Notes, summaries, assignments, exams, and exercises for Mathematics for University

Practice 4: Salaries, Overtime, SSO, PHL

Basic Salary

• = (Additional Table at $[$D$24] * Time Worked)

Total Overtime

• Fx = IF(logical test = E10 [Overtime] > 40)
• True-Value: E10 - 40
• False-value: 0

Triple Overtime

• Fx = IF Function
• Logic Test: Total Overtime [G10 > 8]
• True-Value: G10 - 8
• False-value: 0

Payment of Extra Time Triple

• Triple Overtime (H10) * Pay Per Hour (D24) * 3

Double Overtime

• = G10 (Total Overtime) - H10 (Triple Overtime)

Payment of Extra Time Double

• = J10 (Double Extra Time) * D24 (Pay per hour) * 2

Compulsory Social Security (SSO)

• = (F10 [Basic Salary] + I10 [Payment of Triple Overtime] + K10 [Payment of Double Overtime]) * 5%

Housing Policy Act (HPL)

• = (F10 [Basic Salary] + I10 [Payment of Triple Overtime] + K10 [Payment of Double Overtime]

Limit Theorems and Convergence

• Root Test: lim ⁿ√a_n = L
• Ratio Test: lim a_n/a_n-1 = L
• Stolz Theorem: lim a_n/b_n = lim (a_n-a_n-1)/(b_n-b_n-1)
• Arithmetic Mean: lim (a₁ +...+ a_n)/n = lim a_n
• Geometric Mean: lim ⁿ√(a₁...a_n) = lim a_n

Convergence Criteria

• Raabe: lim n(a_n/a_n+1 - 1) > 1 (Convergent)
• Pringsheim: lim n^αa_n (if α > 1, Convergent)
• Root Test (n-th): lim ⁿ√a_n < 1 (Convergent)
• Logarithmic: lim log(1/a_n) / log(n) > 1 (Convergent)
• Absolute Convergence: If ∑|(-1)ⁿa_n| converges, then ∑(-1)ⁿa_n converges.
• Leibniz Criterion: 1) lim a_n = 0; 2) a_n+1 - a_n < 0

Series Types

• Hypergeometric Series: a_n+1/a_n = (an + b)/(n + c). Convergent if (c-b)/a > 1.
• Telescoping Series: ∑a_n = x_n - x_n+1. Sum = x₁ - lim x_n+1.

Asymptotic Equivalences

sin(a_n) ≈ a_n;...

Accounting: It uses information systems to register technical summaries, classify, and analyze transactions based on operations and along the timeline of the company. Accounting Steps: Identification and economic analysis of differences, quantifying the value of the operation, and booking entries to decide (journals, ledgers, and auxiliary) for the preparation of accounts, balance sheets, and analysis of balances. Characteristics of Accounting: Order, adequacy, relevance, objectivity, rigor, and standardization. Normalization: Accounting is understandable for all persons who need the information it contains. Standard Accounting Plan Types: General Types of Accounting: Microaccounting: Economic domestic, profit entities without profit motive,...

Data Types and Vector Creation

• Nominal → names
• Ordinal → order
• Interval → equal spacing
• Ratio → real math possible

Creating Vectors

c(1, 2, 3) # numeric
c("a", "b") # text
c(TRUE, FALSE) # logical

Vector Functions

numeric(5) # 0 0 0 0 0
rep(2, 5) # 2 2 2 2 2
seq(1, 10) # 1 to 10

Matrix Operations

A matrix is a table of numbers: matrix(1:12, nrow=3)

• + → add
• %*% → matrix multiply
• t() → transpose
• solve() → inverse
• det() → determinant

Note: Standard deviation is the square root of the variance.

Understanding trim=0.10 in R

It means to trim 10% from each end of the dataset.

Reading Data

return <- fund_return[,1]

Descriptive Statistics Functions

length(return)

Gives the number of observations (e.g., 76).

mean(return)

Calculates the ordinary average.

median(

Regression Statistics

• Multiple R: Coefficient of correlation (0.099). 9.9% of variability in Y is connected with 9.95% of variability in X.
• R-squared: Coefficient of determination (0.0099). 0.99% of variance in Y is explained by our regression model.
• Standard Error: The prediction of Y made using our model will differ from reality by approximately [number].
• Observations: The model contains [x] units.

Intercept (B0)

Coefficients: If we do not take X into consideration, Y will be [..].

T-stat: Calculated as (coefficient / standard error).

P-value: Level of risk is nearly 0, indicating a 99.99% probability.

Lower/Upper 95%: We are 95% confident that our coefficient B0 falls between 27.4 and 30.8.

Age (B1)

Coefficients: If X increases by 1 year, Y will increase...

1. The role of business statistics is to convert data into meaningful info.

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

Understanding Linguistic Vices

Linguistic vices refer to any defect or impairment that may present in words or sentences, hindering clear and correct communication.

Common Linguistic Vices

Here are some common linguistic errors:

• Cacophony: This is a very obvious error, consisting of the repetition of syllables or sounds that are contiguous or in close proximity, creating an unpleasant effect.
• Monotony: A linguistic vice produced by the frequent use of the same words or expressions to refer to different situations, leading to a lack of variety in language.
• Ambiguity or Amphibology: This vice involves expressing ideas so obscurely that they are not clearly understood, or can be interpreted in two or more ways, leading to confusion.
• Solecisms: These

**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...