €12,000 (calculated as €1,000 x 12 months). If the contract duration were, for example, 5 years, the calculation would multiply... Continue reading "Spanish VAT & TPO: Leases, Concessions, Vehicles Taxation" »

Understanding Mathematical Competence

Mathematical competence is the ability to use and relate numbers, basic operations, and forms of expression and mathematical reasoning. This skill is used both to produce and interpret different types of information, to expand knowledge on quantitative and spatial aspects of reality, and to resolve problems related to everyday life and the workplace.

Components of Mathematical Competence

Mathematical competence (Comp) is part of the ability to interpret and express with clarity and precision information, data, and arguments. This competency:

• Increases the real possibility to continue learning throughout life, both within and outside of school.
• Favors effective participation in social life.

This competition also... Continue reading "Understanding Mathematical Competence in Everyday Life" »

Precision Measurement Techniques and Instruments

Action

This is the procedure of comparing a magnitude, known as drive power, with another of the same nature to find the relation between them.

Magnitude

Everything is likely to be measured, such as length, mass, or time.

Metrology

The science that studies the measurement of magnitudes. It is currently attempting to standardize so that it will be unique for everyone, and called the International System of Units (SI).

Accuracy of Measurement

Accuracy of measurement is determined by its degree of approximation to the actual value of the magnitude or conventional that is measured. Accuracy is the ability of a measuring instrument to give results with very high accuracy.

Weighing

1. A) Direct measurement: We

Statistical Hypothesis Testing

1. Statistical Hypothesis

A statistical hypothesis is an assertion about a characteristic or parameter of a population. It's used to perform analysis and can be either rejected or accepted based on the provided information. There are two types of hypotheses:

• Null Hypothesis (H₀): Represents the status quo or the default assumption.
• Alternative Hypothesis (H₁): Represents the claim or the hypothesis we want to test.

Both H₀ and H₁ can be simple (if the parameter has only one value) or compound (if the parameter can take multiple values).

2. Significance Level (α)

The significance level is the probability of making a Type I error (rejecting H₀ when it's actually true). It represents the level of risk we're willing to... Continue reading "Statistical Hypothesis Testing: Errors, Power, and Inference" »

Phases of a File Report

Depending on the activity or inactivity of files, a file in healthcare (HC) can be categorized into three stages:

• Active Archive
• Passive File
• Historical Archive

• Active file: This is one that meets the active healthcare compliance (HHCC), i.e., records subject to continued use and consultation.
• Archive candidate: This is one that meets the inactive HHCC, i.e., one that you have to transfer from active files when a query in a time interval of 3 to 5 years is nil. These documents remain here until disposal or transfer to the historical archive.
• Historical Archive: This is where documentation is transferred from the passive file after 10 years without being consulted. These documents are kept permanently because they were not

Payment Process

Payments can be made in cash or deferred. Cash payments can be made in different ways:

• Cash: A receipt will be issued to prove delivery.
• Bank Transfer: Cash deposited directly into a current account.
• Checks
• Credit and Debit Cards
• Letters of Credit

Other common payment instruments include:

• Bills of Exchange
• Promissory Notes

Checks

A check is a document regulated by law, instructing a bank to pay a specified amount from the drawer's funds to the payee. The drawer is entitled to dispose of these funds by check.

Key Parties in a Check Transaction

• Drawer (Maker): The person or entity who issues the check.
• Drawee (Bank): The bank ordered to pay the check.
• Payee (Holder): The person or entity to whom the check is payable.
• Endorser: The party who transmits

Checks: A Comprehensive Overview

What is a Check?

A check is a document instructing a bank (the drawee) to pay a specific amount of money to the check holder (the payee) from the account of the person who wrote the check (the drawer).

Parties Involved

• Drawer: The person who writes and signs the check, authorizing the payment.
• Drawee: The bank or financial institution where the drawer has an account.
• Payee/Holder: The person or entity to whom the check is made payable.
• Guarantor: A person who guarantees payment if the drawer's account has insufficient funds.
• Endorser: The payee who signs the back of the check to transfer ownership.
• Endorsee: The person to whom the check is endorsed.

Types of Checks

Forms of Writing

• Bearer: Payable to the person holding

Slope, Inclination, and Lines

PENDING

Slope

Inclination and Tilt

This refers to the straight tilt or angle of a line.

Parallel Lines Definition

Two lines are parallel if their slopes are equal: L₁ || L₂ if m₁ = m₂.

To find the angle (theta), the slope is used, often in conjunction with trigonometric tables or functions.

Perpendicular Lines Definition

Two lines are perpendicular if they form an angle of 90⁰. This occurs when the product of their slopes is -1:

(m₁)(m₂) = -1

General Equation of a Line

To formulate the general equation of a line, two components are typically needed:

• The slope (m)
• A specific point on the line (x₁, y₁)

The variables (x, y) in the equation represent any point on that line.

Midpoint of a Line Segment

The coordinates of the midpoint... Continue reading "Core Concepts in Analytical Geometry: Lines, Conics, and Algebra" »

Critical Path Method (CPM) vs. PERT

HL (time to completion may be delayed without affecting the beginning of another and final term), HM (the worst case of free float.) Critical path: the path of longer duration and is defined by the sequence of activities that mark critical events in the network. These activities are styled with a double arrow. An activity is critical when it has no slack time, and an event is critical when its TE (earliest time) and TL (latest time) are equal. We must pay critical attention to these routes, as any delay may affect the entire project. Beginning and ending events are critical.

PERT (Program Evaluation Review Technique): It is a probabilistic system that assigns each possible activity three durations: pessimistic,... Continue reading "Critical Path Method (CPM) vs. Program Evaluation Review Technique (PERT)" »