A fourth-grade teacher gives homework every night in both mathematics and language arts. the time to complete the mathematics homework has a mean of 10 minutes and a standard deviation of 3 minutes. the time to complete the language arts assignment has a mean of 12 minutes and a standard deviation of 4 minutes. assuming the times to complete homework assignments in math and language arts are independent, the standard deviation of the time required to complete the entire homework assignment is

Answer:4Step-by-step explanation:Given that:X = time taken to complete mathematics homeworkY= time taken to complete language homeworkStandard deviation of X ; SD(X) = 3Standard deviation of Y ; SD(Y) = 4rho = - 0.375rho = Cov(X, Y) / SD(X) * SD(Y)-0.375 = COV(X, Y) / 3 * 4COV(X, Y) = 12 * - 0.375COV(X,Y) = - 4.5Variance(X, Y) = V(X, Y)V(X, Y) = V(X) + V(Y) + 2COV(X,Y)V(X) =SD(X)² = 3² = 9V(Y) = SD(Y)² = 4² = 16V(X,Y) = 9 + 16 + 2(-4.5)V(X, Y) = 16SD(X, Y) = sqrt(V(X, Y)) = sqrt(16) = 4Hence, standard deviation to complete entire homework, SD(X, Y) = 4