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Home » She Deserves a Stunning Happy Birthday GIF—Surprise Her with This Fire! - DNSFLEX

She Deserves a Stunning Happy Birthday GIF—Surprise Her with This Fire! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Solution:** The sequence 2, 5, 8, 11, ... is arithmetic with first term \( a = 2 \) and common difference \( d = 3 \).

📌 The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence is:

📌 S_n = \frac{n}{2} (2a + (n - 1)d)

📌 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?

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\[ \frac{4}{3}r^3 = 288 \]
\[ r^3 = 288 \times \frac{3}{4} = 216 \]
\[ r = \sqrt[3]{216} = 6 \, \text{cm} \]
Substituting \( l = 4 \), \( w = 5 \), \( h = 6 \):
\[ SA = 2(4 \times 5 + 4 \times 6 + 5 \times 6) \]
\[ SA = 2 \times 74 = 148 \, \text{square centimeters} \]
A loan of $5,000 is taken out with a simple interest rate of 6% per an...
Simple interest \( I \) is calculated by:
\[ I = P \times r \times t \]
Where \( P = 5,000 \), \( r = 0.06 \), \( t = 4 \):

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