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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Dr. Elena assesses a mixed sample with two contributors. Each has an independent 8% chance of triggering a false match in a search. What is the probability that at least one contributor produces a false match in the same sample?

📌 Probability of no false match: 1 – 0.08 = 0.92.

📌 Probability both pass: 0.92 × 0.92 = <<0.92*0.92=0.8464>>0.8464.

📌 So, probability of at least one false match: 1 – 0.8464 = <<1-0.8464=0.1536>>0.1536.

📌 #### 0.154**Question:

📌 Find all angles \( \theta \in [0^\circ, 360^\circ] \) that satisfy the equation \(\sin(2\theta) = \cos(\theta)\).

📌 The equation \(\sin(2\theta) = \cos(\theta)\) can be rewritten using the double angle identity for sine:

📌 \sin(2\theta) = 2\sin(\theta)\cos(\theta).

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