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08 Jan 2023, 08:27
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C
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48% (02:32) correct
52%
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The vertices of rectangle ABCD are (12,5), (-12,5), (-12,-5) and (12,-5). What is the approximate probability that the coordinate of a random point within the rectangle is such that x^2 + y^2 < 25?
A. 12.5%
B. 25%
C. 33%
D. 40%
E. 50%
A. 12.5%
B. 25%
C. 33%
D. 40%
E. 50%
08 Jan 2023, 09:23
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Bunuel
\( x^2 + y^2 = 25\) represents a circle with radius 5 and center at (0,0).
We can plot the rectangle ABCD as shown.
Probability = Area of Favorable Region / Area of Total Region
Required Probability = \(\frac{\pi * (5)^2 }{ 24 * 10} * 100\)
We can approximate the value to ease out the simplification.
Approx. 33%
Option C
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16 Jun 2024, 05:30
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Given: The vertices of rectangle ABCD are (12,5), (-12,5), (-12,-5) and (12,-5).
Asked: What is the approximate probability that the coordinate of a random point within the rectangle is such that x^2 + y^2 < 25?
Area of rectangle ABCD = 24*10 = 240
Random point lies within a circle with center at origin (0,0) and radium = 5
Area of circle that lies completely within rectangle ABCD = \(\pi 5^2 = 25\pi\)
The approximate probability that the coordinate of a random point within the rectangle is such that x^2 + y^2 < 25 =\( 25\pi/240 = 25*22/7*240 = .3273 = 32.73% = 33%\)
IMO C
Asked: What is the approximate probability that the coordinate of a random point within the rectangle is such that x^2 + y^2 < 25?
Area of rectangle ABCD = 24*10 = 240
Random point lies within a circle with center at origin (0,0) and radium = 5
Area of circle that lies completely within rectangle ABCD = \(\pi 5^2 = 25\pi\)
The approximate probability that the coordinate of a random point within the rectangle is such that x^2 + y^2 < 25 =\( 25\pi/240 = 25*22/7*240 = .3273 = 32.73% = 33%\)
IMO C
