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Home » \( r = 0.05 \) (سعر الفائدة السنوي)، - wispro

\( r = 0.05 \) (سعر الفائدة السنوي)، - wispro

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The equation of a circle is \( (x - 3)^2 + (y + 2)^2 = 25 \). Find the center and radius of the circle.

📌 The standard form of a circle's equation is \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.

📌 Comparing, \( h = 3 \), \( k = -2 \), and \( r^2 = 25 \).

📌 Thus, the center is \( (3, -2) \) and the radius \( r = \sqrt{25} = 5 \).

📌 #### Center: (3, -2), Radius: 5

📌 A geometric series has a first term of 3 and a common ratio of 2. Find the sum of the first 5 terms.

📌 The sum \( S_n \) of the first \( n \) terms of a geometric series is given by:

📌 where \( a = 3 \), \( r = 2 \), and \( n = 5 \).

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Choose 2 positions for primes: $ \binom{4}{2} = 6 $
Assign (2,2) to them: 1 way
Assign (4 or 6, 4 or 6, 4 or 6, 4 or 6) to non-primes: $ 3 \times 3 =...
We need the two non-prime rolls to both be even → 2 choices each → $ 2...
Odd contributions only matter if we have odd primes, but here none → a...
So for Case 1:
6 position choices
1 prime assignment (2,2)
4 non-prime even pairs
→ $ 6 \times 1 \times 4 = 24 $ sequences

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