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Home » Total time: \(3 + 4 = 7\) hours - AMAZONAWS

Total time: \(3 + 4 = 7\) hours - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Next, find the remainder of 12 when divided by 6:

📌 \equiv 0 \pmod{6}

📌 Thus, the remainder is \(\boxed{0}\).

📌 Question:** A zoologist studying animal migration patterns observes that certain species return every few years, forming a sequence similar to an arithmetic progression. How many of the first 50 positive integers are congruent to 3 (mod 7)?

📌 We seek integers \( n \) such that \( n \equiv 3 \pmod{7} \). The sequence of such integers is \( 3, 10, 17, \ldots \).

📌 This is an arithmetic sequence with the first term \( a = 3 \) and common difference \( d = 7 \). The general term is given by:

📌 n_k = 3 + 7(k-1) = 7k - 4

📌 We require \( n_k \leq 50 \):

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