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stars of to kill a mockingbird - Malaeb

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 The sum of the first n terms of a geometric series is \( S_n = a \frac{r^n - 1}{r - 1} \).

📌 Here, \( a = 5 \), \( r = 2 \), and \( n = 4 \).

📌 So, \( S_4 = 5 \frac{2^4 - 1}{2 - 1} = 5 \times (16 - 1) = 5 \times 15 = 75 \).

📌 #### Sum: 75Question: A computational biologist is analyzing a gene sequence with 5 distinct nucleotides. How many unique 2-nucleotide combinations can be formed if the order does not matter?

📌 Solution: To determine the number of unique 2-nucleotide combinations from 5 distinct nucleotides without considering order, we use the combination formula $ \binom{n}{r} $, where $ n = 5 $ and $ r = 2 $.

📌 \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10

📌 Thus, there are $ \boxed{10} $ unique combinations.

📌 Question: On a Mars colony, two supply drones arrive at random times between 08:00 and 09:00. What is the probability that the second drone arrives more than 15 minutes after the first?

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