A CBS News poll conducted January 5, 2017, among a nationwide random sample of 1042 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US
economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the
table below.
185
40
better same worse
Republican
45 83
Democrat
63 186
none 142 118
Use the two-way table above, please answer the following questions. Please enter your answers as
reduced fractions.
180
a. What fraction of all survey respondents identified themselves as affiliated with neither party?
b. What fraction of all survey respondents thought the economy was about the same?
c. What fraction of the those affiliated with neither party thought the economy was about the same?
d. Among all survey respondents who thought the economy was about the same, what fraction were
affiliated with neither party?
e. What fraction of all survey respondents were affiliated with neither party and thought the economy
was about the same?

my answer is$ 12

step-by-step explanation:

because 15 -2=12

10

step-by-step explanation:

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.

step-by-step explanation: