A) a fair die has six sides labeled 1 through 6. what is the sample space (s) if the die is thrown once? b) list the possible outeomes for the following events) a = the event that the number thrown is even: b = the event that the number thrown is at least 2: c- an odd number greater than 3 a n b: auc: not a: a) determine the following probabilities i) p(a) ii) p(c) iv) use the general addition rule to find p(a ub) e) are a and b mutually exclusive? explain

What value of x is in the solution set of –5x – 15 > 10 + 20x?

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

The area of a rectangle is 10 cm^2. one side of the rectangle is x cm. express the perimeter of the rectangle in terms of x and show that this rectangle cannot have a perimeter of 12 cm. the perimeter of the rectangle in terms of x is __ cm