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Home » \(3 - 1.5 = 0.10x\). - AMAZONAWS

\(3 - 1.5 = 0.10x\). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Thus, the number of lattice points is \( \boxed{4} \).

📌 Question:** How many of the 150 smallest positive integers are congruent to 3 (mod 7)?

📌 Solution:** We want integers \( n \) such that \( 1 \leq n \leq 150 \) and \( n \equiv 3 \pmod{7} \).

📌 Such numbers are of the form \( n = 7k + 3 \).

📌 Find the smallest and largest such \( n \) in range:

📌 Smallest: \( k = 0 \Rightarrow n = 3 \)

📌 Largest: solve \( 7k + 3 \leq 150 \Rightarrow 7k \leq 147 \Rightarrow k \leq 21 \)

📌 So \( k = 0, 1, 2, \dots, 21 \) → total of \( 22 \) values.

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