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Exactly two of the four rolls to be prime - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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🔥 Popular Posts

The \( n \)-th term is given by \( a_n = a + (n-1)d \).
Use \( n = 15 \): \( a_{15} = 3 + (15-1) \times 4 \).
Simplify: \( a_{15} = 3 + 14 \times 4 = 3 + 56 = 59 \).
Therefore, the 15th term is 59.
#### 59
The ratio of the number of apples to oranges in a basket is 5:3. If th...
Let the number of oranges be \( x \). The ratio equation is \( \frac{4...
Cross-multiply: \( 5x = 3 \times 40 \).
Solve for \( x \): \( 5x = 120 \).
Divide by 5: \( x = 24 \).

📝 Recent Posts

5Question: Let \( a, b, c \) be positive real numbers such that \( a +...
Solution: We are given \( a + b + c = 1 \) with \( a, b, c > 0 \), so...
\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b}
This is a well-known inequality in symmetric form. By the **Nesbitt’s...
\frac{a}{b + c} + \frac{b}{a + c} + \frac{c}{a + b} \geq \frac{3}{2}
with equality if and only if \( a = b = c \). Since \( a + b + c = 1 \...
\frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}}...
So the sum is \( 3 \cdot \frac{1}{2} = \frac{3}{2} \).
Thus, the minimum value is \( \boxed{\frac{3}{2}} \).
Question: Compute \( \sum_{n=1}^{50} \frac{1}{\sqrt{n} + \sqrt{n+1}} \...

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