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Home » We apply the Chinese Remainder Theorem step by step. - Appfinity Technologies

We apply the Chinese Remainder Theorem step by step. - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \binom{5}{1} \cdot \binom{7}{1} \cdot \binom{3}{2} = 5 \cdot 7 \cdot 3 = 105

📌 ### Step 3: Total favorable outcomes

📌 \text{Favorable} = 210 + 315 + 105 = 630

📌 ### Step 4: Compute the probability

📌 P(\text{at least one of each color}) = \frac{630}{1365}

📌 \frac{630}{1365} = \frac{6}{13}

📌 \boxed{\frac{6}{13}}

📌 Question: A transportation analyst is analyzing a network with 6 red buses, 4 green buses, and 5 blue buses. If she randomly selects 5 buses for maintenance, what is the probability that she selects at least two buses of each color?

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x = \frac{4 \pm \sqrt{64}}{4}
x = \frac{4 \pm 8}{4}
The roots are:
x = \frac{4 + 8}{4} = 3 \quad \text{and} \quad x = \frac{4 - 8}{4} = -...
If \(f(x) = 3x^2 - 2x + 1\) and \(g(x) = x - 4\), find \(f(g(2))\).
First, calculate \(g(2)\):
g(2) = 2 - 4 = -2
Next, substitute into \(f(x)\):
f(-2) = 3(-2)^2 - 2(-2) + 1
f(-2) = 3(4) + 4 + 1

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