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.

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

'110' (6 in decimal) + '101' (5 in decimal) = '1011' (11 in decimal).

The order is E < D < B < A < C, indicating E read the least.

The expression with a coefficient of 5 for x and a constant term of -3 is 5x - 3.

Since A is to the left of B and C is to the right of A, D being to the left of C means A is indeed to the right of D.

Since A is taller than B and B is shorter than C, it follows that C is taller than B.

Since X is to the right of Y and Z is to the left of Y, Y must be in the middle.

Let the base be 'b'. Then, A3 = 10*b + 3 = 163. Solving gives b = 12.

The probability that both are smokers is 0.3 * 0.3 = 0.09.

The probability that it does not rain = 1 - P(rain) = 1 - 0.1 = 0.9.

If the ratio of boys to girls is 3:2, then for every 3 boys, there are 2 girls. If there are 30 boys, we can set up the proportion: 3/2 = 30/x. Solving for x gives us x = 20. Therefore, there are 20 girls.

Each letter is shifted by one position in the alphabet, so 'BIRD' becomes 'CJSF'.

Let the number of managers be x. According to the ratio, 5/2 = 70/x. Cross-multiplying gives 5x = 140, so x = 28.

Since 125 can be expressed as 5^3, we have 5^(x+1) = 5^3, thus x + 1 = 3, leading to x = 2.