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

Annual Accounts

• Balance Sheet: Reflects the equity, representing the resources available to the employer to carry out activities.
  • Profit and Loss Account: Measures the income generated by the business.
  • Statement of Changes in Equity: Collects the variation in the company's equity.
  • Cash Flow Statement: Reports on the origin and use of monetary assets, representing cash and cash equivalents classified by activity.
  • Notes to the Accounts: Expands the information collected in the annual accounts and contains additional details.

Corporate Social Responsibility and Audits

• Social Balance of the Company: A document that extends the study of the business's effects on its environment, determining direct or indirect impacts on public welfare.
• Audit: An analysis

Secondary Data Analysis: Sources and Elaboration

Secondary data analysis considers both qualitative and quantitative perspectives. It uses references like coding sheets in quantitative designs and identifies interviews or focus groups for qualitative data. Official statistics and public sources are used to verify field data.

Desrosieres argues that statistical indicators from official sources reflect social reality in institutions. These indicators are presented without analysis, as tables of results. This means the original data has been elaborated, which is typical of secondary sources. Secondary sources have developed, summarized, and synthesized the data. The degree of elaboration is the key difference between secondary data analysis and... Continue reading "Secondary Data Analysis: Sources, Types, and Elaboration" »

Angles 2001: Antonio Banderas

• A: 1.a, 2.c, 3.d, 4.b, 5.a, 6.b, 7.d, 8.c, 9.c, 10.d
• B: 1. continuing, 2. received, 3. debut, 4. role/part, 5. previous
• C: 1.b, 2.c, 3.a, 4.b, 5.c

Angles 2001: Brad Pitt

• A: 1.d, 2.c, 3.a, 4.b, 5.d, 6.c, 7.d, 8.a, 9.b, 10.d
• B: 1. key, 2. movies, 3. trouble, 4. hopped, 5. top
• C: 1.c, 2.b, 3.b, 4.a, 5.c

Angles 2001: Jacques Cousteau

• A: 1.d, 2.c, 3.b, 4.a, 5.b, 6.a, 7.c, 8.d, 9.b, 10.c
• B: 1. teens, 2. best-known, 3. machine, 4. locate, 5. purchased
• C: 1.c, 2.a, 3.c, 4.b, 5.b

Angles 2003: Africa's New Tech Warriors

• A: 1.c, 2.b, 3.a, 4.d, 5.b, 6.a, 7.a, 8.d, 9.c, 10.b
• B: 1. change, 2. persuaded, 3. aim, 4. instructor, 5. dream
• C: 1.b, 2.c, 3.a, 4.d, 5.c

Angles 2003: Best Friend Donates Kidney

• A: 1.a, 2.c, 3.b, 4.a, 5.d, 6.c, 7.d, 8.a,

Accounting Obligations and Responsible Parties

Every employer shall keep proper accounts, appropriate to the activity of the company, to allow for the chronological tracing of all operations and the preparation of periodic reports and inventories. The records shall be maintained directly by employers or other authorized persons, without prejudice to their responsibility.

Compulsory Accounting Books

• Book of inventories and annual accounts
• Journal
• Minute book or record books (for corporations)

Legalization of Books

Legalization will take place in the Commercial Register at the address of the enterprise. It can be done a priori (before use) or afterwards in the event that the accounting entries are made on sheets which will then be bound to be correlatively... Continue reading "Accounting Regulations and Bookkeeping for Entrepreneurs" »

Hurwicz Criterion: Coefficient of Optimism

In this approach, a decision-maker may have an intermediate attitude. Since no probabilities are associated with each state of nature, this author suggests using a coefficient of optimism, simultaneously called C, and a coefficient of pessimism, (1 - C), where 0 ≤ C ≤ 1.

The coefficient C indicates the decision-maker's stance toward risk. When it is closer to 1, the decision-maker will be more optimistic, while closer to 0, the decision-maker is more pessimistic.

This criterion focuses only on the extreme scores of each alternative, weighing the result of maximum optimism with the coefficient C and the result of minimal value with the coefficient of pessimism (1 - C). The sum of these two products... Continue reading "Decision-Making Under Uncertainty: Criteria and Tables" »

Fundamental Data Mining Tasks and Concepts

Prediction: Forecasting Time Series Data

Prediction involves estimating the future value of a variable that is subject to random changes over time. This technique is strictly applied to time series, which are datasets whose domain is time.

Regression Analysis: Modeling Relationships

Regression is a generalization of classification (when the domain involves continuous classes) and prediction. The resulting model (classification or prediction) depends on the significance of the dependent and independent variables.

The goal is to find a mathematical or statistical model that properly relates the dependent variable with the independent variables. Geometrically, regression seeks a function that passes as close... Continue reading "Fundamental Data Mining Tasks and Algorithmic Approaches" »

The Concept of Materiality in Auditing

The auditor assesses the amount of errors or omissions that could affect the decisions of a reasonable user. This concept involves:

• Flexible guidelines.
• Both quantitative and qualitative elements.

Stages in the Application of Materiality

1. Establish a Preliminary Judgment on Materiality (Planning)

   This is the maximum amount of misstatement the auditor believes can exist in the financial statements without affecting the decisions of reasonable users. It is affected by the relative size of the company being audited.

   First, the auditor establishes a base (e.g., total assets, profits, turnover), which is multiplied by a percentage factor to determine an initial quantitative judgment. This initial judgment is then adjusted

Cutting speed depends on mining velocity. The cutter's speed must remain constant throughout its journey through the ore flow.

Sampling Methods

Sampling can be performed using manual or mechanical methods. Manual methods include cone and quartering, sampling with scoops or shovels, and using sampling tubes.

Manual Sampling Techniques

Cone and Quartering

1. Stack material into a conical pile by shoveling.
2. Form a cake or 'qeqe'.
3. Divide the cake into four equal fractions.
4. Take two opposite quarters as the sample; reject the other two.
5. If the sample size is adequate, combine the two retained quarters and reduce their size.
6. Repeat steps 1-4 as necessary until the desired sample size is achieved.

Sampling Scoop or Shovel

This procedure is used when ore is moved... Continue reading "Mining Ore Sampling Techniques and Procedures" »

Fundamental Accounting Principles

• Basis: The van should be evaluated by its purchase price as it has been purchased for use and not for sale.
• Accrual: November 1, 20XX [2,400 / 12 = 200] [200 x 2 = 400]. For November and December: 200 + 200.
• Uniformity: To change the method, there needs to be a valid reason, such as altered circumstances that prompted the company to choose the original criteria. You should also explain the reasons for the change and its impact on the annual accounts, applying it to all elements with the same features.
• Prudence: Until the completion of the sale, it is not reflected in the accounts.
• No Compensation: Balances must be included in two different accounts: a right to receive and a payment obligation. This avoids loss of