document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029790>Question 1029790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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. \r<BR>\n" );
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document.write( "Answer:0.4727\r<BR>\n" );
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document.write( "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!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644724 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52834)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "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 <BR>\n" );
document.write( "consisting of the sum of the 28 original line segments. A point is picked at random on the line segment that was formed. <BR>\n" );
document.write( "Find the probability that the point that was picked was a point on one of the original face diagonals. <BR>\n" );
document.write( "Express your answer as a decimal rounded to the nearest ten-thousandth. \r<BR>\n" );
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document.write( "Answer:0.4727\r<BR>\n" );
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document.write( "So, I can visualize what is being asked; however, I was tripped up with the probability of the whole line segment/face diagonal. <BR>\n" );
document.write( "Could you please explain? Your help is most sincerely appreciated!!! Thank you so much!!!<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "1. Let \"a\" be the length of the cube edge.\r\n" );
document.write( "   Then the length of the face diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"a%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "   The length of the \"true 3D\" diagonal is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"a%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "2. The length of the entire long segment consisting of all 28 elements is \r\n" );
document.write( "   \r\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a+%2B+12%2Asqrt%282%29+%2B+4a%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"12a+%2B+12%2Asqrt%282%29+%2B+4a%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2A%2812+%2B+12%2Asqrt%282%29+%2B+4%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"a%2A%2812+%2B+12%2Asqrt%282%29+%2B+4%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.     (1)\r\n" );
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document.write( "3. The length of 12 face diagonals is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12a%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"12a%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   (2)\r\n" );
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document.write( "4. The probability you are asked for is the ratio (2) to (1), which is \r\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2Asqrt%282%29%29%2F%2812+%2B+12%2Asqrt%282%29+%2B+4%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%2812%2Asqrt%282%29%29%2F%2812+%2B+12%2Asqrt%282%29+%2B+4%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.4727.\r\n" );
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