The retailing manager of a supermarket chain wants to determine whether product location has any effect on sale of pet toys. Three different aisle locations are being considered: front, middle, and rear. A random sample of 18 stores is selected with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all stores. At the end of a 1-month trial period, the sales volumes (in thousands of dollars) of the product in each store were as follows: Berenson, Levine, and Krehbiel (2002, 405). AISLE LOCATION Front 8.6 7.2 5.4 6.2 5.0 4.0 Middle 3.2 2.4 2.0 1.4 1.8 1.6 Rear 4.6 6.0 4.0 2.8 2.2 2.8 a. At the 5% level of significance, is there evidence of a significant difference in b. If appropriate, which aisle locations appear to differ significantly in average c At the 5% level of significance, is there evidence of a significant difference in the average sales among the various aisle locations? sales? variation in sales among the various aisle locations?

the workers who do no drive has no reasonable reason to buy gasoline due to they don't have anything to use it for

answer: i literally just answered this question but they want me to do it again

step-by-step explanation:

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.