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Which stakeholders focus mainly on the liquidity of a business?
- Government
- Lenders
- Public and environmental bodies
- Suppliers
Option D (2 and 4) is correct.
- Lenders: Need to know if the business can meet short-term obligations and repay loans.
- Suppliers: Need to know if the business can pay its bills on time.
Government focuses on profitability/tax. Public/environmental bodies focus on social impact.
All five-letter words (meaningful or not) are formed using the letters of the word SMALL and listed in alphabetical (dictionary) order. What is the position of the word SMALL in this list?
Letters in SMALL: A, L, L, M, S (sorted: A, L, L, M, S). Note L repeats twice.
Words starting with A: remaining letters M, L, L, S — arrangements $= \frac{4!}{2!} = 12$
Words starting with L: remaining A, L, M, S — arrangements $= 4! = 24$
Words starting with M: remaining A, L, L, S — arrangements $= \frac{4!}{2!} = 12$
Words starting with SA: remaining L, L, M — arrangements $= \frac{3!}{2!} = 3$
Words starting with SL: remaining A, L, M — arrangements $= 3! = 6$
Words starting with SM: next is SMA... then SMALL itself.
Words starting with SMA: remaining L, L — arrangements $= \frac{2!}{2!} = 1$ (i.e., SMALL itself is next after SMAAL... )
Total before SMALL: $12+24+12+3+6=57$, so SMALL is at position $\mathbf{58}$.
For each $x\in\mathbb{R}$, let $[x]$ be the greatest integer $\leq x$. Find: $\displaystyle\lim_{x\to0^-}\dfrac{x([x]+|x|)\sin[x]}{|x|}$
For $x\to0^-$: $x<0$, $|x|=-x$, $[x]=-1$.
$\dfrac{x((-1)+(-x))\sin(-1)}{-x} = \dfrac{x(-1-x)(-\sin1)}{-x}$
$= \dfrac{x(1+x)\sin1}{x} = (1+x)\sin1$
As $x\to0^-$: limit $= 1\cdot\sin1$... wait: $= \dfrac{x(-1-x)(-\sin1)}{-x} = \dfrac{(1+x)\sin1 \cdot x}{x}=(1+x)\sin1\to\sin1$? Re-doing: numerator $= x(-1-x)\sin(-1)=x(-1-x)(-\sin1)=x(1+x)\sin1$; denominator $=-x$. So $=\dfrac{x(1+x)\sin1}{-x}=-(1+x)\sin1\to-\sin1$. Answer: $\mathbf{-\sin 1}$.
The Oral Polio Vaccine (OPV) is the most heat-sensitive of all vaccines used in the Expanded Programme on Immunization (EPI). It must be stored at -15°C to -25°C at the national and provincial level. However, at the district/peripheral level, OPV can be stored at +2°C to +8°C for short periods. The option -15°C to -25°C is the standard cold chain requirement. Mismanagement of cold chain is a leading cause of vaccine failure — a Head Nurse must strictly monitor this.
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