While visiting Zagreb, Croatia, Arthur Van de Lay visits the Mimara Art Museum and then takes in the great architecture of the city. He stops at a caf$$ in the old town and orders a bottle of mineral water. The reported chemical concentration of this water is $[$Na$+]=0\mathrm{.}65=$ mg$/$L$,[$K$+]=0\mathrm{.}4$ mg$/$L$,[$Mg$2+]=19$ mg$/$L$,=[$Ca$2+]=35$ mg$/$L$,=[$Cl$]=0\mathrm{.}8$ mg$/$L$,=[$SO$42]=14\mathrm{.}3$ mg$/$L$,[$HCO$3]=189$ mg$/$L$,[$NO$3]=3\mathrm{.}8$ mg$/$L$.$

The pH of the water is $7\mathrm{.}3.($a$)$ What is the hardness of the water in mg$/$L CaCO$3?($b$)$ Is the chemical analysis correct?