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Answer :
Sure, let's go through each question step-by-step:
9. Finding the total number of students:
We know that 58% of the total number of students are boys, and there are 840 boys in the school. To find the total number of students, we set up the equation:
[tex]\[ 0.58 \times \text{Total Students} = 840 \][/tex]
To find the total number of students, divide both sides by 0.58:
[tex]\[ \text{Total Students} = \frac{840}{0.58} \approx 1448 \][/tex]
So, the total number of students in the school is approximately 1448. Since this doesn't exactly match any of the multiple-choice options, let's assume the closest correct choice should be selected. However, given this estimate, it might have been a typo in the options.
10. Time for the interest to reach 180 Birr:
The simple interest formula is:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Given:
- Principal = 300 Birr
- Rate = 6% or 0.06
- Interest = 180 Birr
To find the time, rearrange the formula:
[tex]\[ \text{Time} = \frac{\text{Interest}}{\text{Principal} \times \text{Rate}} = \frac{180}{300 \times 0.06} = 10 \][/tex]
It will take 10 years for the interest to become 180 Birr.
11. Decimal form of [tex]\(\frac{3}{4}\%\)[/tex]:
First, convert [tex]\(\frac{3}{4}\%\)[/tex] into its decimal form:
1. [tex]\(\frac{3}{4}\% = \frac{3}{4} \times \frac{1}{100}\)[/tex]
2. [tex]\(\frac{3}{4} = 0.75\)[/tex]
3. [tex]\(0.75 \times 0.01 = 0.0075\)[/tex]
The decimal form is 0.0075.
12. Annual interest rate:
The formula for simple interest is given by:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Given:
- Principal = 400 Birr
- Interest = 12 Birr
- Time = 4 months (which is [tex]\(\frac{1}{3}\)[/tex] of a year)
To find the annual rate, we use:
[tex]\[ \text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} = \frac{12}{400 \times \frac{1}{3}} \][/tex]
Multiply by 3 to adjust for annual rate:
[tex]\[ \text{Rate} = \frac{12 \times 3}{400} \][/tex]
Convert into percentage by multiplying by 100:
[tex]\[ \text{Rate} = \left(\frac{36}{400}\right) \times 100 = 9\% \][/tex]
The annual interest rate is 9%.
13. Sum of [tex]\(a + b + c\)[/tex]:
Given the ratio [tex]\(a:b:c = 1:3:4\)[/tex] and [tex]\(c = 28\)[/tex],
Convert the ratio into real numbers:
- Let [tex]\(a = x\)[/tex], [tex]\(b = 3x\)[/tex], [tex]\(c = 4x\)[/tex].
Since [tex]\(c = 28\)[/tex], [tex]\[4x = 28\][/tex]
Calculate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{28}{4} = 7\][/tex]
Substitute [tex]\(x\)[/tex] to find [tex]\(a, b, c\)[/tex]:
- [tex]\(a = 7\)[/tex]
- [tex]\(b = 3 \times 7 = 21\)[/tex]
- [tex]\(c = 4 \times 7 = 28\)[/tex]
The sum is:
[tex]\[ a + b + c = 7 + 21 + 28 = 56 \][/tex]
The sum of [tex]\(a + b + c\)[/tex] is 56.
9. Finding the total number of students:
We know that 58% of the total number of students are boys, and there are 840 boys in the school. To find the total number of students, we set up the equation:
[tex]\[ 0.58 \times \text{Total Students} = 840 \][/tex]
To find the total number of students, divide both sides by 0.58:
[tex]\[ \text{Total Students} = \frac{840}{0.58} \approx 1448 \][/tex]
So, the total number of students in the school is approximately 1448. Since this doesn't exactly match any of the multiple-choice options, let's assume the closest correct choice should be selected. However, given this estimate, it might have been a typo in the options.
10. Time for the interest to reach 180 Birr:
The simple interest formula is:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Given:
- Principal = 300 Birr
- Rate = 6% or 0.06
- Interest = 180 Birr
To find the time, rearrange the formula:
[tex]\[ \text{Time} = \frac{\text{Interest}}{\text{Principal} \times \text{Rate}} = \frac{180}{300 \times 0.06} = 10 \][/tex]
It will take 10 years for the interest to become 180 Birr.
11. Decimal form of [tex]\(\frac{3}{4}\%\)[/tex]:
First, convert [tex]\(\frac{3}{4}\%\)[/tex] into its decimal form:
1. [tex]\(\frac{3}{4}\% = \frac{3}{4} \times \frac{1}{100}\)[/tex]
2. [tex]\(\frac{3}{4} = 0.75\)[/tex]
3. [tex]\(0.75 \times 0.01 = 0.0075\)[/tex]
The decimal form is 0.0075.
12. Annual interest rate:
The formula for simple interest is given by:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} \][/tex]
Given:
- Principal = 400 Birr
- Interest = 12 Birr
- Time = 4 months (which is [tex]\(\frac{1}{3}\)[/tex] of a year)
To find the annual rate, we use:
[tex]\[ \text{Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Time}} = \frac{12}{400 \times \frac{1}{3}} \][/tex]
Multiply by 3 to adjust for annual rate:
[tex]\[ \text{Rate} = \frac{12 \times 3}{400} \][/tex]
Convert into percentage by multiplying by 100:
[tex]\[ \text{Rate} = \left(\frac{36}{400}\right) \times 100 = 9\% \][/tex]
The annual interest rate is 9%.
13. Sum of [tex]\(a + b + c\)[/tex]:
Given the ratio [tex]\(a:b:c = 1:3:4\)[/tex] and [tex]\(c = 28\)[/tex],
Convert the ratio into real numbers:
- Let [tex]\(a = x\)[/tex], [tex]\(b = 3x\)[/tex], [tex]\(c = 4x\)[/tex].
Since [tex]\(c = 28\)[/tex], [tex]\[4x = 28\][/tex]
Calculate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{28}{4} = 7\][/tex]
Substitute [tex]\(x\)[/tex] to find [tex]\(a, b, c\)[/tex]:
- [tex]\(a = 7\)[/tex]
- [tex]\(b = 3 \times 7 = 21\)[/tex]
- [tex]\(c = 4 \times 7 = 28\)[/tex]
The sum is:
[tex]\[ a + b + c = 7 + 21 + 28 = 56 \][/tex]
The sum of [tex]\(a + b + c\)[/tex] is 56.
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