To find the probability that a random point placed in the rectangle is not inside the circle or the square, we'll follow these steps:
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Calculate the area of the rectangle: \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 21 , \text{inches} \times 19 , \text{inches} = 399 , \text{square inches} \]
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Calculate the area of the circle: Given the radius \( r = 4 \) inches, \[ \text{Area}_{\text{circle}} = \pi r^2 = \pi (4^2) = 16\pi \approx 50.27 , \text{square inches} \quad (\text{using } \pi \approx 3.14) \]
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Calculate the area of the square: The side length of the square is \( s = 8 \) inches, \[ \text{Area}_{\text{square}} = s^2 = 8^2 = 64 , \text{square inches} \]
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Calculate the total area occupied by the circle and square: \[ \text{Area}{\text{occupied}} = \text{Area}{\text{circle}} + \text{Area}_{\text{square}} \approx 50.27 + 64 = 114.27 , \text{square inches} \]
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Calculate the area not occupied by the circle or square: \[ \text{Area}{\text{not occupied}} = \text{Area}{\text{rectangle}} - \text{Area}_{\text{occupied}} \approx 399 - 114.27 \approx 284.73 , \text{square inches} \]
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Calculate the probability that a random point is not inside the circle or the square: \[ \text{Probability} = \frac{\text{Area}{\text{not occupied}}}{\text{Area}{\text{rectangle}}} \approx \frac{284.73}{399} \approx 0.713 \]
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Round this value to the nearest hundredth: \[ 0.713 \text{ rounds to } 0.71 \]
Thus, the probability that a random point placed in the figure is not inside the circle or inside the square is \( \boxed{0.71} \).