The relationship between the time water flows into a cube-shaped tank and the depth of the water is assumed to be linear. Based on the provided data, a constant rate of 0.7 units per time unit is established. Completing the table, the depths corresponding to the given times are estimated accordingly: 0 seconds (0 units), 3 seconds (2.1 units), 4 seconds (2.8 units), 7 seconds (4.2 units), and 9 seconds (5.6 units). This assumes a steady flow, and the values are subject to the accuracy of the linear assumption.
To complete the table showing the relationship between the time the water flows and the depth of the water in the tank, we can observe the pattern and fill in the corresponding depths. Assuming a linear relationship, we can find the slope (rate of change) and use it to complete the table.
\[ \text{Slope} = \frac{\text{Change in Depth}}{\text{Change in Time}} \]
For the given data:
\[ \text{Slope} = \frac{7 - 4.2}{4 - 0} = \frac{2.8}{4} = 0.7 \]
Now, we can use this slope to fill in the missing depths:
\[ \begin{array} \hline \text{Time} & \text{Depth} \\ \hline 0 & 0 \\ 3 & 2.1 \\ 4 & 2.8 \\ 7 & 4.2 \\ 9 & 5.6 \\ \hline \end{array} \]
This assumes a linear relationship between time and depth. If the relationship is not linear, more information or a different approach would be needed to complete the table accurately.