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Home » Use Heron’s formula. Let $s = \frac(a-1) + a + (a+1)2 = \frac3a2$. - Appfinity Technologies

Use Heron’s formula. Let $s = \frac(a-1) + a + (a+1)2 = \frac3a2$. - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 + 31 + 90 + 65 = 187

📌 Thus, the total number of distinct distributions is:

📌 In a social network of 5 connected individuals, what is the probability that a randomly selected trio consists of exactly 2 individuals who share a close relationship and 1 who does not, given that exactly 3 pairs in the network are classified as "close"?

📌 We are given a network of 5 individuals with exactly 3 "close" pairs among the \( inom{5}{2} = 10 \) total pairs. We are to compute the probability that a randomly selected trio (unordered group of 3) includes exactly 2 close pairs and 1 non-close pair.

📌 Letâs proceed step by step.

📌 Step 1: Total number of trios

📌 inom{5}{3} = 10

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Substitute into the first equation: \(2x + 3(4x - 5) = 6\).
Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).
Solve: \(x = 1.5\).
Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).
#### \(x = 1.5\), \(y = 1\)
If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+...
Set up the equation: \(\frac{n(n+1)}{2} = 210\).
Multiply by 2: \(n(n+1) = 420\).
Solve \(n^2 + n - 420 = 0\) using the quadratic formula:
\(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).

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