8: Peanut allergies are considered to be the most serious food allergies. According to the National Institute of Allergy and Infectious Diseases, roughly 1% of children under the age of 5 are allergic to peanuts. Suppose a random sample of daycare centers in Connecticut is selected for the purpose of studying allergies in children. 1275 children in these daycare centers are sampled. Let the random variable X = the number of children with peanut allergies. Assuming that the incidence of peanut allergies in children in daycare centers in Connecticut is the same as the national rate, find the mean and standard deviation for the binomial random variable X.

Look at this system of equations. -3x + 3y = 12 y = x + 4 the solution set of this system is best explained by which of these statements? a) the graphs of the equations are the same line because the equations have the same slope and the same y-intercept. the system has infinitely many solutions. b) the graphs of the equations are parallel lines because they have the same slope but different y-intercepts. the system has no solution. c) the graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. the system has exactly one solution. d) the graphs of the equations are lines that intersect at one point because the equations have the same slope and the same y-intercept. the system has exactly one solution.