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Home » Now, calculate the area using the formula: - 500apps

Now, calculate the area using the formula: - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 There are 101 total years (from 1800 to 1900 inclusive).

📌 So the probability that a single randomly chosen year is divisible by 4 is:

📌 \frac{26}{101}

📌 Since the selections are independent, the probability that all three years are divisible by 4 is:

📌 \left( \frac{26}{101} \right)^3 = \frac{17576}{1030301}

📌 \boxed{\frac{17576}{1030301}}

📌 Question: A historian is analyzing three randomly selected scientific papers from a collection of 12, where 5 are written by Newton and 7 by Leibniz. What is the probability that exactly two of the selected papers are by Newton?

📌 Solution: The total number of ways to choose 3 papers from 12 is:

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Solve for \( x \) in the equation \( 4x^2 - 12x + 9 = 0 \).
This is a quadratic equation, which can be factored as:
Recognize it as a perfect square: \( (2x - 3)^2 = 0 \).
Solve for \( x \): \( 2x - 3 = 0 \).
Add 3: \( 2x = 3 \).
Divide by 2: \( x = \frac{3}{2} \).
Therefore, the solution is \( x = \frac{3}{2} \).
#### \(\frac{3}{2}\)
A circle has a circumference of 31.4 meters. What is the radius of the...
Set up the equation: \( 31.4 = 2 \times 3.14 \times r \).

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