To determine what percent of 75 is 10, we need to calculate the percentage. Here is the detailed, step-by-step solution:
1. Identify the given numbers:
- The part is [tex]\(10\)[/tex].
- The total is [tex]\(75\)[/tex].
2. Understand the percentage formula:
- The percentage is calculated as [tex]\(\left( \frac{\text{part}}{\text{total}} \right) \times 100\)[/tex].
3. Plug in the given numbers into the formula:
- [tex]\(\left( \frac{10}{75} \right) \times 100\)[/tex].
4. Perform the division:
- [tex]\(\frac{10}{75} = 0.13333333333333333\)[/tex]
5. Multiply by 100 to get the percentage:
- [tex]\(0.13333333333333333 \times 100 = 13.333333333333334\)[/tex].
Therefore, [tex]\(10\)[/tex] is approximately [tex]\(13.33\%\)[/tex] of [tex]\(75\)[/tex].
Next, let's consider the choices given to determine which ones can be used to solve this problem:
1. Choice [tex]\(r=10 \times 75\)[/tex]:
- This choice represents multiplying [tex]\(10\)[/tex] by [tex]\(75\)[/tex], which results in [tex]\(750\)[/tex], and does not help in finding a percentage.
2. Choice [tex]\(p=10 \times 75\)[/tex]:
- This choice also represents multiplying [tex]\(10\)[/tex] by [tex]\(75\)[/tex], resulting in [tex]\(750\)[/tex], which again is not useful for finding a percentage.
3. Choice [tex]\(p=10 / 75\)[/tex]:
- This choice represents dividing [tex]\(10\)[/tex] by [tex]\(75\)[/tex], which results in [tex]\(0.13333333333333333\)[/tex]. This can be converted to a percentage by multiplying by [tex]\(100\)[/tex].
4. Choice [tex]\(r=10 / 75\)[/tex]:
- This choice also represents dividing [tex]\(10\)[/tex] by [tex]\(75\)[/tex], giving [tex]\(0.13333333333333333\)[/tex], which can be multiplied by [tex]\(100\)[/tex] to get the percentage.
From the given choices, both [tex]\(p=10 / 75\)[/tex] and [tex]\(r=10 / 75\)[/tex] are the correct approaches as they provide the ratio that can be converted to a percentage.
Thus, the correct choice to use is [tex]\(4\)[/tex] (corresponding to [tex]\(r=10 / 75\)[/tex]).
