Answer :
Sure, let's go through each question step-by-step:
Question 29: Find [tex]\(7 \frac{1}{6} \%\)[/tex] of 500 to 1 decimal place.
1. Convert the percentage from a mixed number to an improper fraction:
[tex]\[ 7 \frac{1}{6} = 7 + \frac{1}{6} = \frac{43}{6} \][/tex]
2. Convert this fraction to a decimal percentage:
[tex]\[ \frac{43}{6} \% = \frac{43}{6} \times \frac{1}{100} \][/tex]
3. Calculate the percentage of 500:
[tex]\[ 500 \times \frac{43}{6} = \frac{2150}{3} \approx 716.6667 \][/tex]
4. Multiply by 1% (or 0.01):
[tex]\[ 716.6667 \times 0.01 = 7.16667 \][/tex]
5. Round the result to 1 decimal place:
[tex]\[ \text{Result} \approx 35.8 \][/tex]
Question 30: What are the next two terms of the pattern [tex]\(-3, 5, 2, 7, 9\)[/tex]?
1. Observe the differences between consecutive terms:
- From [tex]\(-3\)[/tex] to [tex]\(5\)[/tex], the difference is [tex]\(+8\)[/tex].
- From [tex]\(5\)[/tex] to [tex]\(2\)[/tex], the difference is [tex]\(-3\)[/tex].
- From [tex]\(2\)[/tex] to [tex]\(7\)[/tex], the difference is [tex]\(+5\)[/tex].
- From [tex]\(7\)[/tex] to [tex]\(9\)[/tex], the difference is [tex]\(+2\)[/tex].
2. Predict the pattern:
- After [tex]\(9\)[/tex], add [tex]\(+8\)[/tex] to get the next term.
- After the next term, subtract [tex]\(3\)[/tex] to get the subsequent term.
3. Calculate the next terms:
- Next term after [tex]\(9\)[/tex]: [tex]\(9 + 8 = 17\)[/tex].
- Following term: [tex]\(17 - 3 = 14\)[/tex].
Thus, the next two terms are [tex]\(17\)[/tex] and [tex]\(14\)[/tex].
Question 31: Find the ratio of 2 days to 5 weeks.
1. Establish the time units in the same scale:
- 1 week = 7 days, therefore 5 weeks = [tex]\(5 \times 7 = 35\)[/tex] days.
2. Set the ratio of 2 days to 35 days:
[tex]\[ \text{Ratio} = 2:35 \][/tex]
This is your complete and detailed solution for the questions provided.
Question 29: Find [tex]\(7 \frac{1}{6} \%\)[/tex] of 500 to 1 decimal place.
1. Convert the percentage from a mixed number to an improper fraction:
[tex]\[ 7 \frac{1}{6} = 7 + \frac{1}{6} = \frac{43}{6} \][/tex]
2. Convert this fraction to a decimal percentage:
[tex]\[ \frac{43}{6} \% = \frac{43}{6} \times \frac{1}{100} \][/tex]
3. Calculate the percentage of 500:
[tex]\[ 500 \times \frac{43}{6} = \frac{2150}{3} \approx 716.6667 \][/tex]
4. Multiply by 1% (or 0.01):
[tex]\[ 716.6667 \times 0.01 = 7.16667 \][/tex]
5. Round the result to 1 decimal place:
[tex]\[ \text{Result} \approx 35.8 \][/tex]
Question 30: What are the next two terms of the pattern [tex]\(-3, 5, 2, 7, 9\)[/tex]?
1. Observe the differences between consecutive terms:
- From [tex]\(-3\)[/tex] to [tex]\(5\)[/tex], the difference is [tex]\(+8\)[/tex].
- From [tex]\(5\)[/tex] to [tex]\(2\)[/tex], the difference is [tex]\(-3\)[/tex].
- From [tex]\(2\)[/tex] to [tex]\(7\)[/tex], the difference is [tex]\(+5\)[/tex].
- From [tex]\(7\)[/tex] to [tex]\(9\)[/tex], the difference is [tex]\(+2\)[/tex].
2. Predict the pattern:
- After [tex]\(9\)[/tex], add [tex]\(+8\)[/tex] to get the next term.
- After the next term, subtract [tex]\(3\)[/tex] to get the subsequent term.
3. Calculate the next terms:
- Next term after [tex]\(9\)[/tex]: [tex]\(9 + 8 = 17\)[/tex].
- Following term: [tex]\(17 - 3 = 14\)[/tex].
Thus, the next two terms are [tex]\(17\)[/tex] and [tex]\(14\)[/tex].
Question 31: Find the ratio of 2 days to 5 weeks.
1. Establish the time units in the same scale:
- 1 week = 7 days, therefore 5 weeks = [tex]\(5 \times 7 = 35\)[/tex] days.
2. Set the ratio of 2 days to 35 days:
[tex]\[ \text{Ratio} = 2:35 \][/tex]
This is your complete and detailed solution for the questions provided.
