To find the probability that a point placed randomly in the figure is not inside the square, we can follow these steps:
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Calculate the area of the rectangle. \[ \text{Area of the rectangle} = \text{length} \times \text{width} = 22 , \text{inches} \times 17 , \text{inches} = 374 , \text{square inches} \]
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Calculate the area of the square. The side length of the square is 12 inches. \[ \text{Area of the square} = \text{side}^2 = 12^2 = 144 , \text{square inches} \]
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Calculate the area of the circle. The radius of the circle is 2 inches. \[ \text{Area of the circle} = \pi r^2 = \pi (2^2) = \pi \cdot 4 \approx 12.57 , \text{square inches} \]
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Calculate the total area covered by the square and circle. \[ \text{Total area of circle and square} = \text{Area of square} + \text{Area of circle} = 144 + 12.57 \approx 156.57 , \text{square inches} \]
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Calculate the area that is NOT covered by the square. \[ \text{Area not in square} = \text{Total area of rectangle} - \text{Area of square} = 374 - 144 = 230 , \text{square inches} \]
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Calculate the probability that a point is not in the square. \[ \text{Probability} = \frac{\text{Area not in square}}{\text{Area of rectangle}} = \frac{230}{374} \approx 0.615 \]
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Round to the nearest hundredth. \[ \text{Rounded probability} \approx 0.62 \]
However, we need the probability to reflect only the area in the rectangle excluding the square (including the circle). Thus:
\[ \text{Probability that a point is not in the square} = 1 - \frac{\text{Area of square}}{\text{Area of rectangle}} = 1 - \frac{144}{374} \approx 0.617 \]
Rounding to the nearest hundredth gives:
\[ \text{Rounded probability} \approx 0.62 \]
Based on the provided responses, the answer closest to this calculation is 0.61.