To determine what percent of 75 is 10, follow these steps:
1. Set up the problem:
The aim is to find the percentage representation of 10 with respect to 75. This is done using the basic percentage formula:
[tex]\[
\text{percent} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100
\][/tex]
2. Substitute the values:
Here, the part is 10 and the whole is 75. Substituting these values into the formula:
[tex]\[
\text{percent} = \left( \frac{10}{75} \right) \times 100
\][/tex]
3. Calculate the fraction:
First, calculate the value of the fraction:
[tex]\[
\frac{10}{75} \approx 0.13333333
\][/tex]
4. Convert the fraction to a percentage:
Now, multiply the decimal by 100 to convert it to a percentage:
[tex]\[
\text{percent} \approx 0.13333333 \times 100 = 13.3333333
\][/tex]
Thus, 10 is approximately [tex]\(13.33\%\)[/tex] of 75.
Next, let's analyze the given choices:
- [tex]\( p = \frac{10}{75} \)[/tex]:
This expression gives us the fraction of 10 with respect to 75, which is then multiplied by 100 to find the percentage. This choice is correct.
- [tex]\( p = 10 \times 75 \)[/tex]:
This is incorrect because multiplying 10 by 75 gives a product, not a percentage. The result does not relate to the problem.
- [tex]\( r = \frac{10}{75} \)[/tex]:
Similar to the first choice, this expression correctly defines the fraction of 10 with respect to 75. This choice is correct as well.
- [tex]\( r = 10 \times 75 \)[/tex]:
This is the same erroneous approach as [tex]\( p = 10 \times 75 \)[/tex], which does not solve the problem of finding a percentage.
Therefore, the correct choices that can be used to solve this problem are [tex]\( p = \frac{10}{75} \)[/tex] and [tex]\( r = \frac{10}{75} \)[/tex]. These correspond to indices 1 and 3 in the provided list.
