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Home » Factor the numerator: \( x^2 - 9 = (x - 3)(x + 3) \). - Aurero

Factor the numerator: \( x^2 - 9 = (x - 3)(x + 3) \). - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Question: An AI-driven agricultural system monitors 6 crop fields, each with a 20% chance of requiring immediate irrigation. What is the probability that exactly 2 fields require irrigation?

📌 Solution: Using the binomial formula:

📌 \binom{6}{2} (0.20)^2 (0.80)^4 = 15 \cdot 0.04 \cdot 0.4096 = 0.24576

📌 The probability is $\boxed{0.2458}$.Question: What is the remainder when the sum of the first 5 terms of the sequence $ a_n = 3n + 2 $ is divided by 7?

📌 Solution: The first 5 terms are $ a_1 = 5 $, $ a_2 = 8 $, $ a_3 = 11 $, $ a_4 = 14 $, and $ a_5 = 17 $. Their sum is $ 5 + 8 + 11 + 14 + 17 = 55 $. Dividing 55 by 7 gives a quotient of 7 and a remainder of $ 55 - 7 \times 7 = 55 - 49 = 6 $.

📌 Question: What is the least common multiple of the number of eggs laid by three different snake species, which are 12, 18, and 30?

📌 Solution: Factorize each number: $ 12 = 2^2 \times 3 $, $ 18 = 2 \times 3^2 $, and $ 30 = 2 \times 3 \times 5 $. The LCM is the product of the highest powers of all primes: $ 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180 $.

📌 \boxed{180}

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