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Percentage \(= \dfrac{21}{25} \times 100 = 84\%\)
A projectile has initial velocity $(2\hat{i}+3\hat{j})\text{ m/s}$ at point A (at ground level). At point B (on the x-axis, same height as A), its velocity is:
Horizontal component is unchanged throughout: $v_x = 2\text{ m/s}$.
When the projectile returns to the same height, the vertical component reverses: $v_y = -3\text{ m/s}$.
Velocity at B $= \mathbf{2\hat{i} - 3\hat{j}}$
The concept of corporate social responsibility refers to:
Corporate social responsibility refers to the extent to which companies should and do channel resources toward improving one or more segments of society other than the firm's owners or stockholders. It involves balancing commitments to investors, employees, customers, other businesses, and communities.
Jean Watson originally described 10 carative factors in her 1979 theory. In her later evolution of the theory (Caring Science), she renamed them Caritas Processes (from the Latin caritas, meaning love/charity).
Key concepts in Watson's theory:
- Transpersonal Caring Relationship: A special kind of human connection that transcends the physical
- Caring Occasion/Moment: A moment when nurse and patient come together β each with their own phenomenal field
- Caritas Processes: 10 processes guiding caring practice, emphasizing love, faith, hope, and sensitivity
A trader provided the following data:
| Item | Jan 1 ($) | Dec 31 ($) |
|---|---|---|
| Bank (Debit) | 4,240 | 6,320 |
| Cash balance | 264 | 271 |
During the year: Cheques issued were $19,950. All sales takings were banked except for $5,400 used for drawings and $7,200 for wages. Additionally, $3,000 was banked from the sale of a motor vehicle. Calculate total sales.
1. Cash banked from sales = Closing Bank ($6,320) + Cheques issued ($19,950) - Opening Bank ($4,240) - Sale of Asset ($3,000) = $19,030.
2. Total Sales = Banked Sales ($19,030) + Cash Drawings ($5,400) + Cash Wages ($7,200) + (Closing Cash $271 - Opening Cash $264) = $19,030 + $5,400 + $7,200 + $7 = $31,637.
Two fair six-faced dice $A$ and $B$ are rolled together. Define events:
$E_1$: die $A$ shows 4, $\quad E_2$: die $B$ shows 2, $\quad E_3$: sum of both dice is odd.
Which of the following statements is NOT true?
Total outcomes $= 36$.
$P(E_1)=\frac{6}{36}=\frac{1}{6}$, $P(E_2)=\frac{1}{6}$, $P(E_3)=\frac{18}{36}=\frac{1}{2}$
$E_1$ and $E_2$: $P(E_1\cap E_2)=\frac{1}{36}=\frac{1}{6}\cdot\frac{1}{6}$ β Independent.
$E_1$ and $E_3$: For sum odd with die A showing 4 (even), die B must be odd: 3 outcomes. $P(E_1\cap E_3)=\frac{3}{36}=\frac{1}{12}=\frac{1}{6}\cdot\frac{1}{2}$ β Independent.
$E_2$ and $E_3$: For sum odd with die B showing 2 (even), die A must be odd: 3 outcomes. $P(E_2\cap E_3)=\frac{3}{36}=\frac{1}{12}=\frac{1}{6}\cdot\frac{1}{2}$ β Independent.
$E_1\cap E_2\cap E_3$: Die A=4, Die B=2, sum=6 (even) β impossible! $P(E_1\cap E_2\cap E_3)=0$.
But $P(E_1)\cdot P(E_2)\cdot P(E_3)=\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{2}=\frac{1}{72}\neq 0$.
So $E_1,E_2,E_3$ are not mutually independent (as a triple), even though pairwise independent.
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