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What mass of \(\mathrm{Al}_2\mathrm{O}_3\) is produced from 18.5 g Al? \(4\mathrm{Al} + 3\mathrm{O}_2 \rightarrow 2\mathrm{Al}_2\mathrm{O}_3\)
Molar mass Al = 27 g/mol: moles Al = 18.5/27 = 0.685 mol. From stoichiometry: 4 mol Al → 2 mol Al₂O₃, so mol Al₂O₃ = 0.685/2 = 0.3425 mol. Molar mass Al₂O₃ = 102 g/mol: mass = 0.3425×102 = 34.94 g ≈ 34.9 g.
For a levered firm (a firm that uses debt financing), which of the following ratios would ideally indicate the highest return to equity shareholders?
A levered firm uses debt, which creates a financial leverage effect. When a firm earns more on borrowed funds than it pays in interest, the surplus accrues to equity shareholders — amplifying returns. Return on Common Equity (ROE) $= \dfrac{\text{Net Income}}{\text{Shareholders' Equity}}$ captures this magnified return because the denominator (equity) is smaller when the firm uses debt. ROA and ROCE use total assets or capital employed (including debt) as the base, which dilutes the leverage effect.
In the four HRM challenges (Attract, Develop, Motivate, Retain), the sequence suggests:
The sequence represents a logical progression in the employee lifecycle: First attract talented people → then develop their capabilities → motivate them to perform → finally retain the best performers. Each stage builds on the previous, creating a comprehensive talent management approach.
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