An algebra placement test was used to determine placement in mathematics courses. a sample of calculus students gave 50 scores. it is known stack sum space space with i equals 1 below and 50 on top x subscript i superscript 2 equals 20500 comma space sum from i equals 1 to 50 of space x subscript i equals 821. space use the sample standard deviation as the population deviation. if you want mu to be captured in a 96% confidence interval with length equal to 4, what is the minimum sample size?

Eric drove 275 miles in 5 hours. at the same rate how long would it take him to drive 495 miles?

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?

If the square of a positive integer is added to 2 times the integer the result is 48. find the integer.