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Home » \mathbfa \cdot \mathbfa = 1^2 + 1^2 + 1^2 = 3 - Tacotoon

\mathbfa \cdot \mathbfa = 1^2 + 1^2 + 1^2 = 3 - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Alex determines that a suspect’s DNA is in 1 out of 2,000 individuals in a database of 15,000. How many individuals in the database are expected to match, and if the investigation includes a high-profile target list of 350 people, how many matches would be statistically expected?

📌 Expected matches: 15,000 × (1/2000) = <<15000/2000=7.5>>7.5.

📌 For 350 targets: 350 × (1/2000) = <<350/2000=0.175>>0.175.

📌 Since partial matches aren’t acceptable, but statistically expected value is 0.175.

📌 #### 0.175

📌 Dr. Elena reviews a case where two DNA profiles match across 8 loci. If mismatch probability per locus is 0.05, and matches are independent, what is the probability of all 8 loci matching in a true match?

📌 Probability of matching one locus: 1 – 0.05 = 0.95.

📌 For 8 independent loci: 0.95⁸ ≈ <<0.95^8=0.66342>>0.66342.

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We now solve the system $ a + b = 35 $, $ a^2 + b^2 = 625 $. Use ident...
\Rightarrow 2ab = 600 \Rightarrow ab = 300
A = \frac{1}{2}ab = 150
Area of the inscribed circle:
A_{\text{circle}} = \pi r^2 = \pi \cdot 25 = 25\pi
\frac{A_{\text{circle}}}{A_{\text{triangle}}} = \frac{25\pi}{150} = \f...
Thus, the ratio is $ \boxed{\frac{\pi}{6}} $.Question: A plant biologi...
The rate of change of $ f(t) $ is given by its derivative:
f'(t) = -A\omega \sin(\omega t + \phi)
The maximum rate of change occurs when $ \sin(\omega t + \phi) = \pm 1...

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