Let Y1, Y2,..., Y5 be a random sample of size 5 from a normal population with mean 0 and variance 1 and let Y = (1/5) 5 i=1 Yi . Let Y6 be another independent observation from the same population. What is the distribution of a W = 5 i=1 Y 2 i ? Why? b U = 5 i=1 (Yi − Y )2? Why? c 5 i=1 (Yi − Y )2 + Y 2 6 ? Why?

The table above shows approximate conversions from gallons to liters. what is the value of x?

() at a farm, animals are fed bales of hay and buckets of gain. each bale of hay is in the shape of a rectangular prism. the base side lengths 2 feet and 3 feet, and the height is 5 feet. each bucket of grain is a cylinder with diameter of 3 feet. the height of the bucket is 5 feet as the height of bale. a. which is larger in area, the rectangular base of the bale or the circular base of the bucket? explain how you know b. which is larger in volume, the bale or the bucket? explain how you know

List the sides of δrst in ascending order (shortest to longest) if: m∠r =x+28°, m∠s = 2x+16°, and m∠t = x+12