One method to estimate the flow rate of blood delivered by the heart $($called the "cardiac output"$)$ is to continuously inject a dye into the artery $($aorta$)$ entering the main circulatory system and measure the dye concentration in the outlet from that circulatory system $($right atrium$).$ In one such measurement, the dye is injected at a rate of $20\frac{g}{m}in,$ and the measured dye content at the outlet is $0\mathrm{.}39$ wt$.\%.$ The dye concentration in the blood is $0$ before the dye is injected $($this procedure obviously must be completed in a short time to avoid interference from the recirculation of blood containing the dye$).$

a$.$ What is the mass flow rate of blood and dye exiting the circulatory system?

b$.$ What is the mass flow rate of just the blood through the circulatory system $($without the dye$)?$

c$.$ If the density of blood is $1\mathrm{.}06\frac{g}{c}{m}^3,$ what volumetric flow rate is indicated by the answer to part $($b$)?$