A university health services physician is concerned about how much sleep freshmen are getting. She asks a simple random sample of 50 students if they got at least 8 hours of sleep the previous night. Then she constructs a 95% confidence interval for the true proportion of all freshman college students who got at least 8 hours of sleep the previous night.(a) Explain what would happen to the width of the interval if the confidence level were decreased to 90%.

Plzzz plzz maths ! quadratic sequences =an^2+bn 1) 1,6,15,28,45 2)5,18,39,68,105 3) 1,8,21,40,65 4) 7,24,51,88,135 5) -1,2,9,20,35

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α. part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part b suppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i.e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part c now try a numerical problem. what is the direction of the vector w = < -1, 6 > ?

Which rotation about its center will carry a regular hexagon onto itself