Complete the table by calculating the values of the given expressions for each value of Y.

The table requires calculating the values of the given expressions for each value of $Y$. I will assume the "5%" in the first row, second column is a typo and should be "5".

Here is the completed table:

$$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline Y & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 \\ \hline 3+Y & 5 & 7 & 9 & 11 & 13 & 15 & 17 & 19 \\ \hline \frac{1}{2}Y+1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline (3+Y)^2 & 25 & 49 & 81 & 121 & 169 & 225 & 289 & 361 \\ \hline \left(\frac{1}{2}Y+1\right)^2 & 4 & 9 & 16 & 25 & 36 & 49 & 64 & 81 \\ \hline \end{array}$$

To illustrate the calculations, let's use $Y=2$ as an example for each expression:

Step 1: Calculate for $Y=2$.

• For $3+Y$: Substitute $Y=2$ into the expression.

$$3+2 = \boxed{5}$$

• For $\frac{1}{2}Y+1$: Substitute $Y=2$ into the expression.

$$\frac{1}{2}(2)+1 = 1+1 = \boxed{2}$$

• For $(3+Y)^2$: Substitute $Y=2$ into the expression.

$$(3+2)^2 = 5^2 = \boxed{25}$$

• For $\left(\frac{1}{2}Y+1\right)^2$: Substitute $Y=2$ into the expression.

$$\left(\frac{1}{2}(2)+1\right)^2 = (1+1)^2 = 2^2 = \boxed{4}$$

The remaining values in the table are calculated similarly by substituting each $Y$ value into the respective expression.