Option D (24.85%) is correct.

ROCE = Profit from operations ÷ Capital Employed × 100

Capital Employed = Shareholders' equity + Non-current liabilities = $423,000 + $80,000 = $503,000

(Current liabilities are excluded from capital employed.)

ROCE = $125,000 ÷ $503,000 × 100 = 24.85%

High QWL is related to job satisfaction, which is a strong predictor of absenteeism and turnover. Investments in improving QWL also pay off in the form of better customer service. All three elements are interconnected in the QWL framework.

Aristotle famously argued that human beings are meant to live in a 'polis' or city-state.

Roots: $x=\frac{-2\pm\sqrt{4-8}}{2}=-1\pm i$. So $\alpha=-1+i, \beta=-1-i$.

In polar form: $|\alpha|=\sqrt{2}$, $\arg(\alpha)=\frac{3\pi}{4}$. So $\alpha=\sqrt{2}\,e^{i3\pi/4}$.

$\alpha^{15}=(\sqrt{2})^{15}e^{i\cdot45\pi/4}=2^{15/2}e^{i\pi/4}$ (since $45\pi/4=11\pi+\pi/4$, so $e^{i45\pi/4}=e^{i\pi/4}\cdot(-1)^{11}=-e^{i\pi/4}$... careful: $45/4=11.25$, $11\pi+\pi/4$, $e^{i(11\pi+\pi/4)}=e^{i\pi}\cdot e^{i\pi/4} \cdot (-1)^{10}... $)

More cleanly: $\alpha^{15}+\beta^{15}=2\,\text{Re}(\alpha^{15})=2(\sqrt{2})^{15}\cos\!\left(\frac{45\pi}{4}\right)$. Since $\cos(45\pi/4)=\cos(\pi/4+11\pi)=-\cos(\pi/4)=-\frac{1}{\sqrt{2}}$: $=2\cdot2^{15/2}\cdot(-\frac{1}{\sqrt{2}})=-2^{15/2+1-1/2}=-2^8=-\mathbf{256}$

For maximum power, R_L = R_source (Thévenin resistance).

From the definition of Bulk Modulus $K$:

$\frac{\Delta V}{V} = \frac{P}{K}$ (Volume strain due to pressure)

From thermal expansion, the increase in volume is:

$\frac{\Delta V}{V} = \gamma \Delta T = 3\alpha \Delta T$

To restore the original size, the thermal expansion must equal the pressure compression:

$3\alpha \Delta T = \frac{P}{K} \implies \Delta T = \frac{P}{3\alpha K}$

The roots of $x^2-x+1=0$ are $x=\frac{1\pm\sqrt{-3}}{2}=-\omega,-\omega^2$ where $\omega=e^{2\pi i/3}$.

Let $\alpha=-\omega, \beta=-\omega^2$. Then:

$\alpha^{101}=(-\omega)^{101}=-\omega^{101}=-\omega^{101\mod3}=-\omega^2$ (since $101=33\times3+2$)

$\beta^{107}=(-\omega^2)^{107}=-\omega^{214}=-\omega^{214\mod3}=-\omega^1$ (since $214=71\times3+1$)

$\alpha^{101}+\beta^{107}=-\omega^2-\omega=-(w+\omega^2)=-(-1)=\mathbf{1}$