SOLUTION: A cube has 12 edges, 12 face diagonals, and 4 diagonals. These 28 objects are placed end to end to form a single line segment consisting of the sum of the 28 original line segments

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Question 1029790: A cube has 12 edges, 12 face diagonals, and 4 diagonals. These 28 objects are placed end to end to form a single line segment consisting of the sum of the 28 original line segments. A point is picked at random on the line segment that was formed. Find the probability that the point that was picked was a point on one of the original face diagonals. Express your answer as a decimal rounded to the nearest ten-thousandth.
Answer:0.4727
So, I can visualize what is being asked; however, I was tripped up with the probability of the whole line segment/face diagonal. Could you please explain? Your help is most sincerely appreciated!!! Thank you so much!!!
Answer by ikleyn(52817) (Show Source):
You can put this solution on YOUR website!
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A cube has 12 edges, 12 face diagonals, and 4 diagonals. These 28 objects are placed end to end to form a single line segment
consisting of the sum of the 28 original line segments. A point is picked at random on the line segment that was formed.
Find the probability that the point that was picked was a point on one of the original face diagonals.
Express your answer as a decimal rounded to the nearest ten-thousandth.
Answer:0.4727
So, I can visualize what is being asked; however, I was tripped up with the probability of the whole line segment/face diagonal.
Could you please explain? Your help is most sincerely appreciated!!! Thank you so much!!!
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1. Let "a" be the length of the cube edge. Then the length of the face diagonal is . The length of the "true 3D" diagonal is . 2. The length of the entire long segment consisting of all 28 elements is = . (1) 3. The length of 12 face diagonals is . (2) 4. The probability you are asked for is the ratio (2) to (1), which is = 0.4727.