A container contains 4 red marbles and 8 blue marbles. A second container contains 6 red marbles and x blue marbles. One marble is drawn from each of the two containers. If the probability of drawing a pair of marbles of the same color is \frac{1}{2}, what is the value of x

Asquare picture with sides of 32 inches is to be mounted on a square mat with sides of 52 inches. find the area of the mat that will remain uncovered by the picture.

Which expression is the factorization of x^2+10+21

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10