document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95587>Question 95587</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131250892/algebrahomeworkh>Prentice Hall Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my grandson with his Algebra homework.  I guess I have forgotten much of what I knew at one time.  I appreciate any help you can give me on this problem.\r<BR>\n" );
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document.write( "Suppose that a dart lands at random on the dartboard shown at the right.  Find each theoretical probablility.<BR>\n" );
document.write( "17.  The dart lands in the bull's eye<BR>\n" );
document.write( "18.  The dart lands in a green region<BR>\n" );
document.write( "19.  The dart scores at least 10 points<BR>\n" );
document.write( "20.  The dart scores less than 10 points.\r<BR>\n" );
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document.write( "The dart board shows:  r= 1.5 in          Width of each ring = 1.5 in.<BR>\n" );
document.write( "Bulls eye is 20 points, next ring is 10 points, next 5 points, outside ring 2 points.  \r<BR>\n" );
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document.write( "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 #69630 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=69630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that a dart lands at random on the dartboard shown at the right.  Find each theoretical probablility.<BR>\n" );
document.write( "17.  The dart lands in the bull's eye<BR>\n" );
document.write( "18.  The dart lands in a green region<BR>\n" );
document.write( "19.  The dart scores at least 10 points<BR>\n" );
document.write( "20.  The dart scores less than 10 points.\r<BR>\n" );
document.write( "\n" );
document.write( "The dart board shows:  r= 1.5 in          Width of each ring = 1.5 in.<BR>\n" );
document.write( "Bulls eye is 20 points, next ring is 10 points, next 5 points, outside ring 2 points.  \r<BR>\n" );
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document.write( "To find the theoretical probabilities  it is necessary to determine<BR>\n" );
document.write( "the area of of the center, each ring and the whole board.<BR>\n" );
document.write( "For example:<BR>\n" );
document.write( "If I read your dimensions correctly, the radius of the board is 6 inches<BR>\n" );
document.write( "The total area of the board is 6^2pi  = 36pi sq. in.<BR>\n" );
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document.write( "Area of the \"2\" ring is 6^2pi-4.5^2pi = (36-20.25)pi = 15.75pi sq. in.<BR>\n" );
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document.write( "Area of the \"5\" ring is 4.5^2pi - 3^2pi = (20.25-9)pi = 11.25pi sq in<BR>\n" );
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document.write( "Area of the 10 ring is 3^2pi-1.5^2pi = (9-2.25)pi = 6.75pi sq in<BR>\n" );
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document.write( "Area of the bull's eye = 1.5^2pi = 2.25pi sq. in.<BR>\n" );
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document.write( "Now you can figure out the probabilities:<BR>\n" );
document.write( "17.  The dart lands in the bull's eye<BR>\n" );
document.write( "P(bull's eye) = 2.25pi/36pi = 0.0625<BR>\n" );
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document.write( "18.  The dart lands in a green region<BR>\n" );
document.write( "I don't know what the green region area is.<BR>\n" );
document.write( "Figure that out and divide by 36pi sq in<BR>\n" );
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document.write( "19.  The dart scores at least 10 points<BR>\n" );
document.write( "P(10 area) = 6.75pi/36pi= 0.1875<BR>\n" );
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document.write( "20.  The dart scores less than 10 points.<BR>\n" );
document.write( "P(less than 10) = (2 area + 5 area)/36pi = (15.75+11.25)pi/36pi = 27pi/36pi<BR>\n" );
document.write( "= 0.75<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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