document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203687>Question 1203687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> X: 8,9,10,11,12,13,14<BR>\n" );
document.write( "Y: 1,2,3,4,5,6,7\r<BR>\n" );
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document.write( "1. ∑X ∑Y<BR>\n" );
document.write( "2. ∑X²Y<BR>\n" );
document.write( "3. 3∑(x+y) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839459 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=839459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Tutor @mananth is mostly correct.\r<BR>\n" );
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document.write( "The only mistake is ∑(X²Y)= 875*28 is false\r<BR>\n" );
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document.write( "We cannot say  ∑(X²Y) = ∑X²*∑Y because ∑(A*B) = ∑A*∑B isn't true.\r<BR>\n" );
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document.write( "Consider the small sets<BR>\n" );
document.write( "A = {1,2,3}<BR>\n" );
document.write( "B = {4,5,6}\r<BR>\n" );
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document.write( "They have these sums<BR>\n" );
document.write( "∑A = 1+2+3 = 6<BR>\n" );
document.write( "∑B = 4+5+6 = 15\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "C = A*B = pairwise multiplication<BR>\n" );
document.write( "C = {1*4, 2*5, 3*6}<BR>\n" );
document.write( "C = {4,10,18}<BR>\n" );
document.write( "∑C = 4+10+18 = 32<BR>\n" );
document.write( "But,<BR>\n" );
document.write( "∑A*∑B = 6*15 = 90<BR>\n" );
document.write( "which does not match with ∑C = 32\r<BR>\n" );
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document.write( "This is one counter-example to show why ∑A*∑B = ∑(A*B) is false.\r<BR>\n" );
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document.write( "This is how I would compute ∑(X²Y)<BR>\n" );
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document.write( "<tr><TD >x</TD><TD >y</TD><TD >x^2</TD><TD >x^2y</TD></tr><tr><TD >8</TD><TD >1</TD><TD >64</TD><TD >64</TD></tr><tr><TD >9</TD><TD >2</TD><TD >81</TD><TD >162</TD></tr><tr><TD >10</TD><TD >3</TD><TD >100</TD><TD >300</TD></tr><tr><TD >11</TD><TD >4</TD><TD >121</TD><TD >484</TD></tr><tr><TD >12</TD><TD >5</TD><TD >144</TD><TD >720</TD></tr><tr><TD >13</TD><TD >6</TD><TD >169</TD><TD >1014</TD></tr><tr><TD >14</TD><TD >7</TD><TD >196</TD><TD >1372</TD></tr>\n" );
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document.write( "I recommend using a spreadsheet.<BR>\n" );
document.write( "Then we sum the items in the X²Y column:<BR>\n" );
document.write( "64 + 162 + 300 + 484 + 720 + 1014 + 1372 = <font color=red>4116</font><BR>\n" );
document.write( "This value is not equal to the result of 875*28.\r<BR>\n" );
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document.write( "Therefore, ∑(X²Y) = <font color=red>4116</font><BR>\n" );
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