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Home » Big-Foot? Small-Body? Ski Size Chart Finally Fits You! - Abbey Badges

Big-Foot? Small-Body? Ski Size Chart Finally Fits You! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 5Question: Let \( \mathbf{v} \) be a vector in \( \mathbb{R}^3 \) such that \( \|\mathbf{v}\| = 1 \) and \( \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) = \frac{1}{2} \), where \( \mathbf{w} = \langle 1, 0, 1 \rangle \), \( \mathbf{u} = \langle 0, 1, 2 \rangle \). Find the maximum possible value of \( \|\mathbf{v}\| \) under the constraint—wait, correction: \( \|\mathbf{v}\| \) is fixed at 1, so instead reinterpret: find the maximum of \( \|\mathbf{v}\|^2 \) given the dot product condition, but since \( \|\mathbf{v}\| = 1 \), we instead seek consistent interpretation.

📌 Wait—reformulate properly.

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\binom{8}{4} = 70,\quad \binom{12}{2} = 66,\quad \binom{20}{6} = 38760
\frac{70 \cdot 66}{38760} = \frac{4620}{38760} = \frac{77}{646}
\boxed{\frac{77}{646}}
Question: A philosopher of science is analyzing 12 key scientific theo...
We use combinations to find the probability.
Total number of ways to choose 4 theories from 12:
\binom{12}{4} = 495
Number of favorable outcomes (choosing 2 from the 5 20th-century theor...
\binom{5}{2} \cdot \binom{7}{2} = 10 \cdot 21 = 210
\frac{210}{495} = \frac{14}{33}

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