Solve the equation:
x^3+3x^2-x+12=0

Step-by-step explanation:

The synthetic division shown below both confirms that x=-4 is a solution and gives the reduced quadratic as

  x^2 -x +3 = 0

Using the quadratic formula with a=1, b=-1, c=3, we find the other two solutions to be ...

____

The graph of the cubic shows it has one real root at x=-4. Dividing the function by the corresponding factor shows the quadratic factor to have its vertex at (0.5, 2.75). This means the remaining roots are 0.5±i√2.75, matching the above result.

c

step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560