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Home » Here, \(a_1 = 5\), \(d = 3\), and \(n = 50\). - Feedz API

Here, \(a_1 = 5\), \(d = 3\), and \(n = 50\). - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Problem:** A weather station records that over a week, the temperature rose on 5 days, dropped on 3 days, and remained stable on 2 days. On 2 days, both rising and stable were recorded due to mixed weather, but these are not mutually exclusive. If on 1 day the temperature both rose and dropped due to anomalies, how many days showed a clear rise?

📌 Let \( R \) be days temperature rose, \( D \) days dropped, and \( T_{\text{stable}} \) days stable.

📌 Given: \( |R| = 5 \), \( |D| = 3 \), \( |T_{\text{stable}}| = 2 \), and 1 day both rose and stable, 1 day both rose and dropped.

📌 The anomalous 2-day record (rising and stable) implies overlap but doesn't reduce clear rises.

📌 Days with a clear rise include those that rose but are not overlapped into non-rising categories. Since only common issues are rise and stable or rise and drop, the greatly overlapping region does not eliminate rose days.

📌 Total days: 7. Days with temperature change or stability: \( 5 + 3 + 2 = 10 \), but with overlaps, actual distinct days is at most 7.

📌 The only consistent interpretation: 5 days rose, with overlaps not affecting this count since "both rising and stable" are separate outcomes.

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