bar (E)=sqrt (((Delta bar (m))/(bar (m)))^2+((bar (h)bar (h))/(bar (h)))^2+((2Delta bar (D))/(bar (D)))^2)= sqrt (((0.0487)/(12.124))^2+((0.01)/(4.10))^2+((0.0076)/(1.59))^2)approx

To calculate the value of $\bar{E}$, we need to substitute the given values into the formula and perform the calculations.<br /><br />$\bar{E} = \sqrt{(\frac{\Delta \bar{m}}{\bar{m}})^{2} + (\frac{\bar{h}\bar{h}}{\bar{h}})^{2} + (\frac{2\Delta \bar{D}}{\bar{D}})^{2}}$<br /><br />Substituting the given values:<br /><br />$\bar{E} = \sqrt{(\frac{0.0487}{12.124})^{2} + (\frac{0.01}{4.10})^{2} + (\frac{0.0076}{1.59})^{2}}$<br /><br />Now, let's calculate the values inside the square root:<br /><br />$\bar{E} = \sqrt{(0.004) + (0.00024) + (0.)}$<br /><br />$\bar{E} = \sqrt{0.00472}$<br /><br />$\bar{E} \approx 0.0687$<br /><br />Therefore, the value of $\bar{E}$ is approximately 0.0687.