Correct Answer: D. Average cost

Correct Answer: D. atmosphere

Correct Answer: D. under-population

Correct Answer: A. fulani

Correct Answer: B. 40°

Correct Answer: A. 1001 101

Explanation

\(\begin{array}{c|c} 2 & 77 \\ \hline 2 & 38 R1 \\ 2 & 19 R0 \\ 2 & 9 R1 \\ 2 & 4 R1 \\ 2 & 2 R0 \\ 2 & 1 R0 \\ & 0 R1\end{array}\)

77_ten = 1001101_two

Correct Answer: D. 1.330m

Correct Answer: C. 6m

Explanation

Here's how to solve the problem step-by-step:

1. Initial Situation:

• The man is 4m in front of the mirror. This is the object distance (u = 4m).

• For a plane mirror, the image is formed behind the mirror at the same distance as the object is in front of it. So, the initial image distance (v = 4m).

• The distance between the man (object) and his image is the sum of the object distance and the image distance:

Distance (man to image) = u + v = 4m + 4m = 8m.

2. Mirror Moves:

• The mirror moves 1m towards the man.

3. New Situation:

• The man's original distance from the initial mirror position was 4m.

• Since the mirror moved 1m closer to the man, the new distance between the man and the mirror is:

New object distance (u') = 4m - 1m = 3m.

• For a plane mirror, the new image will also be 3m behind the new position of the mirror. So, the new image distance (v' = 3m).

• The new distance between the man (object) and his new image is the sum of the new object distance and the new image distance:

New Distance (man to new image) = u' + v' = 3m + 3m = 6m.

Therefore, the distance between the man and his new image is 6m.

The final answer is 6m

Correct Answer: A. 2¹/₂ years

Correct Answer: A) 10s

Explanation

In order to explain this question, we need to understand the concept of diffusion and how it relates to the molecular weight of gases. Diffusion is the process of a substance spreading out to evenly occupy its container or environment. In the case of gases, lighter gases diffuse faster than heavier gases under the same conditions.

Graham's law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be represented as:

\[\frac{Rate_1}{Rate_2} = \sqrt{\frac{Molar\ Mass_2}{Molar\ Mass_1}}\]

Here, we are given that methane (CH₄) diffuses in 20 seconds, and we have to find the time taken for the same volume of sulfur (IV) oxide (SO₂) to diffuse under the same conditions. First, we need to calculate the molar mass of both gases.

The molar mass of methane (CH₄): C = 12, H = 1 (4 hydrogen atoms) = 4, so the molar mass of CH₄ = 12 + 4 = 16 g/mol.

The molar mass of sulfur (IV) oxide (SO₂): S = 32, O = 16 (2 oxygen atoms) = 32, so the molar mass of SO₂ = 32 + 32 = 64 g/mol.

Now, applying Graham's law of diffusion:

\[\frac{Rate_{CH_4}}{Rate_{SO_2}} = \sqrt{\frac{Molar\ Mass_{SO_2}}{Molar\ Mass_{CH_4}}}\]

Let the time taken for SO₂ to diffuse be x seconds. Since rate is inversely proportional to time, we can write:

\[\frac{20}{x} = \sqrt{\frac{64}{16}}\]

Solving for x:

\[x = 20 \times \sqrt{\frac{16}{64}} = 20 \times \frac{1}{2} = 10\]

So, it will take 10 seconds for the same volume of sulfur (IV) oxide to diffuse under the same conditions.