What percentage of 0.75 is 0.45?
A. $50 \%$
B. $30 \%$
C. $36 \%$
D. $60 \%$
Arrange the following fractions in ascending order.
A. $\frac{2}{3}, \frac{3}{4}, \frac{5}{8}, \frac{7}{12}$
B. $\frac{7}{12}, \frac{5}{8}, \frac{2}{3}, \frac{3}{4}$
C. $\frac{5}{8}, \frac{7}{12}, \frac{3}{4}, \frac{2}{3}$
D. $\frac{3}{4}, \frac{5}{8}$
The average score of 30 students in a mathematics test is 6. If 28 out of 30 students obtained a total of 160 marks, find the average mark of the two remaining students.
A. 4
B. 20
C. 10
D. 6
In the diagram below, calculate the value of X.
A. 164
B. 6
C. 20
D. 36
What is the sum of $15438, 2431, 1626$ and 502492?
A. 520897
B. 421987
C. 521987
D. 520789
Answer (2)
Calculate the percentage: 0.75 ∗ ( x /100 ) = 0.45 , which gives x = 60 .
Order the fractions: 12 7 , 8 5 , 3 2 , 4 3 .
Calculate the sum: 15438 + 2431 + 1626 + 502492 = 521987 .
The final answers are: 1. 60% , 2. 12 7 , 8 5 , 3 2 , 4 3 , 3. Cannot be solved due to inconsistencies, 4. Cannot be solved without the diagram, 5. 521987 .
Explanation
Introduction Let's tackle these math problems one by one!
Percentage Calculation Question 1: What percentage of 0.75 is 0.45? To find the percentage, we set up the equation: 0.75 × 100 x = 0.45 . Solving for x , we get x = 0.75 0.45 × 100 = 60 . So the answer is 60%.
Fraction Ordering Question 2: Arrange the fractions 3 2 , 4 3 , 8 5 , 12 7 in ascending order. Converting these fractions to decimals, we have: 3 2 ≈ 0.667 , 4 3 = 0.75 , 8 5 = 0.625 , 12 7 ≈ 0.583 . Arranging these in ascending order, we get: 12 7 , 8 5 , 3 2 , 4 3 .
Average Score Calculation Question 3: The average score of 30 students is 6. If 28 students scored 160 marks, find the average mark of the two remaining students. There seems to be an error in the problem statement. It's highly improbable for 28 students to score 160 each when the average of 30 students is only 6. I will assume that the average score of 30 students is 'a'. Calculate the total score of the 30 students: 30 × a . Calculate the total score of the 28 students: 28 × 160 = 4480 . Let the sum of the scores of the remaining two students be S. Then S = 30 × a − 4480 . Calculate the average score of the two remaining students: S /2 . However, since the average score of 30 students is 6, the problem statement is incorrect. Assuming the average score of the 30 students is 'a', we have 30 a = 180 . This is not possible since 28 students scored 160 each. Let's assume the average score of the 30 students is 'x'. Then 30 x = 28 × 160 + 2 y , where y is the average score of the remaining two students. 30 x = 4480 + 2 y . If we assume the average score of the 30 students is 6, then 180 = 4480 + 2 y , which gives 2 y = − 4300 , so y = − 2150 . This is not possible. There must be a typo in the question. Let's assume the 28 students scored an average of 'b' marks. Then 30 × 6 = 28 b + 2 y . 180 = 28 b + 2 y . If we assume b = 5, then 180 = 140 + 2 y , so 2 y = 40 , and y = 20 . So, if the 28 students scored an average of 5 marks, the remaining two students would have an average of 20. However, the question states that 28 students scored 160 marks, which makes the question impossible to solve with the given information. Assuming the average score of the 30 students is 'x', we have 30 x = 28 × 160 + 2 y , where y is the sum of the scores of the remaining two students. 30 x = 4480 + 2 y . If the average score of the 30 students is 6, then 30 × 6 = 180 . So 180 = 4480 + 2 y , which means 2 y = − 4300 , and y = − 2150 . This is impossible. There must be a typo in the question. I will assume that the average score of the 30 students is 160. Then 30 × 160 = 28 × 160 + 2 y . 4800 = 4480 + 2 y . 2 y = 320 . y = 160 . The average mark of the two remaining students is 160.
Missing Diagram Question 4: In the diagram below, calculate the value of X. Since the diagram is not provided, this question cannot be solved.
Sum Calculation Question 5: What is the sum of 15438 , 2431 , 1626 and 502492? Adding these numbers, we get 15438 + 2431 + 1626 + 502492 = 521987 .
Conclusion Final Answers: 1. The percentage is 60%. 2. The fractions in ascending order are 12 7 , 8 5 , 3 2 , 4 3 . 3. Due to inconsistencies in the problem statement, I'm unable to provide a reasonable answer for the average score of the remaining two students. Assuming the average score of the 30 students is 160, the average score of the two remaining students is 160. 4. Cannot be solved without the diagram. 5. The sum is 521987.
Examples
Understanding percentages is crucial in everyday life, from calculating discounts while shopping to understanding interest rates on loans. Ordering fractions helps in cooking when you need to measure ingredients accurately. Calculating averages is useful in sports to determine a player's performance or in finance to analyze investment returns. These basic math skills are fundamental for making informed decisions in various real-world scenarios.
The answers to the questions are: 1. 60% (Option D), 2. Order is 12 7 , 8 5 , 3 2 , 4 3 (Option B), 3. Average mark is 10 (Option C), 4. Sum is 521987 (Option C).
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