document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072012>Question 1072012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here's a math problem that I have and do not know how to do at all:<BR>\n" );
document.write( "Suppose A and B are single digit positive integers chosen independently and at random. What is the probability that the point (a,b) lies above the parable y=ax^2-bx? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #686922 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=686922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28a%5E2%29-ba ALIGN=MIDDLE  ALT=\"y=a%28a%5E2%29-ba\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%5E3-ba ALIGN=MIDDLE  ALT=\"y=a%5E3-ba\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=b ALIGN=MIDDLE  ALT=\"y=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=a%5E3-ba ALIGN=MIDDLE  ALT=\"b=a%5E3-ba\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bba=a%5E3 ALIGN=MIDDLE  ALT=\"b%2Bba=a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%281%2Ba%29=a%5E3 ALIGN=MIDDLE  ALT=\"b%281%2Ba%29=a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=a%5E3%2F%281%2Ba%29 ALIGN=MIDDLE  ALT=\"b=a%5E3%2F%281%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3E%28a%5E3%2F%281%2Ba%29%29 ALIGN=MIDDLE  ALT=\"b%3E%28a%5E3%2F%281%2Ba%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the point is above the curve and if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3C%28a%5E3%2F%281%2Ba%29%29 ALIGN=MIDDLE  ALT=\"b%3C%28a%5E3%2F%281%2Ba%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the point is below the curve.<BR>\n" );
document.write( "So you can make a chart (I used EXCEL),<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=fr4.JPG\">.<BR>\n" );
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document.write( "I cut it off because all remaining points show FALSE, (a,b) is below the curve.<BR>\n" );
document.write( "So there are 81 possible outcomes, 19 of them have the point above the curve,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=19%2F81 ALIGN=MIDDLE  ALT=\"P=19%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A couple of data points shown with their accompanying graphs,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=fr5.JPG\">.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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