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Home » Glass Ornaments That Glow Like Magic—Discover the Secret Behind Their Breathtaking Design! - Aurero

Glass Ornaments That Glow Like Magic—Discover the Secret Behind Their Breathtaking Design! - Aurero

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 \frac{3\dbinom{17}{3} + \dbinom{16}{3} + 17 \times 17 \times 16}{\dbinom{50}{3}} = \frac{3 \times 680 + 560 + 4568}{19600} = \frac{2040 + 560 + 4568}{19600} = \frac{6168}{19600} = \boxed{\dfrac{1542}{4900}}

📌 Pregunta: ¿De cuántas maneras pueden sentarse 5 miembros distinguibles y 3 no miembros distinguibles alrededor de una mesa circular si se consideran equivalentes las rotaciones y las reflexiones?

📌 Solución: Para arreglos en círculo con reflexión, fijo un miembro para eliminar simetrías rotacionales y de reflexión. Los 4 miembros restantes se pueden arreglar de \(4!\) maneras, y los 3 no miembros de \(3!\) maneras. Total de arreglos:

📌 4! \times 3! = 24 \times 6 = \boxed{144}

📌 Pregunta: Calcula \(\dbinom{12}{5} - \dbinom{12}{4}\).

📌 Solución: Usando las propiedades de los coeficientes binomiales:

📌 \dbinom{12}{5} = \dbinom{12}{7}, \quad \dbinom{12}{4} = \dbinom{12}{8}

📌 Pero directamente:

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Now evaluate $ T(3) $:
T(3) = (3)^2 - 6(3) + 13 = 9 - 18 + 13 = 4
Thus, the minimum time predicted by the model is $ \boxed{4} $.
Question: Factor the expression $ 16x^2 - 40x + 25 $ completely.
Check if the trinomial is a perfect square trinomial:
16x^2 = (4x)^2, \quad 25 = (5)^2, \quad -40x = 2(4x)(-5)
This confirms the expression is of the form $ a^2 - 2ab + b^2 = (a - b...
16x^2 - 40x + 25 = (4x - 5)^2
Thus, the factored form is $ \boxed{(4x - 5)^2} $.
Question: If $ x + \frac{1}{x} = 4 $, what is the value of $ x^2 + \fr...

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