Powers and Roots: Decimal numbers

According to the order of operations, we should first solve the expression inside of the parentheses:

$(\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)$

In the next step, we will proceed to solve the exponentiation, and finally the subtraction:

$(19)^2-11=(19\times19)-11=361-11=350$

To solve the expression $4\times\sqrt{0.49}+4^2 =$, we will follow the order of operations, which prioritizes operations inside parentheses, exponents and roots, followed by multiplication and division, and finally addition and subtraction.

1. Calculate the Square Root:
The first step is to solve the square root part of the expression. $\sqrt{0.49}$.
$0.49$ is a simple decimal number whose square root is $0.7$, because $0.7 \times 0.7 = 0.49$.
So,$\sqrt{0.49} = 0.7$.

2. Multiply:
Next, we multiply the result of the square root by 4:
$4 \times 0.7 = 2.8$.

3. Calculate the Power:
Evaluate $4^2$.
$4^2 = 16$, because $4 \times 4 = 16$.

4. Addition:
Now, add the results from the previous steps:
$2.8 + 16 = 18.8$.

The final result of the expression $4\times\sqrt{0.49}+4^2$ is $\boxed{18.8}$.