Algebra.Com's Answer #852367 by ikleyn(52879)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observations
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document.write( "then the combined HM is given by
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document.write( "As the answer given is : 70.36
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document.write( " The answer 70.36, to which you refer, is INCORRECT.\r
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document.write( " The solution by @Theo is INCORRECT, too.\r
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document.write( " See my solution below.\r
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document.write( "According to the problem, we have a set of 15 numbers  ,  , . . . ,  \r\n" );
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document.write( "and the set of 13 numbers  ,  , . . . ,  such that\r\n" );
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document.write( "  =  +  + . . . +  , (1)\r\n" );
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document.write( "  =  +  + . . . +  . (2)\r\n" );
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document.write( "We want to find the harmonic mean H of the union set <  > U <  >.\r\n" );
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document.write( "It is \r\n" );
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document.write( "  = + + . . . + + + + . . . + . (3)\r\n" );
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document.write( "We represent this long sum as the sum of two addends in parentheses\r\n" );
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document.write( " = ( + + . . . + ) + ( + + . . . + ).\r\n" );
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document.write( "Next, we replace each of the two sums in parentheses by their values from (1) and (2)\r\n" );
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document.write( " = + ,\r\n" );
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document.write( "and calculate\r\n" );
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document.write( " =  =  =  \r\n" );
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document.write( "Now find \r\n" );
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document.write( " H =  =  = 14*5 = 70.\r\n" );
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document.write( "ANSWER. The combined harmonic mean is 70.\r\n" );
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document.write( "At this point, the problem is solved completely.\r
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document.write( "The answer 70.36, to which you refer, is INCORRECT.\r
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document.write( "The solution by @Theo is INCORRECT, too.\r
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