c$)$ Rewrite using list comprehensions and filter. Hint: you can nest list comprehen$-$ sions $($use one inside another$).$ Yes, this will be much easier with numpy arrays, but we are

not doing that yet. The intent here is to practice with list comprehensions so solutions using numpy will be graded as incorrect. $[7$pts$]$

$x=$ list$($range$(101))$

$y=$ list$($range$(101))$

$z=$ list$($range$(101))$

for $i$ in range$(101)$:

$x[i]=x[i]**0\mathrm{.}01$

$y[i]=y[i]**0\mathrm{.}01$

$z[i]=z[i]**0\mathrm{.}01$

rho $=[]$

$s=0.$

for $k$ in range$(101)$:

rho $=$ rho $+\left[\begin{array}{c}?\end{array}\right]$

for $j$ in range$(101)$:

$[k]=[k]+\left[\begin{array}{c}?\end{array}\right]$

for $i$ in range$(101)$:

$(y[j]-0\mathrm{.}5{)}^{****}2+1$

$(z[k]-0\mathrm{.}5{)}^{****}2$

if rho$[$k$][$j$][$i$]>0\mathrm{.}5$:

$s=s+[k][j][i]$