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

Explanation

0.009/x = 0.01

To isolate x, we can divide both sides by 0.009, which gives us:

1/x = 0.01/0.009

1/x = 1.111 (approximately)

Now, take the reciprocal of both sides:

x = 1/1.111

x ≈ 0.9

So, the value of x is approximately 0.9.

Explanation

To find the average, we need to add the numbers and divide by the total count of numbers.

First, let's add the numbers:

0 + 0 + 4 + 10 + 5 + 5 = 24

There are 6 numbers in the list. To find the average, divide the sum by 6:

24 ÷ 6 = 4

So, the average is 4.

Explanation

To find the percentage of the second number to the first, divide the second by the first and multiply by 100:

(1.2x / 1.6x) × 100 = (12/16) × 100 = 75%

Explanation

Let the smaller number be 3x and the larger number be 5x, since their ratio is 3:5.

When 9 is subtracted from each number, the new numbers are 3x - 9 and 5x - 9.

The ratio of these new numbers is 12:23, so we can set up the equation:

(3x - 9) / (5x - 9) = 12/23

Cross-multiplying and simplifying the equation, we get:

69x - 207 = 60x - 108

Solving for x, we get:

9x = 99

x = 11

So, the smaller number is 3x = 3(11) = 33.

Explanation

Explanation

The correct indirect speech is "I asked him why he was working so hard."

The question structure changes to a statement format, and "are" changes to "was" to maintain tense consistency in reported speech.

Explanation

The correct indirect speech is "Ali asked how long it would take to travel from Germany to South Africa."

Here, "will" changes to "would" in reported speech to match the past tense of the reporting verb "asked."