Consider the Venn diagram below. Each of the dots outside the circle represents a patient questioned in a medical student's survey. In this experiment, 5 patients were asked about their Vitamin C use and whether they had had a cold in the past two months. The patients are labeled with their names: Amelia, Charlotte, Daniel, Emery, and Paul. The two events represented in the Venn diagram are: Event A: The event that a patient takes a daily Vitamin C pill. Event B: The event that a patient has had a cold in the past two months. Amelia, Charlotte, and Emery state that they take a daily Vitamin C pill. Emery and Paul state that they have had a cold in the past two months. Place the dots in the appropriate event given the information above (you may not use all of the dots), then determine if the events are mutually exclusive.

In a test for esp (extrasensory perception), the experimenter looks at cards that are hidden from the subject. each card contains either a star, a circle, a wave, a cross or a square.(five shapes) as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. when the esp study described above discovers a subject whose performance appears to be better than guessing, the study continues at greater length. the experimenter looks at many cards bearing one of five shapes (star, square, circle, wave, and cross) in an order determined by random numbers. the subject cannot see the experimenter as he looks at each card in turn, in order to avoid any possible nonverbal clues. the answers of a subject who does not have esp should be independent observations, each with probability 1/5 of success. we record 1000 attempts. which of the following assumptions must be met in order to solve this problem? it's reasonable to assume normality 0.8(1000), 0.2(1000)%30 approximately normal 0.8(1000), 0.2(1000)% 10 approximately normal srs it is reasonable to assume the total number of cards is over 10,000 it is reasonable to assume the total number of cards is over 1000

Solve the inequaliy: (x^2+2)(x−2)^2(6−2x)> 0

Determine the area of a triangle with (see picture below)