The u. s. national toxicology program (ntp) studies the toxicity and carcinogenicity of agents potentially causing a risk to human health. electromagnetic fields around electrical installations are harmless in theory, but they might have a long-term effect on health (for instance, in triggering tumors). observational studies in human populations have suggested a potential association. an ntp study looked at the occurrence of cancers in otherwise healthy rats after two years of daily exposure to 60-hertz electromagnetic fields of various intensities. here are the numbers of male and female rats with a tumor after the two-year study period. note that 2 gauss is approximately 1000-fold greater than what is considered high exposure for humans. male rats female ratscontrol: no exposure 16 ( n=99 ) 19 ( n=100 )0.02-gauss exposure 31 (n = 100) 22 (n = 100)2-gauss exposure 30 (n = 100) 22 (n = 100)in rats not exposed to an electromagnetic field (sample size in parentheses), is there significant evidence of a difference in the tumor rates between males and females? h0: pmale = pfemaleha: pmale ≠ pfemalei have figured out the null but not sure how to go about getting the χ exsplain than you. what is the value of the test statistic? (round your answer to two decimal places.)χ2 =

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.

answer: sorry i dont really know but can we talk all my friends r gone and im bored

step-by-step explanation: