A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) = 0.12 P(A2) = 0.08 P(A3) = 0.05
P(A1 U A2) = 0.14 P(A1 U A3) = 0.14
P(A2 U A3) = 0.11 P(A1 ⋂ A2 ⋂ A3) = 0.01

a. Given that the system has a type 1 defect, what is the probability that it has a type 2 defect?
b. Given that the system has a type 1 defect, what is the probability that it has all three types of defects?
c. Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect?
d. Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect?

Rose bought a new hat when she was on vacation. the following formula describes the percent sales tax rose paid b=t-c/c

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.

Abox of chocolates cost $7 which equation relates the number of boxes sold parentheses x parentheses and total cost of the boxes sold parentheses y parentheses