Notes, summaries, assignments, exams, and problems for Other languages

Probability Concepts

• Union of Events: P(A∪B) = P(A) + P(B) - P(A∩B)
• Complement of an Event: P(A^c) = 1 - P(A)
• Intersection of B and Complement of A: P(B∩A^c) = P(B) - P(A∩B)
• Conditional Probability: P(B|A) = P(A∩B) / P(A)
• Intersection of Complements: P(A^c∩B^c) = 1 - P(A∪B)
• Mutually Exclusive Events: P(A∩B) = 0
• Independent Events: P(A∩B) = P(A)·P(B)

Binomial Distribution Parameters

• Mean (μ): μ = n·p
• Standard Deviation (σ): σ = √(n·p·q)

Binomial Distribution

Notation: B(n, p)

Probability Mass Function: P(X=a) = (ⁿ_a) p^a q^n-a

Where:

• n = number of trials
• p = probability of success
• q = complement of p (q = 1-p)

Normal Distribution

Notation: X ∼ N(μ, σ)

Important Probabilities:

• P(Z < a) or P(Z > a) can be found using a standard normal

English Grammar: Verb Tenses

Present Simple

• Used for actions that happen regularly (but are not happening at this moment).
• Examples: schedules, calendars

Present Continuous

• Used for actions happening now.
• Examples: fixed and sure plans, orders

Past Simple

• Used for actions that were completed in the past.
• Regular verbs: Verb + -ed
• Irregular verbs: second column of the irregular verb list
• Negative: didn't + subject + verb
• Interrogative: did + subject + verb

Past Continuous

• Used for actions that lasted for a long time in the past (often with specific times or dates).
• Affirmative: subject + was/were + verb + -ing
• Negative: subject + wasn't/weren't + verb + -ing
• Interrogative: was/were + subject + verb + -ing

Past Perfect Simple

• Used for an action that happened before

Aplicación de NIC 36: Deterioro y Reversión de Activos

El presente caso práctico aborda la aplicación de la Norma Internacional de Contabilidad 36 (NIC 36), que trata sobre el deterioro del valor de los activos. Se analiza la situación de la empresa ALLENDE, que el 1 de enero de 2016 adquiere una línea de producción.

Datos Iniciales de la Línea de Producción

• Fecha de Adquisición: 1 de enero de 2016
• Precio de Adquisición: 1.200.000 €
• Método de Amortización: Lineal a 5 años
• Valor Residual (VR): 200.000 €
• Sistema de Cálculo del Valor Recuperable: Descuento de flujos de efectivo
• Tasa de Descuento: 12%

Flujos de Efectivo Esperados (a 31/12/2016)

La siguiente tabla muestra los flujos de efectivo esperados para los años de vida útil restantes,... Continue reading "NIC 36: Cálculo de Deterioro y Reversión de Activos Fijos" »

Essential English Connectors and Their Meanings

Here's a list of common English connectors with their Spanish translations:

• First of all - En primer lugar
• In my opinion - En mi opinión
• Personally - Personalmente
• As far as I am concerned - Por lo que a mí respecta
• From my point of view - Bajo mi punto de vista
• To begin with - Para empezar
• Firstly - Primeramente
• Secondly - En segundo lugar
• That's why - Esto es por lo que
• Therefore - Por lo tanto
• As a result of - Como resultado
• Consequently - En consecuencia
• As - Como
• So - Así que
• Whereas - Mientras que
• So...that... - Tan...que...
• Such a...that... - Tan...que...
• On the one hand - Por una parte
• However/Nevertheless - Sin embargo
• Anyhow - De todas formas
• Anyway - De cualquier manera
• In spite of/Despite - A pesar de
• On

Ability

Expressing ability with modal verbs:

• Can (present ability): Can you speak French?
• Will be able to (future ability): She will be able to speak French in two months.
• Could (past ability, unrealized potential): I could have gone to university when I was younger.
• Be able to (general ability): She is able to speak Chinese.
• Was/were able to (past ability, achieved action): We were able to escape the fire.
• Couldn't/were not able to (negative past ability): We couldn't/were not able to finish the project.

Possibility

Expressing degrees of possibility:

• May (higher probability): He may be in his office.
• Might (lower probability): She might be 30 years old.

Certainty

Expressing certainty or impossibility:

• Must (certainty): He must be over 70.
• Can't (impossibility)

Key Vocabulary and Their Meanings

• Rented: Tenant.
• Settle: A wooden seat.
• Harm: *Faire mal* (French).
• Bleak: *Ombrívol* (Catalan).
• Farmyard: Corral.
• Realize: To start to understand something.
• Haunt someone: To come back after death to visit someone; ghosts haunt people or places.
• Trembling: Shaking.
• Mistress: The woman in charge of the house.
• Cheated: Something dishonest or unfair.
• Treating: To behave in a certain way towards someone.
• Became lame: *Ser coix* (Catalan).
• Punish: To make somebody suffer because they have done something wrong.
• Swore: To speak very rudely and unpleasantly to someone.
• Ashamed: To feel unhappy or uncomfortable because you think you are not as good as other people.
• Revenge: To harm someone because they have harmed you.
• Pinched: To

About to (+ verb)

A punto de (+ a verb)

According to (PREP)

Según lo que dice (referencing a source)

Actually (S)

Realmente, de hecho, por cierto

After all (BOTH)

Al fin y al cabo - (like “the bottom line”)

All in all (S)

En resumen / tomando todo en cuenta

All over (PREP)

Por todo (mundo, país), en todo

On the Contrary (S)

Todo lo contrario

Although (S)

Aunque

Anyway (S)

En todo caso, de todas maneras, de todas formas

As (BOTH)

Como, mientras, Dado que

As far as (S)

Hasta lo que ---- this expression is essentially just used with AS FAR AS I KNOW and AS FAR AS I’M CONCERNED

As for (PREP)

Referente a, en relación a, con respecto a

As a matter of fact (S)

De hecho, en realidad

As to (PREP)

Referente a, respecto a

As well (AT THE END)

También (use only at the end

TEMA2 VOCABULARY

• adopt an approach to
• analyse
• conduct
• demonstrate the possibility that
• field of study
• major breakthrough
• observe
• procedure
• process data
• provide evidence
• test a theory
• variety of sources
• guinea pig
• light years ahead
• quantum leap
• rocket science
• side effects
• trial and error
• come about
• come to light
• discomfort
• distinguish
• make out
• mutation
• personal hygiene
• pick up
• treatment
• widespread
• bring up
• go over
• hook up
• look at
• plug in
• rely on
• show off
• take after
• take away
• take in

TEMA 3 VOCABULARY

• influence
• make advances in
• make improvements to
• make the world of difference
• overcome difficulties
• remarkable achievement
• seek ways to improve
• transform
• turning point
• considerable change
• dramatic change
• far-reaching change
• refreshing change
• subtle change
• unexpected change
• city-dwelling
• complex
• doorstep
• expand
• go

Mastering English Grammar Essentials

Understanding Punctuation Marks

• Colon (:): Used before explanations, lists, or direct speech.
• Comma (,):
  • To separate items in a list.
  • To set off parenthetical expressions or words/phrases placed in unusual positions. For example: "My father, however, did not agree."
  • To separate a subordinate clause from the main clause when the subordinate clause comes first.
• Dash (-): Can be used in a similar way to colons, semicolons, or brackets. It can also introduce something unexpected or surprising.
• Full Stop (.): Used to mark the end of a sentence or a complete idea.
• Quotation Marks ("): Used to enclose direct speech or titles of short works.
• Semicolon (;): Used instead of a full stop in cases where sentences are grammatically

SUJETO + am/are/is going to + VERBO EN INFINITIVO.