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Home » Next, find $\|\mathbfq\|^2$: - Groen Casting

Next, find $\|\mathbfq\|^2$: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 For \( n = 30 \):

📌 S_{30} = \frac{30}{2} \left(2 \cdot 2 + (30 - 1) \cdot 3 \right) = 15 \left(4 + 29 \cdot 3 \right) = 15 (4 + 87) = 15 \cdot 91 = 1365

📌 Thus, the total number of root branches produced in the first 30 weeks is:

📌 \boxed{1365}

📌 Question:** A statistician is analyzing a discrete uniform distribution over integers from 1 to 84. What is the probability that a randomly selected integer from this range is a multiple of both 7 and 4?

📌 Solution:** A number divisible by both 7 and 4 must be divisible by \( \text{lcm}(7, 4) = 28 \).

📌 Find how many multiples of 28 are in \( \{1, 2, \dots, 84\} \):

📌 28, 56, 84

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