In a cooking contest, the mean score for taste was 20, with a standard deviation of 2.8. one of the contestants received a score of 14. convert this score to a z score and tell if it is “usual” or “unusual.”

Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is π cubic inches.

Find the volume of the solid whose base is the region bounded by f(x), g(x) and the x-axis on the interval [0, 1], and whose cross-sections perpendicular to the y-axis are squares. your work must show the integral, but you may use your calculator to evaluate it. give 3 decimal places for your answe

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.