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From 1997 through 2004, the value of US exports to Mexico was as shown below. Data are in billions of dollars.
Year: 1997 1998 1999 2000
Exports: $71.4 $78.8 $86.9 $111.3
Year: 2001 2002 2003 2004
Exports: $101.3 $97.5 $97.4 $110.8
a. Fit a linear trend equation to the time series. Using this equation, determine the trend estimate for 2012.
b. Fit a quadratic equation to the time series, then use the equation to determine the trend estimate for 2012.
c. Construct a graph of the time series along with the equations fitted in parts (a) and (b). Which equation appears to better fit the data?
The length of a rectangular swimming pool is 2x - 1 meters, and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5).
Solving the expression.
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In solving an equation involving radicals, it is sometimes necessary to square each side of the equation. But doing this can introduce extraneous roots, which do not satisfy the original equation.
Use the previous fact to show that Fermat's equation x^n + y^n = z^n has no integer solutions when n>/= 2 is even and both x and y are odd,
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Using mathematical induction, prove or disprove that all checkerboards of these shapes can be completely covered using right triominoes whenever n is a positive integer.
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