Notes, summaries, assignments, exams, and exercises for Mathematics for Secondary education

 'taula torneig

    If modalitat = "I" Then

hora = InputBox("Introdueixi l'hora en la que es celebrarà el primer partit", "Registre de l'hora")

indi = total / 2

        i = 0

        individual = 6

        For i = i + 6 To indi + 5

        Worksheets("torneig").Range("B" & i).Value = hora + i - 6 & ":00"

        Worksheets("torneig").Range("E" & i).Value = "vs"

        Worksheets("torneig").Range("C" & i).Value = "Individual"

        Worksheets("torneig").Range("D" & i).Value = Worksheets("LlistaAleatoria").Range("A" & individual).Value

        Worksheets("torneig").Range("F" & i).Value = Worksheets("LlistaAleatoria").Range("A" & individual + 1).Value

       ...

Axes: ejes   Increasing: creciente   Gradient: pendiente   Grid: cuadrícula   Decreasing: decreciente   Quadrant: cuadrante   Domain: dominio   Range: recorrido   Slope: pendiente

The coordinate plane, or Cartesian plane, is formed by the horizontal line and vertical line meeting at the point 0.

The horizontal line is called the x-axis.

The vertical line is called the y-axis.

The point where the two lines meet is the origin.

Plotting Points: Starting at the origin, we move 2 units to the right along the x-axis, then move vertically up 1 unit. We describe the location of this point as the ordered pair, also called the coordinates of the point. The x-value is also called the abscissa and the y-value is called the ordinate.

The x and y axes...

Linear Equations

First-degree algebraic expressions with several unknowns.

Linear equations with 2 unknowns correspond to the general equation: ax + by = c

Solution of a Linear Equation

A solution is any pair of values for the unknowns that verifies the equation.

If x1, y1 are real numbers, the pair (x1, y1) is a solution of the linear equation in two unknowns if: ax1 + by1 = c.

Linear equations with 2 unknowns have infinite solutions.

Graphical Representation

The equation ax + by = c is a straight line. Each point on this line is a solution of the equation.

Systems of Linear Equations

A linear system of two linear equations with two unknowns is an algebraic expression of the form:

ax + by = c
a'x + b'y = c'

Solution of a System

A solution is any pair of...

Description: An Explanation of an Observation

Measurement: A Way to Describe the World with Numbers

Estimation: Using Knowledge of Something Familiar to Guess the Size of a New Object

Precision: How Close Measurements Are to Each Other

Accuracy: Comparing the Measurement to the Actual, Accepted, or Real Value

S.I.: International System of Units

Meter: The S.I. Unit of Length

Volume: The Amount of Space an Object Occupies

Mass: The Amount of Matter in an Object (S.I. Uses Kilogram)

Kilogram: S.I. Unit for Mass

Weight: The Measurement for Force (S.I. Uses the Newton)

Kelvin: The SI Measurement of Temperature (Same as C but Starts at -273 C)

Rate: The Amount of Change in a Measurement in a Given Amount of Time

Table: Displays Information in a Row or Columns

Time Series Analysis

Identifying Trends

• Upward trend: Data increases over time.
• Downward trend: Data decreases over time.
• Stationary trend: No clear increase or decrease.

Smoothing Data (Reducing Fluctuations)

• 3-point moving mean: Average of 3 consecutive values.
• 5-point moving mean: Average of 5 consecutive values.

Seasonal Indices (SI)

Formula:

Seasonal Index = Actual Value ÷ Trend Value

• SI > 1 → Above-average season.
• SI < 1 → Below-average season.

Deseasonalising Data

Formula:

Deseasonalised Value = Actual Value ÷ Seasonal Index

Regression Line (Trend Line)

Equation of the line:

y = mx + c

• m = gradient (rate of change).
• c = y-intercept (starting value).

Bivariate Data Analysis

Types of Correlation

• Positive → Both variables increase together.
• Negative

Activity 10: Conditional Probability

Objective

To explain the computation of conditional probability of a given event, assuming event B has already occurred, using the example of throwing a pair of dice.

Method of Construction

• Paste a white paper on a piece of plywood of a convenient size.
• Create a square and divide it into 36 unit squares (1cm each).
• Write the pairs of numbers representing the outcomes.

Demonstration

1. The figure displays all possible outcomes of the experiment, representing the sample space.
2. Suppose we find the conditional probability of event A given event B has occurred, where A is "a number 4 appears on both dice" and B is "4 appears at least once." We must find P(A|B).
3. From the figure: Number of outcomes favorable to B = 11; Number

1. Exponential Distribution: Tax Office Service Time

The service time (in minutes) at the local government tax office is exponentially distributed with λ = 0.025. (15 points)

• a) What are the mean and standard deviation?
  μ = σ = 1/λ = 40 minutes
• b) Find the probability that the service time will be greater than 40 minutes.
  e^{-0.025 × 40} = 0.3678
• c) Find the probability that the service time will be between 20 and 35 minutes.
  (1 - e^{-0.025 × 35}) - (1 - e^{-0.025 × 20}) = 0.583 – 0.393 = 0.19

2. Uniform Distribution: Barcelona Subway Waiting Time

The time a person waits for the Barcelona subway is uniformly distributed from 0 to 6 minutes. (15 points)

• a) What is the probability of each outcome?
  p = 1/(b - a) = 1/6
• b) What are the mean and standard deviation

Unit 7: Statistical Study Fundamentals

Statistical studies are crucial because governments base their environmental management plans on their findings. A proper study requires several key steps:

• Knowing the objective data
• Ordering the data
• Analyzing the data
• Drawing conclusions

Labor 1: Planning

Planning involves addressing two main questions:

What do we know?

This is answered by using a questionnaire. Questionnaire types include:

• Open Questionnaires: Respondents provide answers they deem appropriate.
• Limited Questionnaires: Responses are restricted to a fixed set of options.
• Closed Questionnaires (Note: This often overlaps with limited questionnaires in practice).

The final set of responses collected is called statistical variables. These fall into two...

You requested the full list of major probability distributions used in computational statistics, machine learning, and data science. Below is a classification with key examples.

Types of Probability Distributions

1. Discrete Distributions (Countable Outcomes)

• Bernoulli Distribution: Binary outcome (0 or 1, e.g., a coin toss).
• Binomial Distribution: Number of successes in n independent trials.
• Negative Binomial Distribution: Number of trials required to achieve k successes.
• Geometric Distribution: Number of trials until the first success.
• Poisson Distribution: Number of events occurring in a fixed interval of time or space.
• Multinomial Distribution: Generalization of the binomial distribution for multiple categories.
• Discrete Uniform Distribution: Each

Cost Accounting and Budgeting Fundamentals

• FOH Allocation: Single Plantwide, Departmental, and Activity-Based Rates
• Advantages of Departmental FOH Rates: It doesn't assign other costs such as depreciation.
• Characteristics of Unit, Batch, Facility, and Product Level
• Activity-Based Costing and the Importance of Activity Drivers
• Importance of ABC Costing
• Importance of Matching Strategic Planning with Pricing, Market Penetration, and Expansion
• Contribution Margin Formula: Sales - Variable Costs (VC)
• Fixed Cost and Variable Cost Behavior
• Break-Even Point Concept and Formula: Level of sales at which contribution margin matches fixed expenses, expressed in dollars.
• Direct Labor (DL) Cost per Unit: Given two different levels of production
• Differences Between