Bayes’ theorem deals with the calculation of posterior probabilities, which isn’t always a natural thing to do. we’re used to forward-chaining our probabilities (e. g., if we roll a 3 on a die, what’s the probability the second roll will give us a total of backward-chaining is less intuitive (e. g. if our total on the die was an 8, what’s the probability that the first roll was a since the rules of probability involve simple addition and multiplication, they work fine in both directions. the thing that makes posterior probability more difficult is that we simply aren’t used to thinking about things that way. our chapter reading provides an example of a diagnostic test for a rare disease. the resulting confidence in a positive test result is surprisingly low. discuss why that is so. what is happening in the interaction of the various probabilities that leads to this outcome?

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

cretdit to source

stethere all not eveanp-by-step explanation:

the first option is the answer.

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2