Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area inside the cardioid r equals 1 plus cosine theta until it intersects with r equals 1 plus sine theta. Notice that because of symmetry, this can be doubled to find the area of the region.

Match the vocabulary to the proper definition. in probability, two events in which 1. conditional probability the outcome of one event is independent of the outcome of a second event. 2. dependent events in probability, two events in which the outcome of one event is dependent on the outcome of a second event. the probability of an event in which the outcome of the event is conditional on the outcome of one or more different events. 3. independent events