Two boards, one four inches wide and the other six inches wide, are nailed together to form an x. the angle at which they cross is 60 degrees. if this structure is painted and the boards are separated what is the area of the unpainted region on the four-inch board? (the holes caused by the nails are negligible.) express your answer in simplest radical form.

Find and simplify an expression for the area of five rows of x squares with side lengths of x centimeters .

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

The annual snowfall in a town has a mean of 38 inches and a standard deviation of 10 inches. last year there were 63 inches of snow. find the number of standard deviations from the mean that is, rounded to two decimal places. 0.44 standard deviations below the mean 2.50 standard deviations below the mean 0.44 standard deviations above the mean 2.50 standard deviations above the mean