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Home » Solution: This is a hypergeometric probability problem. - Midis

Solution: This is a hypergeometric probability problem. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A regular hexagon has a side length of 6 cm. Calculate its area.

📌 The formula for the area \( A \) of a regular hexagon with side length \( s \) is:

📌 \( s = 6 \) cm

📌 Substitute the value into the formula:

📌 \[ A = \frac{3\sqrt{3}}{2} \times 6^2 \]

📌 \[ A = \frac{3\sqrt{3}}{2} \times 36 \]

📌 \[ A = 54\sqrt{3} \]

📌 Using \( \sqrt{3} \approx 1.732 \):

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Evaluate at $ y = -1 $:
f(-1) = -1 - 2 + 1 = -2.
Thus, the range of $ f(x) $ is $[-2, 2]$.
\boxed{[-2, 2]}
Question: A mammalogist observes that the social interaction frequency...
Solution: Rewrite $ \tan \theta + \cot \theta = 4 $ as:
\frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta} = 4...
Since $ \sin^2 \theta + \cos^2 \theta = 1 $, this simplifies to:
\frac{1}{\sin \theta \cos \theta} = 4 \implies \sin \theta \cos \theta...
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A car accelerates from rest at a constant rate of \(4 \, \text{m/s}^2\...
Use the formula \(d = \frac{1}{2}at^2\).
Substitute: \(d = \frac{1}{2} \times 4 \times (10)^2 = 200 \, \text{m}...
#### 200 m
2x + 3y &= 6 \\
4x - y &= 5
Substitute into the first equation: \(2x + 3(4x - 5) = 6\).
Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).
Solve: \(x = 1.5\).
Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).

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