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Home » The Girl from the Other Side: Shocking Truth About Her Hidden Identity! - Carbonext

The Girl from the Other Side: Shocking Truth About Her Hidden Identity! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \frac{10}{35} = \frac{2}{7}

📌 Hence, the probability is $ \boxed{\frac{2}{7}} $.

📌 Question: A data scientist trains a model using sequences of 5 binary features, each being 0 or 1. If each feature is independently set to 1 with probability $ \frac{1}{3} $, what is the probability that exactly 3 of the 5 features are 1?

📌 This is a binomial probability with $ n = 5 $, $ k = 3 $, and success probability $ p = \frac{1}{3} $.

📌 P(X = 3) = \binom{5}{3} \left(\frac{1}{3}\right)^3 \left(\frac{2}{3}\right)^2 = 10 \cdot \frac{1}{27} \cdot \frac{4}{9} = 10 \cdot \frac{4}{243} = \frac{40}{243}

📌 Thus, the probability is $ \boxed{\frac{40}{243}} $.

📌 Question: In a biotech lab simulation, 4 identical red enzymes, 3 identical green enzymes, and 2 identical blue enzymes are deployed in a sequence. How many distinct sequences can be formed where all red enzymes are indistinct, green indistinct, and blue indistinct?

📌 Total number of enzymes: $ 4 + 3 + 2 = 9 $.

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subject to $ x + y + z = 1 $, with $ x, y, z > 0 $.
Apply the **Cauchy-Schwarz Inequality** in the following form:
\left( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \right)(y + z + x...
Since $ x + y + z = 1 $, we have:
\left( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \right)(1) \geq 1...
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \geq 1
Equality holds when $ \frac{x}{y} = \frac{y}{z} = \frac{z}{x} $, which...
Check the expression at $ x = y = z = \frac{1}{3} $:
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} = 3 \cdot \frac{(1/3)^2}...
Question: For all real numbers $ a, b, c $, find the number of functio...

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