To find the probability that a dart thrown at a square lands within the inscribed circle (the dartboard), we can use the areas of the circle and the square.
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Area of the Circle: The area of the circle is given as: \[ A_{\text{circle}} = 25\pi \text{ square units} \]
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Area of the Square: The area of the square is given as: \[ A_{\text{square}} = 100 \text{ square units} \]
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Probability Calculation: The probability \( P \) that the dart lands within the circle is the ratio of the area of the circle to the area of the square: \[ P = \frac{A_{\text{circle}}}{A_{\text{square}}} \]
Substituting the areas: \[ P = \frac{25\pi}{100} \]
Simplifying this expression: \[ P = \frac{25\pi}{100} = \frac{\pi}{4} \]
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Numerical Value: To find the probability in numerical form, we approximate \( \pi \): \[ P \approx \frac{3.14}{4} \approx 0.785 \]
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Percentage Conversion: Convert this probability into a percentage: \[ P \times 100 \approx 0.785 \times 100 \approx 78.5% \]
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Rounding: Rounding to the nearest tenth of a percent gives us: \[ \text{Probability} \approx 78.5% \]
Thus, the final answer is: \[ \boxed{78.5%} \]