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Home » So, number of favorable selections: - Carbonext

So, number of favorable selections: - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 P(X < 2) = P(X = 0) + P(X = 1)

📌 $ P(X = 0) = \binom{3}{0} (0.75)^0 (0.25)^3 = 1 \cdot 1 \cdot 0.015625 = 0.015625 $

📌 $ P(X = 1) = \binom{3}{1} (0.75)^1 (0.25)^2 = 3 \cdot 0.75 \cdot 0.0625 = 0.140625 $

📌 P(X < 2) = 0.015625 + 0.140625 = 0.15625

📌 Thus, the probability that fewer than two animations are accepted is:

📌 \boxed{0.15625}

📌 Question: A hydrologist is studying rainfall patterns and notes that in a certain region, the probability of rain on any given day in July is 0.3. What is the probability that it rains on exactly 5 out of 10 randomly selected days in July?

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\boxed{-5}
Question:** A biodiversity specialist is studying the periodic behavio...
First, solve for \(\cos(2z)\):
2\cos(2z) = \sqrt{3} \quad \Rightarrow \quad \cos(2z) = \frac{\sqrt{3}...
The general solutions for \(\cos(2z) = \frac{\sqrt{3}}{2}\) are:
2z = 30^\circ + 360^\circ n \quad \text{or} \quad 2z = 330^\circ + 360...
Divide by 2 to find \(z\):
z = 15^\circ + 180^\circ n \quad \text{or} \quad z = 165^\circ + 180^\...
For \(z \in [0^\circ, 360^\circ]\), evaluate:
\(z = 15^\circ, 195^\circ\) from \(15^\circ + 180^\circ n\)

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