The data below are the gestation periods, in months, of randomly selected animals and their corresponding lifespans, in years. Gestation, x: 8 2.1 1.3 1 11.5 5.3 3.8 24.3Life span, y: 30 12 6 3 25 12 10 40

a. If you want to predict the lifespan of an animal with a certain length of gestation period, which variable will be the response variable and which one will be the explanatory variable? [2 marks]b. Compute the correlation coefficient between the gestation period and the lifespan. Interpret the value. [4 marks]c. At α = 0.05, can you conclude that there is a significant correlation between the two variables? [6 marks] (Hint: Show the key steps of test of Hypothesis.)d. Compute the coefficient of determination r2. Interpret the value. [3 marks]e. Is it gestation period alone that determines lifespan? Are there other factors that need to be considered? Justify your answer. [1 mark]f. Use the method of least squares, compute the linear regression equation that will help you predict the lifespan from the gestation period. [5 marks]g. Interpret the slope of the regression equation with reference to context. [2 marks]h. Predict the lifespan of a moose, which has an 8-month gestation period. Also, compute the residual for this lifespan. [3 marks]

d

step-by-step explanation:

i used the pitagoras theoreme

central angle of a triangle has the same measure as its intercepted arc.

step-by-step explanation:

it would be a on edgenuit y

the diagram below is your final answer

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.