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@Deyse SJ de Assis - Lisboa, Portugal

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LOGICAL REASONING >>

Combinatorial Analysis and Probability

What is it?

It is the part of mathematics that studies:

how many different ways something can happen (combinatorics)

the chance of something happening (probability)

1. Combinatorics (counting possibilities)

Main idea

👉 You want to know how many different ways there are to choose or arrange something.

Example

How many different ways to choose 2 people out of 5?

🔍 Simple step by step:

People: A, B, C, D, E

We want to choose 2:

Correct answer:

👉 10 different ways

Formula (just for understanding):

combination: order does not matter (AB = BA)

2. Probability

What is it?

It is the chance of something happening.

Simple example

A coin is tossed. What is the chance of getting heads?

🔍 Step by step:

Possibilities:

Heads

Tails

Favorable cases: 1

Total cases: 2

Correct answer:

👉 1/2 or 50%

Another example

In a dice (1 to 6), what is the chance of getting an even number?

🔍 Step by step:

Even numbers:

2, 4, 6 → 3 cases

Total:

6 numbers

Correct answer:

👉 3/6 = 1/2 = 50%

Important tips

✔️ Combinatorics = count possibilities

✔️ Probability = measure chances

✔️ Always identify:

total cases

favorable cases

Quick summary

✔️ Combinatorics → “how many ways are there?”

✔️ Probability → “what is the chance of this happening?”

✔️ Very common in exams and logic problems

Did you know?

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Those who liked Combinatorial Analysis and Probability, also liked to explore LOGICAL REASONING

Explore more about What are they?
They are sentences that can have only two values:
✅ True (T)
❌ False (F)
There is no “more or less true”

Examples of propositions:
“2 + 2 = 4” → True
“Lisbon is in Brazil” → False
“10 is greater than 5” → True

What is NOT a proposition
Sentences that cannot be judged as true or false:
❓ Questions → “What time is it?”
📢 Commands → “Close the door”
😮 Exclamations → “What a beautiful day!”
These do NOT belong to logic

Types of propositions

Simple proposition
A single idea:
“It is raining”
“John studies”
Compound proposition
Combination of two or more ideas:
“It is raining and it is cold”
“John studies or works”

Every proposition must:
Be a declarative sentence
Have complete meaning
Be classified as T or F

⚠️ Common trap
Sentence:
“x + 2 = 5”
This is not a proposition because it depends on the value of x.

Quick summary
Proposition = sentence with a logical value (T or F)
Cannot be a question, command, or emotion
Can be simple or compound
It is the foundation of all Logic..

What are they?
They are sentences that can have only two values:
✅ True (T)
❌ False (F)
There is no “more or less true”
Examples of propositions:
“2 + 2 = 4” → True
“Lisbon is in Brazil” → False
“10 is greater than 5” → True
What is NOT a proposition
Sentences that cannot be judged as true or false:
❓ Questions → “What time is it?”
📢..know more

The Rubik's Cube, created by H - About MATH

The Rubik's Cube, created by Hungarian architect and architecture professor Ernő Rubik in 1974, has become one of the world's most popular puzzles and a true cultural icon. Originally invented by Rubik as a teaching tool to teach his students about geometry and spatial transformations, it quickly became a worldwide challenge.
The 3x3x3 cube, the best-known version, has around 43 quintillion possible..know more

What is it? It's a graph that - About MATHEMATICS EN 9TH GRADE

What is it?
It's a graph that represents the distribution of a data set using 5 main values:
Minimum value
Q1 (1st quartile)
Median (Q2)
Q3 (3rd quartile)
Maximum value
👉 Quickly shows dispersion, symmetry, and possible outliers (extreme values).
📌 How to interpret
The box represents the values between Q1 and Q3 (50% of the data)
The line..know more

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Those who liked Combinatorial Analysis and Probability, also liked to explore COMMEMORATIVE DATES

Explore more about On May 13, the feast of Our Lady of Fátima is celebrated, commemorating the first of six apparitions of the Virgin Mary to the three shepherd children at Cova da Iria in 1917. Over the course of those months, messages of peace, conversion, and prayer were conveyed, including the revelations known as the three “Secrets of Fátima,” which involve prophetic visions and a call to devotion to the Immaculate Heart of Mary. Today, the Sanctuary of Fátima is one of the largest Marian pilgrimage sites in the world, attracting millions of faithful who seek to renew their faith in the place where, for many, heaven touched the earth.
..

On May 13, the feast of Our Lady of Fátima is celebrated, commemorating the first of six apparitions of the Virgin Mary to the three shepherd children at Cova da Iria in 1917. Over the course of those months, messages of peace, conversion, and prayer were conveyed, including the revelations known as the three “Secrets of Fátima,” which involve prophetic visions and a call to devotion to the Immaculate..know more

International Firefighters' Da - About BRAZIL TOURISM

Explore more about International Firefighters

International Firefighters' Day is celebrated on May 4, although the date may vary in other countries. In Europe, this day is known as Saint Florian’s Day, the patron saint of firefighters.
Origin
Established in 1999
Motivated by the death of five firefighters in Australia during a forest fire.
Purpose
To honor the heroism and dedication of firefighters
To..know more

The death of Michael Jackson o - About MICHAEL JACKSON

Explore more about The death of Michael Jackson occurred on the morning of June 25, 2009, at his rented mansion in Holmby Hills, Los Angeles.

The Previous Night
Michael was under immense pressure due to rehearsals for the 50-show This Is It residency. He suffered from severe chronic insomnia. That night, after returning from rehearsals around 1:00 a.m., he was unable to sleep. His personal physician, Conrad Murray, administered a series of sedatives (Valium, Ativan, and Versed) throughout the early morning, but none were effective.

The Administration of Propofol
Around 10:40 a.m., in response to Michael’s desperation to rest, Murray administered 25 milligrams of Propofol diluted with lidocaine. Michael finally fell asleep. Murray later admitted that he left the room for about two minutes to go to the bathroom and make phone calls.

The Discovery of the Body
Upon returning to the room, Murray realized that Michael showed no vital signs. The doctor attempted resuscitation efforts, but emergency services were only contacted some time later. A security guard at the residence placed the call to 911 at 12:21.

The Rescue and Death
Paramedics arrived within minutes and found Michael Jackson not breathing and without a pulse. Resuscitation attempts were performed on-site and during transport to the Ronald Reagan UCLA Medical Center. Despite the efforts of medical teams, his death was officially declared at 2:26 p.m.

The Autopsy and Investigation
The coroner’s report determined that the cause of death was acute propofol intoxication, combined with the effects of other sedatives. The examination confirmed that Michael had Vitiligo, explaining the depigmentation of his skin, and showed scars related to previous surgeries and the 1984 accident during a commercial shoot.

Legal Consequences
In 2011, Dr. Conrad Murray was brought to trial and convicted of involuntary manslaughter. The court determined there had been gross negligence in the use of restricted medication in a home setting and a lack of proper patient monitoring...

The death of Michael Jackson occurred on the morning of June 25, 2009, at his rented mansion in Holmby Hills, Los Angeles.
The Previous Night
Michael was under immense pressure due to rehearsals for the 50-show This Is It residency. He suffered from severe chronic insomnia. That night, after returning from rehearsals around 1:00 a.m., he was unable to sleep. His personal physician,..know more

What are compound experiments? - About MATHEMATICS EN 9TH GRADE

Explore more about What are compound experiments?
They are experiments in which more than one action happens sequentially or simultaneously.
👉 Example:
Rolling a die twice
Tossing a coin twice
Drawing balls from an urn without replacement
1. Sample space in compound experiments
When the experiment is compound, the sample space increases.
📌 Example: tossing a coin twice
Possible outcomes:
(heads, heads)
(heads, tails)
(tails, heads)
(tails, tails)
👉 Total outcomes = 4
2. Probability Calculation
General Rule
$ P(A) = \frac{\text{favorable cases}}{\text{possible cases}} $
📌 Example 1 — Coin
👉 Tossing a coin twice
Event: getting at least one head
Possible outcomes: #NL
(heads, heads)
(heads, tails)
(tails, heads)
(tails, tails)
Favorable cases = 3
$ P(A) = \frac{3}{4} $
📌 Example 2 — Dice
👉 Rolling a die twice
Event: sum equals 7
Cases Favorable:
(1,6)
(2,5)
(3,4)
(4,3)
(5,2)
(6,1)
Total possible cases:
$ 6 \times 6 = 36 $
Favorable cases = 6
$ P(A) = \frac{6}{36} = \frac{1}{6} $
3. Probability in experiments with dependence
👉 When the outcome of one event influences another.
📌 Example (without replacement)
Drawing two balls from a box without returning the first.
If there are 5 balls:
Probability changes after the first draw
4. Probability in Independent Experiments
👉 When one event does not affect the other.
📌 Example
Tossing a coin and rolling a die
\( P(A \cap B) = P(A) \times P(B)
📌 Example
Coin (heads) and die (even number):
\( P(\text{heads}) = \frac{1}{2}
\( P(\text{even}) = \frac{3}{6} = \frac{1}{2}
\( P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}..

What are compound experiments?
They are experiments in which more than one action happens sequentially or simultaneously.
👉 Example:
Rolling a die twice
Tossing a coin twice
Drawing balls from an urn without replacement
1. Sample space in compound experiments
When the experiment is compound, the sample space increases.
📌 Example: tossing a coin..know more

Goalkeeper’s Day, celebrated o - About BRAZILIAN SOCCCER

Explore more about Goalkeeper’s Day, celebrated on April 26, honors one of the greatest names in Brazilian football for that position: Aílton Corrêa Arruda, the legendary Manga.
Who was goalkeeper Manga?
Born on April 26, 1937
Considered one of the greatest goalkeepers in Brazilian history
Played for major clubs such as:
Sport Club do Recife
Botafogo de Futebol e Regatas
Grêmio Foot-Ball Porto Alegrense
Coritiba Foot Ball Club
Also represented the Brazil national football team in friendlies and World Cups
👉 His skill, reflexes, and leadership made him a defining figure in football.
How did Goalkeeper’s Day start?
The date was created in 1975 by professionals from the Escola de Educação Física do Exército:
Raul Carlesso (fitness coach)
Reginaldo Pontes Bielinski (captain)
💡 The goal was to highlight the position and recognize the importance of goalkeepers in football.
Interesting fact
Raul Carlesso was a pioneer in Brazil in developing specific training for goalkeepers, especially during the national team’s preparation for the 1974 FIFA World Cup...

Goalkeeper’s Day, celebrated on April 26, honors one of the greatest names in Brazilian football for that position: Aílton Corrêa Arruda, the legendary Manga.
Who was goalkeeper Manga?
Born on April 26, 1937
Considered one of the greatest goalkeepers in Brazilian history
Played for major clubs such as:
Sport Club do Recife
Botafogo de Futebol e Regatas
Grêmio..know more

translate this: Artificial int - About UNIVERSE OF AI

Explore more about translate this: Artificial intelligence é uma tecnologia que permite máquinas realizarem tarefas que normalmente exigem inteligência humana, como aprender, analisar dados, reconhecer padrões e gerar conteúdo.
O que é a IA?
A IA é um conjunto de tecnologias que simula capacidades humanas, como:
aprendizado
tomada de decisão
reconhecimento de linguagem e imagens
automação de tarefas
IA como ferramenta (lado positivo)
Quando bem usada, a IA é vista como uma ferramenta poderosa:
✔ Produtividade
automatiza tarefas repetitivas
acelera trabalhos em empresas e estudos
✔ Saúde
ajuda no diagnóstico de doenças
analisa exames com mais precisão
✔ Educação
personaliza o aprendizado
cria materiais de apoio
✔ Inovação
impulsiona novas tecnologias
melhora serviços digitais
IA como “vilã” (riscos e preocupações)
A IA também levanta debates importantes:
✖ Desemprego tecnológico
substituição de algumas funções humanas
✖ Desinformação
criação de deepfakes e notícias falsas
✖ Privacidade
uso excessivo de dados pessoais
✖ Dependência
excesso de confiança em sistemas automáticos
Então: ferramenta ou vilã?
A resposta mais aceita é:
👉 IA não é boa nem ruim por si só.
👉 O impacto depende de como é usada, regulada e controlada...

translate this: Artificial intelligence é uma tecnologia que permite máquinas realizarem tarefas que normalmente exigem inteligência humana, como aprender, analisar dados, reconhecer padrões e gerar conteúdo.
O que é a IA?
A IA é um conjunto de tecnologias que simula capacidades humanas, como:
aprendizado
tomada de decisão
reconhecimento de linguagem e imagens
automação..know more

Is it just a style choice or i - About ANIME

Explore more about Is it just a style choice or is there a real reason?
Many people think it’s only an artistic choice, but big eyes in anime have deep emotional and historical roots.

Why do big eyes make emotions easier to show?
In anime, expressions need to be understood instantly. Larger eyes make it easier to communicate emotions like happiness, sadness, or surprise.

What is the influence of cinema and Disney?
Early anime creators were influenced by Western animation, where expressive eyes were used to enhance emotional storytelling.

Who popularized this style in Japan?
Osamu Tezuka was one of the key figures who helped establish this style, inspired by Disney animation.

Why do big eyes create emotional connection?
Large eyes give characters a sense of innocence and vulnerability, making it easier for viewers to empathize.

Is this style used in all anime?
No. More realistic anime use smaller eyes and natural proportions depending on the tone of the story.

Why did this style become iconic?
Because it became a visual language of anime: fast emotional communication, clear expression, and a strong global identity...

Is it just a style choice or is there a real reason?
Many people think it’s only an artistic choice, but big eyes in anime have deep emotional and historical roots.

Why do big eyes make emotions easier to show?
In anime, expressions need to be understood instantly. Larger eyes make it easier to communicate emotions like happiness, sadness, or surprise.

What..know more

The vori-vori is one of Paragu - About BRAZILIAN GASTRONOMY
The vori-vori is one of Paraguay’s most traditional dishes and strongly represents the blend between indigenous Guarani cuisine and Spanish influences. It recently gained attention online after appearing in informal food rankings, where it was even mentioned above popular dishes such as Brazilian picanha — although this does not come from any official ranking.
What is vori-vori
Vori-vori..know more

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Those who liked Combinatorial Analysis and Probability, also liked to explore MICHAEL JACKSON
At the peak of Thriller’s success, on January 27, 1984, a catastrophic accident during the filming of a commercial for Pepsi-Cola permanently changed the course of Michael Jackson’s life and health.
The Pyrotechnic Incident
The Error: During the sixth take of the scene, the pyrotechnic effects were triggered too early. Sparks hit Michael’s hair, which was covered in hairspray (a highly..know more

On March 25, 1983, during the - About MICHAEL JACKSON
On March 25, 1983, during the television special Motown 25: Yesterday, Today, Forever, Michael Jackson delivered a performance that would change the history of dance forever.
The "Billie Jean" Glide
The Performance: After a brief reunion with his brothers, Michael remained alone on stage. Wearing a sequined glove and a sparkling black jacket, he began performing "Billie Jean."
The..know more

The Turning Point in "The Wiz" - About MICHAEL JACKSON
The Turning Point in "The Wiz" (1978)
If there is a precise moment when the “King of Pop” began to take shape, it was behind the scenes of The Wiz (an urban, all-Black cast version of The Wizard of Oz).
The Role of the Scarecrow
The Choice: Michael fought for the role of the Scarecrow. He wanted to prove he could act and move differently from his image in the Jackson 5.
Extreme..know more

Released on November 30, 1982, - About MICHAEL JACKSON
Released on November 30, 1982, Thriller was not just an album; it was a cultural event that changed the music industry forever. With impeccable production by Quincy Jones, Michael Jackson achieved what no other artist had ever accomplished.
The Unreachable Record
Global Sales: With over 70 million copies sold, it holds the title of the best-selling album of all time according to the..know more

The death of Michael Jackson o - About MICHAEL JACKSON
The death of Michael Jackson occurred on the morning of June 25, 2009, at his rented mansion in Holmby Hills, Los Angeles.
The Previous Night
Michael was under immense pressure due to rehearsals for the 50-show This Is It residency. He suffered from severe chronic insomnia. That night, after returning from rehearsals around 1:00 a.m., he was unable to sleep. His personal physician,..know more

In 2009, Michael Jackson annou - About MICHAEL JACKSON
In 2009, Michael Jackson announced his return to the stage with the residency This Is It at the The O2 Arena in London. What was meant to be 10 concerts quickly turned into 50 due to record-breaking ticket demand (around 1 million sold within hours).
Technical Precision at 50 Years Old
Unmatched Perfectionism: Rehearsals recorded at the Staples Center showed that Michael had not lost..know more

For decades, the change in Mic - About MICHAEL JACKSON
For decades, the change in Michael Jackson’s skin color was the subject of conspiracy theories and cruel criticism. However, the medical truth is far more complex and painful than tabloids suggested.
The Diagnosis of Vitiligo
What it is: Vitiligo is an autoimmune disease in which the body attacks its own melanocytes (cells that produce pigment). This causes irregular white patches..know more

Michael Jackson didn’t just wa - About MICHAEL JACKSON
Michael Jackson didn’t just want to be the greatest artist in the world; he wanted to heal the world. His humanitarian impact was so vast that it earned him a unique place in history, officially recognized.
The Guinness Record (The Greatest Pop Philanthropist)
The Achievement: Michael is listed in the Guinness World Records as the entertainment artist who supported the most charitable..know more

In the 1980s, there was no mor - About MICHAEL JACKSON
In the 1980s, there was no more famous pet in the world than Bubbles. The chimpanzee became an extension of Michael Jackson’s public image, accompanying him on tours and even in interviews.
The Rescue and the Friendship
The Origin: Michael Jackson acquired Bubbles from a cancer research center in Texas in 1983. The singer’s goal was to save the animal and give him a life of luxury..know more

Located in Santa Ynez, the Nev - About MICHAEL JACKSON
Located in Santa Ynez, the Neverland Ranch was much more than a luxury property; it was the materialization of Michael Jackson’s desire to stop time and recover the years he spent confined in recording studios.
The Purchase and Inspiration (1988)
The Investment: Michael purchased the property for around $19.5 million.
The Name: Inspired by the Peter Pan story, Neverland was the..know more
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