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A function f(x) is a valid probability density function (PDF) if:         Uniform distribution expected value:(a + b)/2

f(x) ≥ 0 for all values of x.          Standard normal distribution: P (a ≤ X ≤ b)= Φ(b) − Φ(a)

∫ −∞∞ f(x)dx = 1.             General Form of a Taylor Polynomial:

                                        P_n(x) = f(a) + f'(a)(x - a) + [f''(a)/2!](x-a)² + [f'''(a)/3!](x-a)³ + ... + [f⁽ⁿ⁾(a)/n!](x - a)ⁿ

Maclaurin series formula:

Causas da Revolução Liberal Portuguesa : Invasões francesas e crise económica grave. / Fuga da família real para o Brasil, deixando Portugal sem rei. /Domínio inglês no governo (general Beresford). / Perda do monopólio comercial com o Brasil, afetando a burguesia. /Miséria da população e destruição do país.

Constituição de 1822 (liberal) : Soberania da nação (poder pelo voto). / Igualdade perante a lei. / Separação de poderes: legislativo (Cortes), executivo (rei), judicial (

Postfix evaluation 

#include<stdio.h>
int stack[20];
int top = -1;

void push(int x)
{
    stack[++top] = x;
}

int pop()
{
    return stack[top--];
}

int main()
{
    char exp[20];
    char *e;
    int n1,n2,n3,num;
    printf("Enter the expression :: ");
    scanf("%s",exp);
    e = exp;
    while(*e != '\0')
    {
        if(isdigit(*e))
        {
            num = *e - 48;
            push(num);
        }
        else
        {
            n1 = pop();
 

Here's a concise and exam-ready answer for your notes:

Cost of Capital

Definition:
Cost of capital is the minimum rate of return that a business must earn on its investments to maintain its market value and attract funds. It represents the opportunity cost of using capital in one investment over another with similar risk.

Relevance of Cost of Capital in Decision Making

1. Investment Decisions (Capital Budgeting):
   Used as a discount rate in evaluating investment projects (NPV, IRR). A project is accepted

"The present was an egg laid by the past that had the future inside its shell."

Part I: Why I Chose This Quote

I chose this quote because it captures the flow of time in a powerful and poetic way.

 It reminded me that nothing exists in isolation — everything happening now is a result

 of something that came before, and everything we do now shapes what’s coming next.

Personally, it made me think about how my own life is constantly being shaped by past

 experiences, decisions,

1. What is meant by vouching (2 marks)

Vouching refers to the process of checking the authenticity of transactions recorded in the books of accounts using supporting documents. It ensures accuracy and reliability in financial reporting.

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2. Features of a good internal check system (5 marks — 6 points)

1. Division of work: Duties are distributed to prevent overlapping.

2. Checks and balances: One employee’s work is automatically checked by another.

3. Responsibility fixing: Each employee