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The relationship $\text{Productivity} = f(\text{Ability}, \text{Motivation})$ indicates that individual productivity depends on:
Individual productivity is a function of BOTH ability (competence in performing a job) and motivation (desire to do the best possible job). If either factor is zero or very low, productivity suffers. Ability can be improved through selection and training; motivation through QWL programs and management practices.
Which form of government does Aristotle consider the 'perverted' form of Aristocracy?
In Aristotle's classification, Oligarchy is the corrupt form of Aristocracy (rule by the few).
Let $p$ be the probability that event $E$ will occur, and let $s$ be the probability that event $E$ will not occur. Compare:
Quantity A: $p + s$
Quantity B: $ps$
Since $p$ and $s$ are complementary probabilities: $p + s = 1$ (one of them must happen).
So Quantity A $= 1$.
For Quantity B: $ps = p(1-p)$. Since $0 \leq p \leq 1$, the product $p(1-p) \leq \dfrac{1}{4}$ (maximum at $p = 0.5$).
Therefore $ps \leq 0.25 < 1 = p + s$.
Quantity A is always greater.
For the reaction $2\text{C}_{57}\text{H}_{110}\text{O}_6(s) + 163\ \text{O}_2(g) \to 114\ \text{CO}_2(g) + 110\ \text{H}_2\text{O}(l)$, find the mass of water produced from 445 g of C$_{57}$H$_{110}$O$_6$.
Molar mass of C$_{57}$H$_{110}$O$_6$: $57(12)+110(1)+6(16)=684+110+96=890\ \text{g mol}^{-1}$
Moles of C$_{57}$H$_{110}$O$_6 = \dfrac{445}{890} = 0.5\ \text{mol}$
From stoichiometry: 2 mol fat β 110 mol H$_2$O
So 0.5 mol fat β $\dfrac{110 \times 0.5}{2} = 27.5\ \text{mol H}_2\text{O}$
Mass of H$_2$O $= 27.5 \times 18 = \mathbf{495\ \text{g}}$
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