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Find the count of natural numbers less than $7000$ that can be formed using the digits $0, 1, 3, 7, 9$ with repetition allowed.
1-digit: $1, 3, 7, 9$ (excluding 0) $= 4$
2-digit: First digit: 4 choices (1,3,7,9); second: 5 choices $= 4 \times 5 = 20$
3-digit: First digit: 4 choices; others: 5 each $= 4 \times 5 \times 5 = 100$
4-digit $< 7000$: First digit must be $1$ or $3$ (2 choices, since 7000 and above excluded — first digit can be 1, 3 only for $< 7000$; digits 7 and 9 give $\geq 7000$): $2 \times 5 \times 5 \times 5 = 250$
Total $= 4 + 20 + 100 + 250 = \mathbf{374}$
When organizations ask HR managers for assistance in 'matching the distinctive competencies of the firm's human resources to the mission of the organization,' this represents:
This represents strategic HR management - aligning human resources (their distinctive competencies) with organizational strategy (mission). It moves HR from purely operational/administrative functions to strategic business partner role.
Angular width $2\theta = \frac{2\lambda}{a} = 60^\circ = \frac{\pi}{3} \text{ rad}$.
$\frac{\lambda}{a} = \frac{\pi}{6} \implies \lambda = \frac{\pi}{6} \times 1 \ \mu\text{m}$.
Fringe width $\beta = \frac{\lambda D}{d} = 1 \text{ cm} = 10^{-2} \text{ m}$.
$d = \frac{\lambda D}{\beta} = \frac{(\pi/6 \times 10^{-6}) \times 0.5}{0.01} \approx 26.1 \ \mu\text{m}$. The closest option is $25 \ \mu\text{m}$.
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