If m∠TUV = (9x + 1)°, m∠TUW = (7x – 9)°, and m∠WUV = (5x – 11)°, find the value of x. *

Step-by-step explanation:

Given

m∠TUV = (9x + 1)°

m∠TUW = (7x – 9)°

m∠WUV = (5x – 11)°

Note that the point line WU bisects <TUV at U

Hence  = ∠TUW  + ∠WUV = ∠TUV

Substituting the given parameters to get x;

(9x +1)° = (7x – 9)°+(5x - 11)°

9x+1 = 12x-20

collect the like terms

9x-12x = -20-1

-3x = -21

divide both sides by -3

-3x/-3 = -21/-3

x = 7

Hence the value of x is 7

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