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Home » For each such group of 4 artifacts (including artifact A), we can arrange them in $4!$ ways: - SUpost

For each such group of 4 artifacts (including artifact A), we can arrange them in $4!$ ways: - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 Since gadgets cannot be sold in fractions, round up: 167 gadgets.

📌 A triangle has sides of length 7 cm, 24 cm, and 25 cm. Verify if it is a right triangle and find its area.

📌 Check using the Pythagorean theorem: \(7^2 + 24^2 = 49 + 576 = 625\), and \(25^2 = 625\).

📌 Since \(7^2 + 24^2 = 25^2\), it is a right triangle.

📌 Area of a right triangle: \(\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 24 = 84\) cm².

📌 A sequence is defined by \(a_n = 3n^2 + 2n + 1\). Find the sum of the first 5 terms.

📌 \(a_1 = 3(1)^2 + 2(1) + 1 = 6\)

📌 \(a_2 = 3(2)^2 + 2(2) + 1 = 17\)

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