As a faculty member at UC Irvine, Erik receives a lot of email, and he is in desperate need of a method for separating important messages from spam. Now that you’ve learned some discrete probability, could you help him out?

The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?

Abcd is reflected across the x- axis, then rotated 90 clockwise about the orgin, and finally reflected across the line y= x to form a’ b’ c’ .