Circle 1, circle 2, and circle 3 have the same center and have radii, respectively, of r1 cm, r2 cm, r3 cm, where r1 < r2 < r3. let a1 be the area of circle 1, let a2 be the area of the region within circle 2 and outside circle 1, and let a3 be the area of the region within circle 3 and outside circle 2, where all areas are in cm2. what are the values of \small \frac{a_{1}}{a_{2}} and \small \frac{a_{2}}{a_{3}} ?

Asurvey of eating habits showed that approximately 5 % of people in a certain city are vegans. vegans do not eat meat, poultry, fish, seafood, eggs, or milk. a restaurant in the city expects 350 people on opening night, and the chef is deciding on the menu. treat the patrons as a simple random sample from the city and the surrounding area, which has a population of about 600,000. if 20 vegan meals are available, what is the approximate probability that there will not be enough vegan meals long dash—that is, the probability that 21 or more vegans will come to the restaurant? assume the vegans are independent and there are no families of vegans.