To solve this question, we will carefully consider the frequencies given for each interval of the amounts paid (in Rands). Here is a detailed, step-by-step solution:
1. Understand the Data:
- The table shows different payment ranges (in Rands) and the corresponding frequencies of those payments.
- The frequencies represent the number of occurrences within each specified range.
2. Extract Known Frequencies:
- For the range [tex]\(0 < x \leq 100\)[/tex], the frequency is 7.
- For the range [tex]\(100 < x \leq 200\)[/tex], the frequency is 12.
- For the range [tex]\(200 < x \leq 300\)[/tex], the frequency is represented by [tex]\(a\)[/tex] (unknown).
- For the range [tex]\(300 < x \leq 400\)[/tex], the frequency is 35.
- For the range [tex]\(400 < x \leq 500\)[/tex], the frequency is represented by [tex]\(b\)[/tex] (unknown).
- For the range [tex]\(500 < x \leq 600\)[/tex], the frequency is 6.
3. Write Down the Known Frequencies:
- We have frequencies for most of the ranges directly from the table, except for the ranges where frequencies are given as [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
4. Result:
- Without additional data or constraints, we are limited to only listing the frequencies that we can determine from the table:
- For [tex]\(0 < x \leq 100\)[/tex] : 7
- For [tex]\(100 < x \leq 200\)[/tex] : 12
- For [tex]\(200 < x \leq 300\)[/tex] : [tex]\(a\)[/tex] (unknown)
- For [tex]\(300 < x \leq 400\)[/tex] : 35
- For [tex]\(400 < x \leq 500\)[/tex] : [tex]\(b\)[/tex] (unknown)
- For [tex]\(500 < x \leq 600\)[/tex] : 6
5. Conclusion:
- The frequencies for the various amounts paid (in Rands) are:
- [tex]\(0 < x \leq 100\)[/tex] : 7
- [tex]\(100 < x \leq 200\)[/tex] : 12
- [tex]\(200 < x \leq 300\)[/tex] : [tex]\(a\)[/tex]
- [tex]\(300 < x \leq 400\)[/tex] : 35
- [tex]\(400 < x \leq 500\)[/tex] : [tex]\(b\)[/tex]
- [tex]\(500 < x \leq 600\)[/tex] : 6
Thus, we have analyzed and outlined the frequencies given in the table in a structured manner, acknowledging the unknowns [tex]\(a\)[/tex] and [tex]\(b\)[/tex] where pertinent.
