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Home » This Ultimate Ki Tana Routine Is Changing Lives—Start Now to Witness Radiant Results! - Appcentric

This Ultimate Ki Tana Routine Is Changing Lives—Start Now to Witness Radiant Results! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 #### 31.8878

📌 Determine the limit \(\lim_{x o 2} rac{x^2 - 4}{x - 2}\).

📌 Factor the numerator: \(x^2 - 4 = (x - 2)(x + 2)\).

📌 \[ rac{(x - 2)(x + 2)}{x - 2} = x + 2 \quad ext{for} \quad x

📌 Evaluate the limit as \(x o 2\):

📌 \[ \lim_{x o 2} (x + 2) = 4 \]

📌 #### 4Question: A physicist analyzing particle collisions observes that in a series of 12 independent trials, each trial results in one of three outcomes: success (S), partial success (P), or failure (F), with probabilities 0.4, 0.3, and 0.3 respectively. What is the probability that exactly 5 successes, 4 partial successes, and 3 failures occur across the 12 trials?

📌 Solution: This is a multinomial probability problem. Let $ X = (X_S, X_P, X_F) $ be the counts of each outcome in 12 independent trials, with probabilities $ p_S = 0.4 $, $ p_P = 0.3 $, and $ p_F = 0.3 $. The probability mass function of a multinomial distribution gives:

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