Explanation

To find the average, we need to first convert each fraction to a decimal:

 5/6 = 0.83

 4/3 = 1.33

 3/4 = 0.75

Then, add the decimals and divide by the number of values:

 0.83 + 1.33 + 0.75 = 2.91

 2.91 ÷ 3 = 0.97

Now, convert the average back to a fraction:

 0.97 ≈ 35/36

Explanation

To find the answer, divide 4.036 by 0.04:

4.036 ÷ 0.04 = 100.9

Explanation

In this scenario, we can use the tangent function, which is the ratio of the opposite side (height of the tower, h) to the adjacent side (the horizontal distance, 70m):

Explanation

Zakat is typically 2.5% of the total wealth.

To find the total amount, divide the Zakat paid by 0.025 (8500 ÷ 0.025 = 340,000).

Explanation

(7^a) (7^b) = (7^c) (7^d)

Using the property of exponents, we get:

7^(a+b) = 7^(c+d)

Equating the exponents, we get:

a + b = c + d

Rearranging the terms, we get:

d = a + b - c

Explanation

The correct inequality that represents the relationship between Jerry's estimate and the actual number of marbles in the jar is m - 10 ≤ n ≤ m + 10.

This inequality states that Jerry's estimate, m, is within 10 marbles (inclusive) of the actual number, n. By subtracting 10 from Jerry's estimate and adding 10 to his estimate, you create a range within which the actual number must fall.

For example, if Jerry estimates there are 50 marbles (m = 50), the actual number of marbles (n) must be between 40 (50 - 10) and 60 (50 + 10), inclusive.

Explanation

To find the number of pieces that can be cut, divide the length of the rod (330 cm) by the length of each piece (13.2 cm):

330 cm ÷ 13.2 cm = 25

So, 25 pieces of 13.2 cm can be cut from the 330 cm long rod.

Explanation

The pattern follows the format n² + 1:

• 2² + 1 = 5
• 3² + 1 = 10
• 4² + 1 = 17
• 5² + 1 = 26

Given these, the correct 8th line should follow the same formula:

9² + 1 = 82

Explanation

To solve this, we can start by expressing the given ratio m:n = 3:2 in terms of a variable, let's say x. So, m = 3x and n = 2x.

Now, let's substitute these expressions into the given ratio (4m+5n):(4m-5n):

(4(3x) + 5(2x)) : (4(3x) - 5(2x))

Expanding and simplifying, we get:

(12x + 10x) : (12x - 10x)

22x : 2x

Now, we can divide both terms by 2x to get: 11 : 1

Explanation

Let smallest angle = x

Then largest angle = 2 x − 24°

But x + 2 x − 24° = 180°

⇒3 x − 24° = 180°

⇒3 x = 180° + 24 = 204°

⇒x = 204/3 = 68°

∴ largest angle = 180 − 68° = 112°