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can you eat potatoes that have sprouted - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Therefore, the number of ways to arrange the flowers such that each type appears at least once is \(\boxed{6}\).

📌 Question:** A community health discussion involves 7 participants, including 4 health professionals and 3 community members. In how many ways can they sit around a circular table if all participants are distinguishable?

📌 For circular arrangements, the formula is \((n-1)!\) because one position is fixed to avoid identical rotations. Here, \( n = 7 \).

📌 Thus, the number of circular permutations is:

📌 Calculating \( 6! \):

📌 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720

📌 Therefore, the number of ways to arrange the participants around the table is \(\boxed{720}\).Question: An equilateral triangle-shaped solar panel array has an area of $ 36\sqrt{3} \, \text{cm}^2 $. If each side is reduced by 4 cm, by how many square centimeters does the area decrease?

📌 Solution: The area of an equilateral triangle is given by $ \frac{\sqrt{3}}{4} s^2 $, where $ s $ is the side length. Setting $ \frac{\sqrt{3}}{4} s^2 = 36\sqrt{3} $, we solve for $ s^2 = 144 $, so $ s = 12 \, \text{cm} $. The new side length is $ 12 - 4 = 8 \, \text{cm} $. The new area is $ \frac{\sqrt{3}}{4} \times 8^2 = 16\sqrt{3} \, \text{cm}^2 $. The decrease in area is $ 36\sqrt{3} - 16\sqrt{3} = 20\sqrt{3} \, \text{cm}^2 $. \boxed{20\sqrt{3}}

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Check: \( 2.62^3 \approx 18 \)? Yes.
But since \( 6x^3 = 108 \Rightarrow x^3 = 18 \Rightarrow x = \sqrt[3]{...
So the width is \( \sqrt[3]{18} \) meters.
But wait — factor:
\( 6x^3 = 108 \Rightarrow x^3 = 18 \Rightarrow x = \sqrt[3]{18} \)
Alternatively, check if integer solution: try \( x = 3 \):
\( 6(27) = 162 > 108 \)
\( x = 2 \): \( 6(8) = 48 < 108 \)
So no integer. Answer is \( \sqrt[3]{18} \), but recheck algebra.
But \( 18 = 27 \cdot \frac{2}{3} \), so no simplification.

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