Estimate the minimum number of subintervals to approximate the value of Integral from negative 4 to 7 9 sine (x plus 7 )dx with an error of magnitude less than 2 times 10 Superscript negative 4 using a. the error estimate formula for the Trapezoidal Rule. b. the error estimate formula for Simpson's Rule.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.