document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195435>Question 1195435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vitrivius, a Roman architect of the first century BCE, set guidelines in his writings for the relationship between the height (rise) and tread (run) of stairs in a building. He wrote that the rise should be between 9 and 10 inches, inclusive, per step, and the run should be between 18 and 24 inches, inclusive. Which of the following could NOT be the ratio of rise to run for a set of stairs that follows this guideline?<BR>\n" );
document.write( "A) 1/3<BR>\n" );
document.write( "B) 5/12<BR>\n" );
document.write( "C) 3/8<BR>\n" );
document.write( "D) 5/9<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827915 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "rise = change in height<BR>\n" );
document.write( "run = change in horizontal direction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+rise%2Frun ALIGN=MIDDLE  ALT=\"slope+=+rise%2Frun\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%3C=+rise+%3C=+10 ALIGN=MIDDLE  ALT=\"9+%3C=+rise+%3C=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%3C=+run+%3C=+24 ALIGN=MIDDLE  ALT=\"18+%3C=+run+%3C=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To get the smallest slope possible, we divide the smallest rise over the largest run.<BR>\n" );
document.write( "We divide rise = 9 over run = 24 to get the smallest slope.<BR>\n" );
document.write( "Recall that A/B is smallest when we minimize A and maximize B. Both are positive values. \r<BR>\n" );
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document.write( "P = smallest slope<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+9%2F24 ALIGN=MIDDLE  ALT=\"P+=+9%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+%283%2A3%29%2F%283%2A8%29 ALIGN=MIDDLE  ALT=\"P+=+%283%2A3%29%2F%283%2A8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+3%2F8 ALIGN=MIDDLE  ALT=\"P+=+3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In contrast, the largest slope occurs when we go for the largest rise and smallest run<BR>\n" );
document.write( "Q = largest slope<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+10%2F18 ALIGN=MIDDLE  ALT=\"Q+=+10%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+%282%2A5%29%2F%282%2A9%29 ALIGN=MIDDLE  ALT=\"Q+=+%282%2A5%29%2F%282%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+5%2F9 ALIGN=MIDDLE  ALT=\"Q+=+5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore we can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+%3C=+slope+%3C=+Q ALIGN=MIDDLE  ALT=\"P+%3C=+slope+%3C=+Q\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8+%3C=+slope+%3C=+5%2F9 ALIGN=MIDDLE  ALT=\"3%2F8+%3C=+slope+%3C=+5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Convert each slope to decimal form<BR>\n" );
document.write( "3/8 = 0.375<BR>\n" );
document.write( "5/9 = 0.556 approximately\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F8+%3C=+slope+%3C=+5%2F9 ALIGN=MIDDLE  ALT=\"3%2F8+%3C=+slope+%3C=+5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.375+%3C=+slope+%3C=+0.556 ALIGN=MIDDLE  ALT=\"0.375+%3C=+slope+%3C=+0.556\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can see that choices C and D can be ruled out because they are the endpoints mentioned earlier. \r<BR>\n" );
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document.write( "Choice B) 5/12 converts to the approximate decimal form of 0.417 and it is between those endpoints mentioned above. So we can rule out choice B\r<BR>\n" );
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document.write( "Choice A) 1/3 = 0.333 approximately is NOT between 3/8 = 0.375 and 5/9 = 0.556<BR>\n" );
document.write( "The slope mentioned for choice A is too small, aka too shallow.\r<BR>\n" );
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document.write( "Answer: <font color=red>Choice A) 1/3</font><BR>\n" );
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