Explanation:
First, find the total sum of grades for the class:
Total sum of grades = Average grade × Number of students = 77 × 50 = 3850
Now, find the total sum of grades for male students:
Sum of grades for male students=80×20=1600
Subtract the sum of grades for male students from the total sum of grades to get the sum of grades for female students:
Sum of grades for female students=3850−1600=2250
Since there are 30 female students (50 total students - 20 male students), find the average grade mark for female students:
Average grade mark for female students = 2250/30 = 75
Explanation:
Length of wire = 80 cm
Length of rectangle = 3 times width
Let's denote the width of the rectangle as w cm.
Perimeter of rectangle = 80 cm
2×(length+width)=80
2×(3w+w)=80
2×4w=80
w=10
So, the width of the rectangle = 10 cm.
Length of rectangle = 3w=3×10=30 cm.
Area of rectangle = length × width = 30×10=300 square centimeters.
Explanation:
Mean of 30 numbers is 520.
Calculate the sum of the original 30 numbers:
Sum = Mean×Number of numbers=520×30=15600
For the new set:
20 numbers increased by 12 each, so add 20×12=240 to the sum.
10 numbers decreased by 6 each, so subtract 10×6=60 from the sum.
The net change in sum is 240−60=180.
Add this to the original sum to get the new sum: 15600+180=15780.
Now, find the new mean: New mean =
15780/30 = 526
So, the mean of the new set of numbers is 526. Therefore, the correct option is C) 5260.
Explanation:
To find the mode (the most frequently occurring value) of John’s grades:
John’s grades: 58, 80, 56, 58, 64, 80, 56, 90, 80
Count the frequency of each grade:
58 appears twice
80 appears three times
56 appears twice
64 appears once
90 appears once
The grade that appears most frequently (the mode) is 80.
Explanation:
If W < 25, it means that W is less than 25. However, there is no constraint on how small W can be as long as it's less than 25. Therefore, W could also be greater than -25.
Explanation:
First, let's solve the equation 4(3x - 8) = 25:
Expand the expression: 4 * 3x - 4 * 8 = 25
This gives us: 12x - 32 = 25
Add 32 to both sides: 12x = 57
Divide both sides by 12: x = 57/12 = 4.75
Now, let's find the value of 3x - 10 when x = 4.75:
3 * 4.75 - 10 = 14.25 - 10 = 4.25
Therefore, none of the provided options match the result.
Explanation:
To find the average of the remaining numbers after removing the largest one:
Find the sum of all numbers (21 numbers) = 30 * 21 = 630.
Subtract the value of the largest number (50) from the sum: 630 - 50 = 580.
Divide the adjusted sum by the new number of numbers (21 - 1 = 20): 580 / 20 = 29.
So, the average of the remaining numbers is 29.
Explanation:
To find a positive integer that leaves a remainder of 5 when divided by 7 and a remainder of 8 when divided by 11, we can test numbers that leave a remainder of 5 when divided by 7 until we find one that also leaves a remainder of 8 when divided by 11.
Starting with 5,12,19,26,…, we find that 19 satisfies both conditions.
Explanation:
To find out how many more boys there are than girls in the class:
1. Determine the ratio of boys to girls: 7 boys for every 5 girls.
2. Calculate the total number of parts in the ratio: 7+5=12.
3. Divide the total number of students by the total parts in the ratio to find the value of each part: 60/12 = 5.
4. Multiply the value of each part by the number of boys and girls to find their respective numbers: Boys: 7×5=35, Girls: 5×5=25.
5. Subtract the number of girls from the number of boys to find how many more boys there are: 35−25=10.
So, there are 10 more boys than girls in the class.
Explanation:
To find out how many years ago Majid was three times as old as Zahid:
Let x be the number of years ago.
At that time:
*Majid's age: 42−x
*Zahid's age: 32−x
According to the given condition, Majid was three times as old as Zahid: 42−x=3(32−x)
Let's solve for x:
42−x=96−3x
2x=54
x=27
So, 27 years ago Majid was three times as old as Zahid.
Explanation:
To find the lengths of the sides of the triangle proportional to 3, 4, and 5:
1. Sum the proportions: 3 + 4 + 5 = 12.
2. Divide the perimeter by the sum of proportions: 240 / 12 = 20.
3. Multiply each proportion by the result:
Side 1: 3 × 20 = 60
Side 2: 4 × 20 = 80
Side 3: 5 × 20 = 100
Therefore, the largest side of the triangle is 100.
