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Before Maria changed jobs, her salary was 24 percent more than Julio's salary. After Maria changed jobs, her new salary was 24 percent less than her old salary.
Compare:
Column A: Julio's salary
Column B: Maria's new salary
Let Julio's salary be $J$ and Maria's old salary be $M_{old}$.
Given: $M_{old} = 1.24J$
Maria's new salary: $M_{new} = M_{old} - 0.24M_{old} = 0.76M_{old} = 0.76(1.24J) = 0.9424J$
Comparing:
- Column A: $J = 1.0J$
- Column B: $0.9424J$
Since $1.0 > 0.9424$, Column A (Julio's salary) is greater than Column B (Maria's new salary).
Therefore, Column A is greater.
What is the primary reason for a business to record a depreciation charge?
- To ensure enough funds are available to replace the asset at the end of its life
- To allocate the cost of the asset across the specific periods that benefit from its use
- To ensure every asset is treated consistently based on the consistency principle
The core purpose of depreciation is the matching principle: charging the cost of a non-current asset to the periods it helps generate revenue. It does not guarantee cash for replacement, nor is it purely about the consistency concept itself.
Find a value of $\theta$ for which $\dfrac{2+3i\sin\theta}{1-2i\sin\theta}$ is purely imaginary.
Multiply numerator and denominator by the conjugate of the denominator $(1+2i\sin\theta)$:
Numerator real part: $(2+3i\sin\theta)(1+2i\sin\theta)$ real part $= 2-6\sin^2\theta$
For purely imaginary, the real part must be zero: $2-6\sin^2\theta=0\Rightarrow\sin^2\theta=\frac{1}{3}\Rightarrow\sin\theta=\frac{1}{\sqrt{3}}$
Therefore $\theta=\sin^{-1}\!\left(\dfrac{1}{\sqrt{3}}\right)$
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