document.write( "Question 1040348: 1.Two dice are rolled. What is the probability that the sum of the outcome is
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Algebra.Com's Answer #655169 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
1.Two dice are rolled.
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document.write( "Here are all 36 possible outcomes when two dice are rolled:\r\n" );
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document.write( "(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)\r\n" );
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document.write( "(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)\r\n" );
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document.write( "(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)\r\n" );
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document.write( "(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)\r\n" );
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document.write( "(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)\r\n" );
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document.write( "(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)  \r\n" );
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\n" ); document.write( "What is the probability that the sum of the outcome is
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document.write( "Let's color the ones red that have sum 5:\r\n" );
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document.write( "(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)\r\n" );
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document.write( "(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)\r\n" );
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document.write( "(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)\r\n" );
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document.write( "(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)\r\n" );
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document.write( "(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)\r\n" );
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document.write( "(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)    \r\n" );
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document.write( "I count 4.  Therefore the probability is \"4 times out of 36\" or \"4%2F36\".\r\n" );
document.write( "That reduces to \"1%2F9\"\r\n" );
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\n" ); document.write( "b.at least 11?
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document.write( "Let's color the ones red that have sum of at least 11:\r\n" );
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document.write( "(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)\r\n" );
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document.write( "(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)\r\n" );
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document.write( "(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)\r\n" );
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document.write( "(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)\r\n" );
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document.write( "(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)\r\n" );
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document.write( "(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)\r\n" );
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document.write( "I count 3.  Therefore the probability is \"3 times out of 36\" or \"3%2F36\".\r\n" );
document.write( "That reduces to \"1%2F12\"\r\n" );
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\n" ); document.write( "c.less than 4?
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document.write( "Let's color the ones red that have sum less than 4:\r\n" );
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document.write( "(1,1)  (1,2)  (1,3)  (1,4)  (1,5)  (1,6)\r\n" );
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document.write( "(2,1)  (2,2)  (2,3)  (2,4)  (2,5)  (2,6)\r\n" );
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document.write( "(3,1)  (3,2)  (3,3)  (3,4)  (3,5)  (3,6)\r\n" );
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document.write( "(4,1)  (4,2)  (4,3)  (4,4)  (4,5)  (4,6)\r\n" );
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document.write( "(5,1)  (5,2)  (5,3)  (5,4)  (5,5)  (5,6)\r\n" );
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document.write( "(6,1)  (6,2)  (6,3)  (6,4)  (6,5)  (6,6)  \r\n" );
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document.write( "I count 3.  Therefore the probability is \"3 times out of 36\" or \"3%2F36\".\r\n" );
document.write( "That reduces to \"1%2F12\"\r\n" );
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document.write( "2. Find the point on the graph of f(x)=x^2+4x-3 where the tangent line is horizontal.\r\n" );
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document.write( "The horizontal line through the vertex would be tangent at the\r\n" );
document.write( "vertex, drawn in green below.\r\n" );
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document.write( "We use the vertex formula:\r\n" );
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document.write( "The x-coordinate of the vertex of f(x) = ax²+bx+c is \"-b%2F%282a%29\"\r\n" );
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document.write( "So the x-coordinate of the vertex of f(x) = x²+4x-3 is \"-4%2F%282%2A1%29\" = -2.\r\n" );
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document.write( "The y-coordinate is found by substituting the x-coordinate of the\r\n" );
document.write( "vertex in f(x) = x²+4x-3\r\n" );
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document.write( "f(2) = (-2)²+4∙(-2)-3 = 4-8-3 = -7\r\n" );
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document.write( "So the point on the graph of f(x)=x²+4x-3 where the tangent line is \r\n" );
document.write( "horizontal is the vertex (-2,-7). \r\n" );
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document.write( "Edwin
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