Explanation

Sum of the ages of 3 friends =3×23= 69 years

Sum of the ages of 4 friends =4×23= 92 years

∴ Age of 4th friend = 92 years - 69 years = 23 years.

Explanation

0.005 × 0.2 = 0.001

So, the product of 0.005 and 0.2 is 0.001.

Explanation

Total weight of (36 + 44) Students,

= (36 × 40 + 44 × 35) kg

= 2980 kg

Therefore average weight of the whole class,

= 298080 kg.

Therefore average weight = 37.25 kg.

Explanation

Explanation

Let the two-digit number be xy, where x is the tens digit and y is the units digit.
The sum of its digits is x + y.
The number is three times the sum of its digits, so we can write an equation: xy = 3(x + y).
Simplify the equation: 10x + y = 3x + 3y.
Rearrange the equation to get: 7x = 2y.
Now, if 45 is added to the number, the digits are reversed, so we can write another equation: xy + 45 = yx.
Simplify the equation: 10x + y + 45 = 10y + x.
Rearrange the equation to get: 9x = 9y - 45.
Divide both sides by 9 to get: x = y - 5.
Now we have two equations:

1. 7x = 2y

2. x = y - 5

Substitute the second equation into the first equation:
7(y - 5) = 2y
Expand and simplify:
7y - 35 = 2y
5y = 35
y = 7
Now that we have found y, substitute it back into one of the original equations to find x:
x = y - 5
x = 7 - 5
x = 2
So, the original number is 27.

Explanation

Let's say the number of girls is x. Then, the number of boys is 2x (since there are twice as many boys as girls).

Total students = x (girls) + 2x (boys) = 3x

Now, let's calculate the number of students who failed:

Girls who failed = 45% of x = 0.45x

Boys who failed = 30% of 2x = 0.6x

Total students who failed = 0.45x + 0.6x = 1.05x

Now, let's calculate the number of students who passed:

Total students who passed = Total students - Total students who failed

= 3x - 1.05x

= 1.95x

Percentage of students who passed = (1.95x / 3x) × 100%

= 65%

Explanation

Explanation

Initially, the total height of the 14 boys = Average height x Number of boys = 5.3 x 14 = 74.2 feet

After the new boy joined, the total height of the 15 boys = New average height x Total number of boys = 5.25 x 15 = 78.75 feet

Since the total height increased by the height of the new boy, we can set up the equation:

74.2 + New boy's height = 78.75

Subtract 74.2 from both sides:

New boy's height = 78.75 - 74.2

New boy's height = 4.55 feet

So, the new boy's height is 4.55 feet.

Explanation

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Given the area is 98.56 cm^2, we can set up the equation:

98.56 = πr^2

Now, divide both sides by π (approximately 3.14):

r^2 = 98.56 / 3.14

r^2 = 31.36

r = √31.36

r ≈ 5.6

Now that we have the radius, we can find the circumference using the formula:

C = 2πr

C ≈ 2 × 3.14 × 5.6

C ≈ 35.2

So, the circumference is approximately 35.2 cm.

Explanation

3889 + 12.952 - X = 3854.002

First, combine the constants on the left side:

3901.952 - X = 3854.002

Now, subtract 3854.002 from both sides:

47.95 - X = 0

Subtract 47.95 from both sides:

-X = -47.95

Multiply both sides by -1:

X = 47.95