With the auxiliary verb 'did' (past tense of 'do'), the main verb must be in its base form: 'know', not 'knew'. 'She didn't know' is correct.

Let $I=\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{\sin^2x}{1+2^x}dx$. Use the property $\int_{-a}^a f(x)dx$: replace $x\to-x$:

$I=\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{\sin^2x}{1+2^{-x}}dx=\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{2^x\sin^2x}{1+2^x}dx$

Adding: $2I=\displaystyle\int_{-\pi/2}^{\pi/2}\sin^2x\,dx=\displaystyle\int_{-\pi/2}^{\pi/2}\dfrac{1-\cos2x}{2}dx=\dfrac{\pi}{2}$

$I=\dfrac{\pi}{4}$

Pancreatic lipase works in the small intestine at a slightly alkaline pH (around 8) due to bicarbonate secretion from pancreas. Gastric lipase works at acidic pH.

Option A ($10) is correct.

Total interest on drawings = $90 + $50 = $140 added to profit available.

Lee's extra profit share = $140 × 4/7 = $80

Net change to Lee's account = −$90 (interest charged) + $80 (extra profit) = −$10

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.