document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164085>Question 1164085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Logic: Set and operations - Cardinal numbers and surveys\r<BR>\n" );
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document.write( "A director of Financial Aid for a small university inspected the records of 100 students and found the following:\r<BR>\n" );
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document.write( "49 receive government scholarships, <BR>\n" );
document.write( "55 receive private scholarships, <BR>\n" );
document.write( "43 receive college aid, <BR>\n" );
document.write( "23 receive government scholarships and private scholarships, <BR>\n" );
document.write( "18 receive scholarships. government and university aid, <BR>\n" );
document.write( "28 receive private scholarships and university aid, <BR>\n" );
document.write( "8 receive aid from all three sources.\r<BR>\n" );
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document.write( "a-How many of the students in the survey have only government scholarships?\r<BR>\n" );
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document.write( "b-How many of the students in the survey have a private scholarship but not a government scholarship?\r<BR>\n" );
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document.write( "c-How many of the students in the survey receive financial aid from only one of these sources?\r<BR>\n" );
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document.write( "d-How many of the students in the survey receive help from exactly two sources?\r<BR>\n" );
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document.write( "e-How many of the students in the survey do not receive financial aid from any of these sources?\r<BR>\n" );
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document.write( "f-How many of the students in the survey do not receive financial aid from the university or the government? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789233 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If Venn diagrams are drawn,<BR>\n" );
document.write( "16 are government only<BR>\n" );
document.write( "of the 18 that are government and college, 10 are just those two; the other 8 are all three (center of the diagram)<BR>\n" );
document.write( "of the 23 that are government and private, 15 are just those two; the other eight are all 3. <BR>\n" );
document.write( "16+10+15+8=49\r<BR>\n" );
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document.write( "Private is 55.<BR>\n" );
document.write( "12 are only, 15 and 8 are shared with government and all three, and 20 more shared with college. <BR>\n" );
document.write( "of the 28 that are private and college, 20 are just those two, for again, the other 8 are all three.\r<BR>\n" );
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document.write( "College is 43<BR>\n" );
document.write( "5 are college alone, 8 are all 3, 20 shared with private alone and 10 shared with government alone.\r<BR>\n" );
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document.write( "The sum of the seven different containers ,A, B, C, AB, AC, BC, and ABC, is 86.\r<BR>\n" );
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document.write( "Therefore, the answer to e, those who don't receive any from these sources, is 100-86 or 14.\r<BR>\n" );
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document.write( "a. is 16<BR>\n" );
document.write( "b. is 32 private alone + private/college<BR>\n" );
document.write( "c.from only one of these sources is 16+12+5=33<BR>\n" );
document.write( "d. from exactly two sources is 10+15+20=45<BR>\n" );
document.write( "f.this is how many are private alone, and that is 12.<BR>\n" );
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