At an art exhibition there are 12 paintings of which 10 are original. a visitor selects a painting at random and before decides to buy he asks the opinion of an expert about the authenticity of the painting. the expert is right in 9 out of 10 cases on average. given that the expert decides the painting is authentic what is the probability it really is? if the expert decides the paining is a copy then the visitor returns it and chooses another one what is the probability that her second choice is an original?

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.

grace would use 12 apple slices