$(50$ points$)$ In a formation in the Permian Basin, the following mineral compositions were

found in $7$ different cores shown in the table below. Please perform the following:

a$.$ Calculate the Brittleness index $(B{I}_1)$ using Eqn. $1\mathrm{.}2$ in the Textbook $(15\%)$

b$.$ Calculate the Brittleness index $(B{l}_2)$ using Eqn. $1\mathrm{.}3$ in the Textbook $(15\%)$

c$.$ Using Excel to develop an equation to correlate $B{l}_1$ and $B{I}_2,($hint: show your plot

together with the correlation equation and the $R^2)(15\%)$

d$.$ Comment on the differences of the two brittleness indexes $(5\%)$