Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.

The number of arrangements of 4 distinct books is 4! = 24.

The number of arrangements of 4 distinct books is 4! = 24.

The balanced equation is 4Al + 3O2 → 2Al2O3, which shows that 4 moles of Al produce 2 moles of Al2O3.

Molality (m) = moles of solute / kg of solvent = 4 moles / 2 kg = 2 m.

In a 1:4 ratio, the total parts = 1 + 4 = 5. Sugar = (1/5) * 40 = 8 liters.

The number of students who like only Mathematics is 40 - 10 = 30.

The number of students who like only Mathematics is 40 - 10 = 30.

The number of students who play only cricket is 40 - 10 = 30.

Using inclusion-exclusion, the total is 40 + 30 - 10 = 60.

The percentage of people who like either tea or coffee is 45% + 35% - 10% = 70%. Therefore, those who like neither = 100% - 70% = 30%.

The percentage of people who like either tea or coffee is 45% + 35% - 15% = 65%. Therefore, those who like neither is 100% - 65% = 35%.

The percentage of people who prefer only tea is |Tea| - |Both| = 45% - 15% = 30%.

Solving gives 4x > 8, thus x > 2. The smallest integer is 3.

The multiplicative inverse of 4 mod 9 is 7, since 4 * 7 = 28 ≡ 1 (mod 9).

Dividing both sides by 4 gives x ≡ 2 (mod 3), so the smallest non-negative solution is 2.

Dividing the equation by 4 gives x ≡ 2 (mod 3). The smallest non-negative solution is x = 2.

4z + 8 = 32 => 4z = 24 => z = 6.

Since 1/16 can be expressed as 4^(-2), we have 4^(x-1) = 4^(-2), thus x - 1 = -2, leading to x = -1.

Since 64 can be expressed as 4^3, we have 4^(x-1) = 4^3, thus x - 1 = 3, leading to x = 4.

Since 64 = 4^3, we have x = 3.

5 cats catch 5 mice in 5 minutes, so 1 cat catches 1 mouse in 5 minutes. To catch 100 mice in 50 minutes, we need 20 cats.

CaCO3 → CaO + CO2. Molar mass of CaCO3 = 100 g, CaO = 56 g. 5 g of CaCO3 produces (5 g * 56 g) / 100 g = 2.8 g of CaO.

Total salt = (0.2*5) + (0.3*15) = 1 + 4.5 = 5.5 liters. Total volume = 5 + 15 = 20 liters. Concentration = (5.5/20)*100 = 27.5%.

Molality (m) = moles of solute / kg of solvent = 5 moles / 1 kg = 5 m.

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Each mole of NaCl dissociates into 1 mole of Na+ ions. Therefore, 5 moles of NaCl will produce 5 moles of Na+ ions.

Let the number be x. The equation is 5x - 3 = 12. Adding 3 to both sides gives 5x = 15. Dividing by 5 gives x = 3.

If 5 workers take 10 days, 10 workers will take 10/2 = 5 days.

Work done = Workers * Days. Total work = 5 * 10 = 50 worker-days. For 10 workers, Days = Total work / Workers = 50 / 10 = 5 days.