• For an FCC lattice, $Z = 4$.
• $M = 63.55\text{ g/mol}$.
• $a = x\text{ \AA} = x \times 10^{-8}\text{ cm}$.
• $N_A \approx 6.022 \times 10^{23}$.

The expression $\dfrac{x}{|x|}$ is the sign function of $x$:

• If $x > 0$: $\dfrac{x}{|x|} = \dfrac{x}{x} = 1$ → equal to Column B
• If $x < 0$: $\dfrac{x}{|x|} = \dfrac{x}{-x} = -1$ → less than Column B

Since $x$ can be positive or negative, and we get different results, the relationship cannot be determined from the information given.

Hess's law states that enthalpy change for a reaction is independent of path, allowing calculation of ΔH by summing known reactions.

A filibuster is a tactic used in the US Senate to delay or block a vote on a piece of legislation.

Option D ($8,385) is correct.

Error 1: Returns $72 credited instead of debited → payable's balance overstated by $144 (wrong side = double error).

Error 2: Discount posted as $45 instead of $54 → understated by $9.

Ledger total = $8,232 + $144 + $9 = $8,385

Acute Asthma Severity Classification in Children (GINA/BTS):

This child: PEFR 35% (<33–50%) + SpO₂ 88% (<92%) + unable to complete sentences = Severe/Life-threatening. PEFR 35% places in severe range.

Management of severe asthma:

• High-flow O₂ to maintain SpO₂ \(\geq 94\%\)
• Salbutamol (back-to-back nebulization) \(2.5{-}5\,\text{mg}\) every 20 minutes
• Ipratropium bromide \(0.25\,\text{mg}\) nebulized (add for severe)
• Systemic corticosteroids: prednisolone \(1{-}2\,\text{mg/kg}\) oral or IV hydrocortisone
• IV MgSO₄ \(40\,\text{mg/kg}\) (max 2 g) in life-threatening asthma
• ICU referral if deteriorating