Let's break down the given question step-by-step:
### Question 4: Calculation of [tex]\( \frac{0.16}{0.004} \)[/tex]
To determine [tex]\( \frac{0.16}{0.004} \)[/tex]:
1. Convert the division into a simpler format by making the divisor a whole number. Specifically:
[tex]\[
\frac{0.16}{0.004} = \frac{0.16 \times 1000}{0.004 \times 1000} = \frac{160}{4}
\][/tex]
2. Now, perform the division:
[tex]\[
160 \div 4 = 40
\][/tex]
The correct answer is:
[tex]\[
\boxed{40}
\][/tex]
### Question 5: Geometric Mean Calculation
To find the geometric mean of the given numbers [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
1. First, calculate [tex]\( x \)[/tex]:
[tex]\[
x = \sqrt{3} \cdot 2\sqrt{3} + 3\sqrt{2} \cdot \sqrt{2}
\][/tex]
- [tex]\( \sqrt{3} \cdot 2\sqrt{3} = 2(\sqrt{3} \cdot \sqrt{3}) = 2 \cdot 3 = 6 \)[/tex]
- [tex]\( 3\sqrt{2} \cdot \sqrt{2} = 3(\sqrt{2} \cdot \sqrt{2}) = 3 \cdot 2 = 6 \)[/tex]
So, add them together:
[tex]\[
x = 6 + 6 = 12
\][/tex]
2. Then, calculate [tex]\( y \)[/tex]:
[tex]\[
y = \frac{\sqrt{18}}{\sqrt{2}}
\][/tex]
Simplify using the property of radicals:
[tex]\[
y = \sqrt{\frac{18}{2}} = \sqrt{9} = 3
\][/tex]
3. Now let's find the geometric mean [tex]\( \sqrt{x \cdot y} \)[/tex]:
[tex]\[
\text{Geometric Mean} = \sqrt{12 \cdot 3} = \sqrt{36} = 6
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6}
\][/tex]
