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Home » Step 2: Count favorable outcomes — sequences of 5 rolls using exactly two distinct values. - DNSFLEX

Step 2: Count favorable outcomes — sequences of 5 rolls using exactly two distinct values. - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Thus, the sum of the first five terms is \(\boxed{160}\).

📌 Question:** A middle school student is exploring functions and their compositions. If \(f(x) = 3x - 2\) and \(g(x) = x^2 + 1\), what is \(g(f(4))\)?

📌 First, evaluate \(f(4)\):

📌 f(4) = 3(4) - 2 = 12 - 2 = 10.

📌 Next, substitute this result into \(g(x)\):

📌 g(f(4)) = g(10) = 10^2 + 1 = 100 + 1 = 101.

📌 Thus, the value of \(g(f(4))\) is \(\boxed{101}\).

📌 Question:** A chemical engineer is modeling biofuel yield based on reactant concentrations. If the yield \(Y\) is given by \(Y = 4x^2 - 12x + 9\), compute the minimum possible yield and the value of \(x\) at which it occurs.

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