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Home » You Won’t Believe How Nintendogs Transformed Your Kids’ Dog Imagination! - DNSFLEX

You Won’t Believe How Nintendogs Transformed Your Kids’ Dog Imagination! - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 A triangle has sides of lengths 7, 24, and 25. Is it a right triangle? If so, what is its area?

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

📌 A cylindrical tank with a radius of 3 meters and a height of 5 meters is filled with water. How many cubic meters of water does it hold?

📌 Volume = \( \pi r^2 h = \pi \times 3^2 \times 5 = 45\pi \).

📌 Approximate volume = \( 45 \times 3.1416 \approx 141.372 \).

📌 A student scored 85, 90, 78, and 92 on four tests. What score must they achieve on the fifth test to have an average of 88?

📌 Total needed for average of 88 over 5 tests = \( 88 \times 5 = 440 \).

📌 Current total = \( 85 + 90 + 78 + 92 = 345 \).

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Solution: We are given a recurrence:
T(1) = 4, \quad T(n) = 2T(n-1) + 3 \text{ for } n \geq 2.
We compute $ T(n) $ for $ n = 1 $ to $ 5 $:
$ T(1) = 4 $
$ T(2) = 2 \cdot 4 + 3 = 8 + 3 = 11 $
$ T(3) = 2 \cdot 11 + 3 = 22 + 3 = 25 $
$ T(4) = 2 \cdot 25 + 3 = 50 + 3 = 53 $
$ T(5) = 2 \cdot 53 + 3 = 106 + 3 = 109 $
Now compute the sum:
S(5) = T(1) + T(2) + T(3) + T(4) + T(5) = 4 + 11 + 25 + 53 + 109 = 202

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s\sqrt{3} = 6\sqrt{3} \quad \Rightarrow \quad s = 6 \text{ cm}
The volume \(V\) of a cube is:
V = s^3 = 6^3 = 216 \text{ cm}^3
Thus, the volume of the cube is:
\boxed{216 \text{ cm}^3}
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