# Math

## Find the upper confidence limit for parts a–c of Exercise 7.42.

Question: Find the upper confidence limit for parts a–c of Exercise 7.42. Answer:

## Show that the stereographic projections of the points z and 1/.z are reflections of each other in the equatorial plane

Question: (a) Show that the stereographic projections of the points z and 1/.z are reflections of each other in the equatorial plane of the Riemann sphere. (b) Show that the stereographic projections of the points z and −1/.z are diametrically opposite points on the Riemann sphere. Answer:

## Creating a Mosaic A mosaic is designed in the shape of an equilateral triangle

Question: Creating a Mosaic A mosaic is designed in the shape of an equilateral triangle, 20 feet on each side. Each tile in the mosaic is in the shape of an equilateral triangle, 12 inches to aside. The tiles are to alternate in color as shown in the illustration. How many tiles of each color will …

## A lab technician controls the temperature T inside a kiln. From an initial temperature of 0 degrees Celsius (°C)

Question: A lab technician controls the temperature T inside a kiln. From an initial temperature of 0 degrees Celsius (°C), he allows the kiln to increase by 2°C per minute for the next 60 min. After the 60th minute, he allows the kiln to cool at the rate of 3°C per minute. The temperature function …

## A shipment of 12 microwave ovens contains three defective units

Question: A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four of these units, and because each is identically packaged, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are …

## A random sample of 150 residents in one community was asked to indicate their first preference for one of three

Question: A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three …