Find the riemann sum for f(x) = sin(x) over the interval [0, 2π], where x0 = 0, x1 = π/4, x2 = π/3, x3 = π, and x4 = 2π, and where c1 = π/6, c2 = π/3, c3 = 2π/3, and c4 = 3π/2. (round your answer to three decimal places.)

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

Write the percent as a fraction or mixed number in simplest form. 0.8%

In july, the average temperature in one us city was 29°c. by december, the average temperature had fallen by 29°c. explain why the average temperature in december was 0°c.