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ymca of the rockies snow mountain ranch - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Rahul, a smart city developer, monitors traffic flow. A sensor detects 680 vehicles passing through an intersection every 15 minutes. What is the average vehicle arrival rate per hour?

📌 #### 2720Jenna, a data scientist, is analyzing transaction patterns to detect anomalies. She observes that a fraudulent user sends transactions every 7 minutes starting at 3:17 AM. A legitimate user sends a transaction every 11 minutes, starting at 3:19 AM. What is the first time after 3:17 AM when both users send a transaction simultaneously?

📌 Since 7 and 11 are coprime, use the Chinese Remainder Theorem.

📌 Set t = 17 + 7k. Substitute into second congruence:

📌 Multiply both sides by the modular inverse of 7 modulo 11.

📌 Then t = 17 + 7(11m + 5) = 17 + 77m + 35 = 52 + 77m

📌 Dr. Liu, a biomedical researcher, models bacterial growth in a petri dish. The bacteria double every 20 minutes. At 1:00 PM, there are 500 bacteria. A treatment is applied at 1:40 PM that kills 30% of the current population immediately, and then further growth resumes. At what time does the population first exceed 100,000?

📌 Now growth resumes: from 1:40 PM, time t minutes elapsed since 1:40

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