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Home » \[ a + b = 14 \] - Blask

\[ a + b = 14 \] - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \times 10 = 280

📌 Therefore, the total number of distinct sundaes is \(\boxed{280}\).

📌 Question:** A virtual museum has 12 digitized manuscripts, and a curator wants to feature 5 in a weekly digital exhibit. If two specific manuscripts (a solution to an ancient equation and a pivotal scientific letter) must both be included, how many valid selections are possible?

📌 Solution:** Since two specific manuscripts must be included, we only need to choose the remaining 3 from the other 10 manuscripts.

📌 The number of ways to choose 3 from 10 is:

📌 \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = \frac{720}{6} = 120

📌 Thus, the number of valid selections is \(\boxed{120}\).**Question:

📌 Define \( f(u) = u - \frac{u^5}{5} \) for every real number \( u \). If \( n \) is a positive integer, define \( b_n \) by \( b_1 = 1 \) and \( b_{n+1} = f(b_n) \). Find all values of \( n \) for which \( b_n < 0.1 \).

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