ElectricPavlov

3 years is  how many standard deviations away from 3.5 ??    .5 / .35 = 1.43 standard deviations below the mean====> z-score table = - 1.43

   from the negative  z-score table this represents .0764    or   7.64 %

The money amounts form an arithmetic sequence with d = -50 dollars

the SUM of an arithmetic sequence is given by    Sn=n(a1+an)/2    where in this case , n = 5   and a1 is the amount given to 1st place and an would be 5thplace (which is $200 less)

   so     SUM_{of prize money} = 5(1^{stplaceamount} + 1^{stplaceamount} - 200) /2      you can simplify this to

                Sum = 5 (2*1st -200)/2

                         = 5 *1st - 500            dollars

.....You'll need to find the inverse functions

for f(0)  you need inverse of    3-x    which is 3-x         f^-1(0) = 3

for 6 you need to find when    -x^3  + 2x^2 + 3x  = 6       or when   f(?) = 6         this occurs at     ? = 2

3+2 = 5

Just set the equation = to -5

2x+7 = - 5

2x = -12

x = -6      this is the first part of the piecemeal equation and - 6 is less than - 2      so first answer = -6

Now for the second part of the equation

-x^2 -x+1 = - 5

-x^2 -x + 6 = 0

x^2 + x-6 = 0

(x-2)(x+3) = 0       for this x can be = to 2   or -3 (throw out...because this part of the equation is only for x >=2)

    so the two possibilities are x = - 6 or 2

I will assume these are only positive numbers

A = 16     B = 96      Difference = 80

If the numbers can be negative

A = -16     B = 96     Difference = 112

There are 100 odd numbers in the interval    sum = 100/2 (301 + 499) = 40 000

Original side length 36/4 = 9 in

PYTHAG THEOREM TO FIND NEW SIDE LENGTH = sqrt ( 4.5^2 + 4.5^2 ) = sqrt 40.5  in

New perimeter = 4 * sqrt 40.5 inches

The shaded area is everything GREATER than but not including the line (because it is dashed)

Find slope of the line using two convenient integer points    slope = rise / run =  2

b, the y axis intercept is shown to be +1

so the line equation is  y = 2x+1

  the shaded area is   y > 2x+1    re-arrange to the requsted form

                                -2x+y -1 > 0

Perimeter = 18 + 18 + 18 = 54

area = sqrt3 /4  * 18^2 =81 sqrt3

81 sqrt3  /  54   =  3/2  * sqrt 3

5/6 has the smallest   4/5 , 3/4 , 2/3 and 1/2 will not fit in the specified interval