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Sales $800,000; Variable costs $480,000; Fixed costs $280,000. What sales revenue is required for a profit of $200,000?
Option C ($1,000,000) is correct.
CS ratio = ($800,000 − $480,000) ÷ $800,000 = 40%
Required sales = (Fixed costs + Target profit) ÷ CS ratio = ($280,000 + $200,000) ÷ 0.40 = $1,000,000
A projectile is launched from the ground with initial velocity $\vec{u} = u_0\hat{i} + v_0\hat{j}$. Gravity acts in the $-y$ direction. The maximum displacement in the $x$-direction is:
Time of flight $= \dfrac{2v_0}{g}$ (time for vertical displacement to return to zero).
Horizontal range $= u_0 \times \dfrac{2v_0}{g} = \mathbf{\dfrac{2u_0 v_0}{g}}$
Using Hooke's Law: $l = L + \frac{TL}{AY} \implies l = L + kT$ where $k = \frac{L}{AY}$.
- $l_1 = L + kT_1$ and $l_2 = L + kT_2$
- Subtracting: $l_2 - l_1 = k(T_2 - T_1) \implies k = \frac{l_2 - l_1}{T_2 - T_1}$
- Substitute $k$ back: $L = l_1 - T_1(\frac{l_2 - l_1}{T_2 - T_1}) = \frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}$.
Five observations have mean $= 4$ and variance $= 5.2$. Three of the observations are $3, 4, 4$. Find the absolute difference between the remaining two observations.
Step 1 β Find the sum: $\sum x_i = 5\times4=20$. Known three: $3+4+4=11$. So $x_4+x_5=9$.
Step 2 β Find sum of squares: Variance $=\frac{\sum x_i^2}{n}-\bar{x}^2 \Rightarrow \frac{\sum x_i^2}{5}-16=5.2 \Rightarrow \sum x_i^2=106$.
Known: $3^2+4^2+4^2=9+16+16=41$. So $x_4^2+x_5^2=65$.
Step 3 β Solve: $x_4+x_5=9$ and $x_4^2+x_5^2=65$.
$(x_4+x_5)^2=81 \Rightarrow 2x_4x_5=81-65=16 \Rightarrow x_4x_5=8$.
$(x_4-x_5)^2=(x_4+x_5)^2-4x_4x_5=81-32=49$
$|x_4-x_5|=\mathbf{7}$
ECG Lead Localization of MI:
| Leads with ST Elevation | Location | Artery |
|---|---|---|
| V1βV4 | Anterior | Left Anterior Descending (LAD) |
| II, III, aVF | Inferior | Right Coronary Artery (RCA) |
| I, aVL, V5βV6 | Lateral | Left Circumflex (LCx) |
| V1βV2 (tall R waves) | Posterior | RCA or LCx |
- Door-to-ECG: \(\leq 10\) minutes
- Door-to-balloon (PCI): \(\leq 90\) minutes
- Door-to-needle (thrombolysis): \(\leq 30\) minutes (if PCI unavailable)
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