(1 point) a study of 12,000 able-bodied male students at the university of illinois found that their times for the mile run were approximately normal with mean 7.11 minutes and standard deviation 0.74 minute. choose a student at random from this group and call his time for the mile y.

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Step   1  : g simplify —— 22 equation at the end of step   1  : g ((4 • • (g + h)) - 4gx = 0 22 step   2  : equation at the end of step   2  : 2g • (g + h) - 4gx = 0 11 step   3  : rewriting the whole as an equivalent fraction :

  3.1      subtracting a whole from a fraction
rewrite the whole as a fraction using   11  as the denominator :

4gx 4gx • 11 4gx = = 1 11

equivalent fraction : the fraction thus generated looks different but has the same value as the whole
common denominator : the equivalent fraction and the other fraction involved in the calculation share the same denominator

adding fractions that have a common denominator :

  3.2            adding up the two equivalent fractions
add the two equivalent fractions which now have a common denominator
combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2g • (g+h) - (4gx • 11) 2g2 + 2gh - 44gx = 11 11 step   4  : pulling out like terms :

  4.1        pull out like factors  :
      2g2 + 2gh - 44gx    =      2g  •  (g + h - 22x) 

equation at the end of step   4  : 2g • (g + h - 22x) = 0 11 step   5  : when a fraction equals zero :   5.1      when a fraction equals zero

where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
now,to get rid of the denominator, tiger multiplys both sides of the equation by the denominator.
here's how:

2g•(g+h-22x) • 11 = 0 • 11 11

now, on the left hand side, the   11  cancels out the denominator, while, on the right hand side, zero times anything is still zero.
the equation now takes the shape  :
      2g  •   (g+h-22x)    =  0

theory - roots of a product :

  5.2      a product of several terms equals zero. 
  when a product of two or more terms equals zero, then at least one of the terms must be zero. 
  we shall now solve each term = 0 separately 
  in other words, we are going to solve as many equations as there are terms in the product 
  any solution of term = 0 solves product = 0 as well.

solving a single variable equation  :

  5.3            solve    :         2g = 0 
  divide both sides of the equation by 2:
                                          g = 0

solving a single variable equation  :

  5.4          solve      g+h-22x    =  0
in this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
we shall not handle this type of equations at this time

one solution was found :                                       g = 0