The sand for a new rapid sand filter is specified to have a uniformity coefficient of $x$ and an effective size of $Y.$ Use the results of the sieve analysis below to confirm that the sand provided meets the specifications. Note that you may you the geometric mean diameters.

Given:

$\backslash$table$[[$U$.$S$.$ Standard Sieve No$.,$Mass percent retained$],[8-12,0],[12-16,0\mathrm{.}4],[16-20,13\mathrm{.}1],[20-30,54\mathrm{.}5],[30-40,30\mathrm{.}2],[40-50,1\mathrm{.}785],[50-70,0\mathrm{.}015]]$

a$.$ Provide a graph of grain size vs$.$ percent of particles retained.

b$.$ What is the uniformity coefficient?

c$.$ What is the effective size?

d$.$ Does the sand meet the specifications?