12. let θ denote the proportion of registered voters in a large city who are in favor of a certain proposition. suppose that the value of θ is unknown, and two statisticians a and b assign to θ the following different prior p. d.f.’s ξa(θ ) and ξb(θ ), respectively: ξa(θ ) = 2θ for 0 < θ< 1, ξb(θ ) = 4θ 3 for 0 < θ< 1. in a random sample of 1000 registered voters from the city, it is found that 710 are in favor of the proposition. a. find the posterior distribution that each statistician assigns to θ. b. find the bayes estimate for each statistician based on the squared error loss function. c. show that after the opinions of the 1000 registered voters in the random sample had been obtained, th

Find the area and perimeter of each composite figure. use 3.14 for π. round your answer to the nearest tenth. a square and a right triangle share a common side. image long description a 3-meter by 0.5-meter rectangle has triangles attached like wings to the 3-meter sides. the other two sides of both triangles measure 2.5 meters. the height of each triangle is 2 meters. a 6-inch by 4-inch rectangle has 2 half-circles attached like wings to the 6-inch sides. the radius of each half-circle is 3 inches. find the surface area and volume of each figure. use 3.14 for π. round your answer to the nearest tenth. a right circular cylinder has a base radius of 6 yards and a height of 20 yards. a rectangular prism has a base that is 9 centimeters long and 7 centimeters wide. the height is 2 centimeters. a rectangular prism has a base that measures 11 millimeters by 11 millimeters. the height is 11 millimeters.

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the of the circle.