document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198452>Question 1198452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information: \r<BR>\n" );
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document.write( "- 347 are taking a Math course<BR>\n" );
document.write( "- 343 are taking a English course<BR>\n" );
document.write( "- 39 are taking both a Science and a English course<BR>\n" );
document.write( "- 8 are taking a Math course, a Science course, and a English course<BR>\n" );
document.write( "- 65 are taking both a Math and a English course<BR>\n" );
document.write( "- 758 are taking a Science course or a English course<BR>\n" );
document.write( "- 221 are taking a Math course but not a Science course nor a English course\r<BR>\n" );
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document.write( "a.) use the information listed to complete a three-circle venn diagram M,E,and S.\r<BR>\n" );
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document.write( "b.) using the results from the venn diagram in question a.), determine how many students:\r<BR>\n" );
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document.write( "i.) are taking a science course:<BR>\n" );
document.write( "ii.) are taking an English course but not a Math course: <BR>\n" );
document.write( "iii.) are not taking a Math course<BR>\n" );
document.write( "iv.) are taking at least two of the types of courses (Math, English and Science):  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832210 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information: \r<BR>\n" );
document.write( "\n" );
document.write( "- 347 are taking a Math course<BR>\n" );
document.write( "- 343 are taking a English course<BR>\n" );
document.write( "- 39 are taking both a Science and a English course<BR>\n" );
document.write( "- 8 are taking a Math course, a Science course, and a English course<BR>\n" );
document.write( "- 65 are taking both a Math and a English course<BR>\n" );
document.write( "- 758 are taking a Science course or a English course<BR>\n" );
document.write( "- 221 are taking a Math course but not a Science course nor a English course\r<BR>\n" );
document.write( "\n" );
document.write( "a.) use the information listed to complete a three-circle venn diagram M,E,and S.\r<BR>\n" );
document.write( "\n" );
document.write( "b.) using the results from the venn diagram in question a.), determine how many students:\r<BR>\n" );
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document.write( "i.) are taking a science course:<BR>\n" );
document.write( "ii.) are taking an English course but not a Math course: <BR>\n" );
document.write( "iii.) are not taking a Math course<BR>\n" );
document.write( "iv.) are taking at least two of the types of courses (Math, English and Science)<BR>\n" );
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;\">As requested, numbers that are taking math, science, and english are M, S, and E, respectively\r\n" );
document.write( "We find that number that take:	math only, is: M, only\r\n" );
document.write( "				science only, is: S, only\r\n" );
document.write( "				english only, is: E, only\r\n" );
document.write( "					\r\n" );
document.write( "				math and science, only, is: M&S\r\n" );
document.write( "				math and english, only, is: M&E\r\n" );
document.write( "\r\n" );
document.write( "				science and english, only, is: S&E\r\n" );
document.write( "				math, science, and english, is: M&S&E\r\n" );
document.write( "					\r\n" );
document.write( "The VENN DIAGRAM below has been labeled as such.\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=MathTherapy&illustration_name=ADC_1198452.png\">.\r\n" );
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document.write( "M   = M, only + M&E + M&S&E + M&S\r\n" );
document.write( "347 = 221 + 57 + 8 + M&S ------ Substituting 347 for M, 221 for M, only, 57 for M&E, and 8 for M&S&E\r\n" );
document.write( "347 = 286 + M&S\r\n" );
document.write( "347 - 286 = M&S\r\n" );
document.write( "61 = M&S\r\n" );
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document.write( "E = 343, so E, only += 343 - (31 + 8 + 57) = 343 - 96 = 247\r\n" );
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document.write( "S or E = S, only + S&E + E, only + M&S&E + M&S + M&E\r\n" );
document.write( "   758 = S, only + 31  +   247   +   8   +  61 + 57 \r\n" );
document.write( "   758 = S, only + 404\r\n" );
document.write( "758 - 404 = S, only\r\n" );
document.write( "      354 = S, only\r\n" );
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document.write( "We now get the following VENN DIAGRAM with all variables’ values entered\r\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=MathTherapy&illustration_name=ADC_1198452_21.png\">.\r\n" );
document.write( "I’ll start you off with: How many i.) are taking a science course:\r\n" );
document.write( "                                               S = S, only + S&E + M&S&E + M&S \r\n" );
document.write( "S, or number of students taking a science course =   354   + 31  +   8   +  61 = <font color = red><font size = 4><b>454</font></font></b></PRE> </SPAN>\n" );
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