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SOLUTION
From the question
[tex]\begin{gathered} z\propto\sqrt[]{x}\text{ and } \\ z\propto\frac{1}{y} \\ \text{combining we have } \\ z\propto\frac{\sqrt[]{x}}{y} \\ \propto\text{ is a proportionality constant } \end{gathered}[/tex]Removing the proportionality sign and introducing a constant, we have
[tex]\begin{gathered} z=k\times\frac{\sqrt[]{x}}{y} \\ z=\frac{k\sqrt[]{x}}{y} \end{gathered}[/tex]Making k the subject, we have
[tex]\begin{gathered} z=\frac{k\sqrt[]{x}}{y} \\ k\sqrt[]{x}=yz \\ k=\frac{yz}{\sqrt[]{x}} \end{gathered}[/tex]Substituting the initial values of z, x, and y, we have
[tex]\begin{gathered} k=\frac{yz}{\sqrt[]{x}} \\ k=\frac{6\times147}{\sqrt[]{16}} \\ k=\frac{882}{4} \\ k=220.5 \end{gathered}[/tex]The relationship becomes
[tex]z=\frac{220.5\sqrt[]{x}}{y}[/tex]Substituting the second values of x and y into the equation for the relationship, we have
[tex]\begin{gathered} z=\frac{220.5\sqrt[]{x}}{y} \\ z=\frac{220.5\sqrt[]{25}}{4} \\ z=\frac{220.5\times5}{4} \\ z=\frac{1,102.5}{4} \\ z=275.625 \end{gathered}[/tex]Hence the answer is 275.63 to the nearest hundredth
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