The decimal number 5 is represented as 21 in base-3 (2*3^1 + 1*3^0 = 5).

'210' in base-3 is 2*3^2 + 1*3^1 + 0*3^0 = 18 + 3 + 0 = 21 in decimal.

To add in base-3, convert to decimal: 12 (base-3) = 3 + 2 = 5 (decimal) and 21 (base-3) = 2 + 0 = 2 (decimal). The sum is 5 + 2 = 7 (decimal), which is 21 in base-3.

'132' in base 4 is calculated as 1*4^2 + 3*4^1 + 2*4^0 = 16 + 12 + 2 = 30.

The sum of '12' and '21' in base-4 is '30' in base-4.

In base-4, the sum of 3 and 2 is 11 (3 + 2 = 5 in decimal, which is 11 in base-4).

To convert from base-5 to decimal, multiply each digit by 5 raised to the power of its position (from right to left, starting at 0). Thus, 2*5^2 + 4*5^1 + 3*5^0 = 2*25 + 4*5 + 3*1 = 50 + 20 + 3 = 73.

2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

In base-5, '23' is 2*5 + 3 = 13 and '14' is 1*5 + 4 = 9. Their sum is 22 in decimal, which is '42' in base-5.

In base-5, '34' is 3*5 + 4 = 19 and '21' is 2*5 + 1 = 11. Their sum is 30, which is '100' in base-5.

The base-5 number 243 is calculated as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 60 in decimal.

The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

In base-5, the decimal number 10 is represented as 20.

In base-5, the decimal number 12 is represented as 22 (2*5^1 + 2*5^0 = 12).

In base-5, the decimal number 7 is represented as 12, since 1*5^1 + 2*5^0 = 5 + 2 = 7.

In a base-5 numeral system, valid digits are 0, 1, 2, 3, and 4; thus, 5 is not valid.

'12' in base-6 is 1*6 + 2 = 8. '3' is 3. Their product is 8*3 = 24, which is '42' in base-6.

'24' in base-6 is 2*6 + 4 = 16 and '13' is 1*6 + 3 = 9. Their product is 16*9 = 144, which is '100' in base-6.

In base-6, '5' * '2' = 10 in decimal, which is '12' in base-6.

To convert from base-7 to decimal, calculate 3*7^2 + 4*7^1 + 5*7^0 = 3*49 + 4*7 + 5 = 147 + 28 + 5 = 180.

7*5 = 35 in decimal, which is '43' in base-8.

Total points scored = 15 + 20 = 35. Average score per half = 35 / 2 = 17.5.

Total points scored = 15 + 20 = 35. The ratio of points scored in the first half to total points is 15:35, which simplifies to 3:7.

Since Team X scored more points than Team Y, Team X won the game.

If component A has a higher vapor pressure than component B, the solution will show positive deviation from Raoult's Law.

The mole fraction of B can be calculated as 1 - mole fraction of A = 1 - 0.6 = 0.4.

Total vapor pressure = P_A + P_B = (0.75 * 80) + (0.25 * 40) = 60 + 10 = 70 mmHg.

The total vapor pressure is the sum of the partial pressures: P_total = P_A + P_B = 80 mmHg + 40 mmHg = 120 mmHg.

Total vapor pressure = (X_A * P_A^0) + (X_B * P_B^0) = (0.4 * 150) + (0.6 * 50) = 60 + 30 = 90 mmHg.

Using Raoult's Law, the vapor pressure of the solution = (0.6 * 80 mmHg) + (0.4 * 40 mmHg) = 64 mmHg.