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Choice A is correct. The result of increasing a positive quantity $w$ by $x\%$ can be represented by the expression $\left(1+\frac{x}{100}\right)w$. Therefore, the result of increasing a positive quantity $w$ by $43\%$ can be found by substituting $43$ for $x$ in the expression $\left(1+\frac{x}{100}\right)w$, which gives $\left(1+\frac{43}{100}\right)w$, or $1.43w$. Thus, the expression $1.43w$ represents the result of increasing a positive quantity $w$ by $43\%$.

Choice B is incorrect. This is the result of decreasing a positive quantity $w$ by $43\%$.

Choice C is incorrect. This is the result of increasing a positive quantity $w$ by $\mathrm{4,200}\%$.

Choice D is incorrect. This is the result of decreasing a positive quantity $w$ by $57\%$.