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When discussing 'opportunities to excel in future' as an attraction factor, it refers to:
Opportunities to excel refer to career development and advancement opportunities - the chance for employees to grow, learn, and advance their careers. This is a key attraction factor alongside quality work environment and benefits.
Find the number of surjective (onto) functions $f$ from $\{1,2,3,\ldots,20\}$ to $\{1,2,3,\ldots,20\}$ such that $f(k)$ is a multiple of 3 whenever $k$ is a multiple of 4.
Multiples of 4 in $\{1,\ldots,20\}$: $\{4,8,12,16,20\}$ β 5 elements. Their images must be multiples of 3 in $\{1,\ldots,20\}$: $\{3,6,9,12,15,18\}$ β 6 elements.
Assign the 5 multiples-of-4 to 5 of the 6 multiples-of-3 (injectively, since $f$ is onto): $6 \times 5 \times 4 \times 3 \times 2 = 6!/(6-5)! = 720$... but we need surjection on all 20 elements.
The remaining 15 domain elements map to the remaining 15 codomain elements (after fixing the 5 images above): $(15)!$ ways. But 1 multiple-of-3 is unused by the multiples-of-4, so it must be covered by remaining 15 elements.
Total $= 6! \times (15)! = (15)! \times 6!$
KDIGO AKI Staging Criteria:
| Stage | Serum Creatinine | Urine Output |
|---|---|---|
| 1 (Risk) | \(\times 1.5 - 1.9\) baseline within 7 days OR \(\uparrow \geq 0.3 \text{ mg/dL}\) within 48h | \(< 0.5 \text{ mL/kg/h}\) for \(6-12\) h |
| 2 (Injury) | \(\times 2.0 - 2.9\) baseline | \(< 0.5 \text{ mL/kg/h}\) for \(\geq 12\) h |
| 3 (Failure) | \(\times 3.0\) baseline OR \(\geq 4.0 \text{ mg/dL}\) OR initiation of RRT | \(< 0.3 \text{ mL/kg/h}\) for \(\geq 24\) h OR anuria \(\geq 12\) h |
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