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Home » Rund auf \( y = 1 \): Festigkeit = \( 10 \times 8 + 7 \times 1 = 87 \geq 85 \). - Abu Waleed Tea

Rund auf \( y = 1 \): Festigkeit = \( 10 \times 8 + 7 \times 1 = 87 \geq 85 \). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{35 \cdot 36}{4368} = \frac{1260}{4368}

📌 \frac{1260}{4368} = \frac{105}{364}

📌 Thus, the probability is $\boxed{\frac{105}{364}}$.

📌 Question: How many 8-digit positive integers composed only of the digits 3 and 4 contain at least one instance of two consecutive 3s?

📌 Solution: First, compute the total number of 8-digit numbers using only digits 3 and 4:

📌 Now count the number of such numbers that do **not** contain two consecutive 3s. Let $a_n$ be the number of valid sequences of length $n$ with no two consecutive 3s, where each digit is 3 or 4.

📌 We define a recurrence:

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We will compute the terms of the sequence step-by-step using the recur...
\(a_1 = 1\)
\(a_2 = 2a_1 + 3 = 2(1) + 3 = 2 + 3 = 5\)
\(a_3 = 2a_2 + 3 = 2(5) + 3 = 10 + 3 = 13\)
\(a_4 = 2a_3 + 3 = 2(13) + 3 = 26 + 3 = 29\)
Therefore, the value of \(a_4\) is:
Question:** In a futuristic navigation system, the position of a space...
To find when \(x(t) = y(t)\), set the expressions equal:
5t^2 + 3t + 2 = 2t^2 + 7t + 1
Subtract \(2t^2 + 7t + 1\) from both sides:

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