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Home » This is a geometric series: a = 8, r = 1.25, n = 5 - Blask

This is a geometric series: a = 8, r = 1.25, n = 5 - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 To solve this, we use the **binomial probability formula**, since each die roll is independent, and we're interested in a specific number of successes (rolling a number greater than 7) in a fixed number of trials (4 rolls).

📌 Numbers greater than 7 on a 10-sided die: 8, 9, 10 → 3 outcomes

📌 Probability of success (rolling >7): $ p = \frac{3}{10} = 0.3 $

📌 Probability of failure (rolling ≤7): $ 1 - p = 0.7 $

📌 Number of trials $ n = 4 $

📌 Number of successes desired $ k = 2 $

📌 P(k) = \binom{n}{k} p^k (1 - p)^{n - k}

📌 Substitute the values:

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f(x^2 + 2) = x^4 + 4x^2 + 2.
Find $ f(x^2 - 2) $.
Solution: We are given that
Let us denote $ y = x^2 + 2 $, so that $ x^2 = y - 2 $. Then
x^4 = (x^2)^2 = (y - 2)^2 = y^2 - 4y + 4.
Now substitute into the expression for $ f(y) $:
f(y) = x^4 + 4x^2 + 2 = (y^2 - 4y +
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