To determine which options have the same value as 5% of 35, we need to understand what 5% of a number means.
"5%" means 5 out of 100, or [tex]\(\frac{5}{100}\)[/tex].
So, 5% of 35 can be written as:
[tex]\[
5\% \text{ of } 35 = \frac{5}{100} \cdot 35
\][/tex]
We can evaluate this to find the numerical value:
[tex]\[
\frac{5}{100} \cdot 35 = \frac{5 \cdot 35}{100} = \frac{175}{100} = 1.75
\][/tex]
So, 5% of 35 is 1.75.
Now we evaluate the given options to find which ones are equal to 1.75:
A) [tex]\(5 \cdot 35\)[/tex]
[tex]\[
5 \cdot 35 = 175
\][/tex]
This is not equal to 1.75.
B) [tex]\(\frac{5}{100} \cdot 35\)[/tex]
[tex]\[
\frac{5}{100} \cdot 35 = 1.75
\][/tex]
This is equal to 1.75.
C) [tex]\(0.5 \cdot 0.35\)[/tex]
[tex]\[
0.5 \cdot 0.35 = 0.175
\][/tex]
This is not equal to 1.75.
D) [tex]\(0.05 \cdot 35\)[/tex]
[tex]\[
0.05 \cdot 35 = 1.75
\][/tex]
This is equal to 1.75.
E) [tex]\(\frac{5}{10} \cdot 35\)[/tex]
[tex]\[
\frac{5}{10} \cdot 35 = \frac{1}{2} \cdot 35 = 17.5
\][/tex]
This is not equal to 1.75.
Based on our evaluations, the correct options that represent 5% of 35 are:
- [tex]\(\frac{5}{100} \cdot 35\)[/tex] (Option B)
- [tex]\(0.05 \cdot 35\)[/tex] (Option D)
