The function f(x) = cos(2πx) for x ∈ [0,1] is approximated by a polynomial pn interpolating f at n + 1 points xi. How should n be chosen so that the error max 0≤x≤1|f(x)−pn(x)|≤ 10−8 (i) if the points xi are equally spaced?

What is the perimeter of trapezoid jklm? + units 2 + + units 9 + units 9 + + units

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. a new supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which size bag provides the best deal, and how much will you save each month? compare the cost of the new supplier to the current one.

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.