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Home » Each layer multiplies the signal by 0.60 (60% retained). - Appcentric

Each layer multiplies the signal by 0.60 (60% retained). - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \boxed{-\frac{1}{2}}

📌 Question:** A digital transformation algorithm rotates a vector in 3D space using $\tan(\theta)$, where $\theta$ is the angle between two planes. If $\cos \theta = \frac{1}{3}$, compute $\tan \theta$.

📌 Solution:** Use identity:

📌 \tan \theta = \frac{\sqrt{1 - \cos^2 \theta}}{\cos \theta}

📌 Given $\cos \theta = \frac{1}{3}$, compute:

📌 \tan \theta = \frac{\sqrt{1 - \left(\frac{1}{3}\right)^2}}{\frac{1}{3}} = \frac{\sqrt{1 - \frac{1}{9}}}{\frac{1}{3}} = \frac{\sqrt{\frac{8}{9}}}{\frac{1}{3}} = \frac{\frac{2\sqrt{2}}{3}}{\frac{1}{3}} = 2\sqrt{2}

📌 $$Question: A venture capitalist invests in 5 startups, each with a 25% chance of success independently. What is the probability that exactly 2 of the startups succeed?

📌 Solution: We model this as a binomial probability problem. The probability of exactly $ k $ successes in $ n $ independent trials, each with success probability $ p $, is given by:

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