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

Grounded Theory: Strategies and Methods

Grounded theory has two main strategies:

Theoretical Sampling

Involves adding to the sample of subjects or situations encountered, additional comments, or further interviews. It seeks to find different cases.

Constant Comparative Method

It is a method to analyze the data at different times in which the researcher interacts with:

1. Classified portions of data:
   • Words
   • Phrases
   • Paragraphs

Categories arise, either intuited or implicit (they are marked, but without a name).

Constant Comparative Method

As the process of selecting pieces of data advances, categories appear with more explicit rules.

The task is to identify:

1. Emerging categories = Issues
   • Categories = Properties
2. Central category = Recurring Themes

Links between categories... Continue reading "Grounded Theory: Strategies, Methods, and Analysis" »

Surveying Measurement Accuracy and Error Propagation

Tolerance should be imposed only by the requirements of the research. It should be conditional on the surveying instrument used for this tolerance; it would be naive to expect very great accuracy using a blunt instrument.

Transmission Error (Mean Square Error of a Sum)

The mean square error (MSE) of a sum is equal to the square root of the sum of the squares of the mean square errors of the summands, provided the measurements are made with different precision. If measurements are performed with equal precision, it can be shown that the mean square error is the same for all addends.

Exercises

1. Six measures of the length of a building's facade were made using a steel tape (listed in the table... Continue reading "Surveying Measurement Accuracy and Theodolite Error Analysis" »

Substance Concentration Data Grouping

The content of a substance in a liquid is given with an accuracy of 5 milligrams per liter. As such, the data can take values from this sequence:

• 120
• 125
• 130
• 135
• 140
• 145

Grouping Amplitude and Frequency Table Construction

The problem states a data set ranging between 110 and 245. However, the provided calculation for the number of steps, (247.7 - 107.5) / 25 = 5.6, implies a wider range. This calculation indicates that 6 steps (intervals) of 25 units each are needed. Since 6 intervals of 25 units cover 150 units, the apparent limits can be started with a round number to accommodate the required range.

**Purchase Operations**

Shopping is any transaction by which a person receives the domain of property for valuable consideration. The purchase consists of two stages or operations:

**Request for Purchase or Requisition of Goods**

This is a formal request made by a department or warehouse operations, being directed to the purchasing department.

**Order Form**

The purchasing department receives the application and analyzes the real need, according to the financial situation and market conditions, as the article refers.

**Reception Guide**

This is a document issued by the warehouse when it acquires the goods from suppliers. Prior to the receipt, the warehouse manager must take care to verify if the merchandise received matches the packing list issued... Continue reading "Purchase and Sales Operations: Essential Documents" »

Key Warehouse Functions

Departure

• Monitor the consumption of items by various departments.
• Suitably distribute articles.

Entry

• Reject material that does not meet the requirements of the order.
• Monitor and handle the exchange of expired material.

Storage

• Protect and oversee all the products stored.
• Register and control the movements of stock.
• Avoid losses in the stored materials.
• Ensure items are consumed before the expiry date.
• Design documents necessary for good control of the warehouse.
• Request resupply when stocks are minimal.

When to Start Product Replacement

Replacement of a product should start before falling below the minimum stock.

High Maximum Stock: Advantages and Disadvantages

Maximum stock refers to the maximum amount of a particular item above... Continue reading "Warehouse Functions and Inventory Management in Healthcare" »

Management Control Instruments

Planning

Establishes lines of action and responsibility within a company's organization to achieve goals. This is executed through programs and embodied in the budget applicable to each program.

Budget

Determines objectives more precisely, specifying amounts and responsible parties. The budget, when applied to the immediate future, is known as operational planning. It is typically performed for a period of days or weeks, using fully quantitative variables and involving the direct participation of each department.

Causes of Deviations

Deviation Definition

A deviation is the difference that arises when comparing expected (planned or budgeted) data with actual results.

Sources of Deviations

• Errors in environmental estimates:

Fundamental Theorems in Probability

The Law of Large Numbers

The Law of Large Numbers is a theorem in probability that describes the average behavior of a succession of random variables as the total number of variables increases. The theorem provides sufficient hypotheses to affirm that the sample average converges to the average of the expectations of the random variables involved.

Chebyshev's Theorem

Chebyshev's Theorem provides an upper bound on the probability that values fall outside a certain range from the average.

Bernoulli's Theorem

Bernoulli's Theorem is a special case of the Law of Large Numbers, which specifies that the approximate frequency of an occurrence converges to the probability p of that occurrence as the experiment is repeated.... Continue reading "Core Principles of Probability and Statistical Inference" »

Case Study 1: Sales Team Head Settlement

Employee Details & Salary Structure

Settlement Calculation Steps

Unpaid Salary

• Period: November 1 - November 3 (3 days)

Monthly Salary = 1,090 + 320 + 90 = 1,500 Euros/month

Unpaid Salary for 3 days = (1,500 / 30) * 3 = 150 Euros

Pro-rata

Tangible Fixed Assets Definition

Tangible fixed assets are a set of rights and resources intended to remain in the business for more than one financial period.

Types of Fixed Assets

• Tangible-Intangible Assets: These assets have a physical entity but are classified as intangible assets or rights subject to economic evaluation.
• Tangible Assets: These assets have a physical entity and are classified as real or personal property, except those that must be classified in other subgroups.

Understanding Depreciation

Depreciation refers to the systematic allocation of the cost of tangible items over their useful life due to three primary reasons:

1. The use made of these elements, which causes deterioration.
2. The passage of time, whether the asset is used or not.

VAT Fees Eligible for Deduction

The following fees can be deducted:

• Submission-entry of goods from another taxable person
• Imports of goods
• Intra-Community acquisitions
• Fees relating to cases of reverse charge

Partial Deduction or Pro Rata

This applies when a company performs two types of activities: operations with deduction and operations without deduction.

The consequence is that only a portion or percentage of the taxes charged can be deducted.

What percentage? To determine the coefficient, calculate the following:

(Sum of output-delivery deduction in the year) / (Sum of all delivery-end of the year)

To calculate the deduction, multiply the percentage by the taxes charged.

Dynamics During the Exercise: Provisionally apply the percentage from the previous... Continue reading "VAT Deduction Rules: Fees, Partial Deduction, and Investment" »