Tangent ad and secant fb intersect at point c, the point of tangency. what is the measure of dcf?

∠DCF is 100°    

Step-by-step explanation:

Given tangent AD and secant FB intersect at point C, the point of tangency. We have to find the measure of ∠DCF.

As, ∠COF=160°

In ΔCOF, by Angle Sum Property of triangle

∠OCF+∠COF+∠OFC=180°

⇒ ∠OCF+160°+∠OCF=180°   (∵OC=OF)

⇒ 2∠OCF=20° ⇒ ∠OCF=10°

Now, we have to find the ∠DCF

∠DCF=∠DCO+OCF

As radius from the center of circle to the point of tangency is perpendicular to the tangent line.

∠DCF=∠DCO+OCF

         =90°+10°=100°          

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