'210' in base 3 is 2*3^2 + 1*3^1 + 0*3^0 = 18 + 3 + 0 = 21. Therefore, '102' in base 3 is 1*3^2 + 0*3^1 + 2*3^0 = 9 + 0 + 2 = 11.

'B' represents 11 in the same system where 'A' is 10.

'AB' means A*base + B = 11. Since A=10, we have 10*base + B = 11, so B=1.

'B' (18) is a multiple of 'A' (12) since 18 can be expressed as 12 multiplied by 1.5.

'A' can be 3 or 4 (factors of 12), and 'B' can be 3, 6, or 9 (multiples of 3). The only combination that fits is 3 and 4, which gives us 24.

'A' can be 1, 2, 3, 4, 6, or 12 (factors of 12) and 'B' can be 3, 6, 9, 12, etc. The only combination that fits is A=3 and B=12, which gives us 36.

In this case, A must be a factor of 12 (1, 2, 3, 4, 6, 12) and B must be a multiple of 3 (3, 6, 9, 12). The pair (2, 6) satisfies both conditions.

The number 1234 is expressed in base 8, as indicated by the powers of 8 used in its representation.

If the original number is x, then x + 12 is a multiple of 5. This implies that x must be one more than a multiple of 5.

If we add 12 to 8, we get 20, which is a multiple of 5.

A number is divisible by 3 if the sum of its digits is divisible by 3.

'B2' in this system is 11*12^1 + 2*12^0 = 132 + 2 = 134 in decimal.

'210' in base 4 is calculated as 2*4^2 + 1*4^1 + 0*4^0 = 32 + 4 + 0 = 36.

'123' in base 3 = 1*3^2 + 2*3^1 + 3*3^0 = 27. '321' in base 3 = 3*3^2 + 2*3^1 + 1*3^0 = 81.

'23' in this system is 15. '32' would represent 22 in decimal.

The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 30 degrees, then the number of sides is 360 / 30 = 12.

In a regular polygon, each interior angle can be calculated using the formula (n-2) * 180/n. Setting this equal to 120 degrees and solving for n gives n = 6, indicating a hexagon.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides n = 360 / 30 = 12.

The sum of the exterior angles of any polygon is 360 degrees. If each exterior angle is 45 degrees, the number of sides is 360 / 45 = 8.

Let the number of cars be x. According to the ratio, 3/2 = 120/x. Cross-multiplying gives 3x = 240, so x = 80.

Let the number of cars be x. According to the ratio, 3/2 = 120/x. Cross-multiplying gives 3x = 240, so x = 80.

If the ratio of men to women is 3:2, then for every 3 men, there are 2 women. If there are 120 men, we can set up the proportion: 3/2 = 120/x. Solving for x gives x = 80. Therefore, there are 80 women.

If the ratio of men to women is 3:2, then for every 3 men, there are 2 women. If there are 120 men, then the number of women can be calculated as follows: (2/3) * 120 = 80 women.

If the ratio of men to women is 3:4, then for every 3 men, there are 4 women. If there are 120 men, we can set up the proportion: 3/4 = 120/x. Cross-multiplying gives us 3x = 480, so x = 160. Therefore, there are 160 women.

If the ratio of men to women is 3:4, then for every 3 men, there are 4 women. If there are 120 men, we can set up the proportion: 3/4 = 120/x. Solving for x gives x = 160. Therefore, there are 160 women.

The inscribed angle is half the measure of the central angle that subtends the same arc. Therefore, the inscribed angle measures 80/2 = 40 degrees.

The angles subtended by the same chord at the circumference are equal.

A radius that is perpendicular to a chord at its endpoint bisects the chord.

The angle subtended at the circumference is half the angle subtended at the center. Therefore, the angle at the circumference is 80/2 = 40 degrees.

The angle subtended at the circumference is half the angle subtended at the center. Therefore, it is 80/2 = 40 degrees.