The complement of A in U is the set of elements in U that are not in A, which is {1, 3, 5, 7, 9, 10}.

The complement of set A consists of elements in the universal set U that are not in set A. Therefore, the complement is {1, 3, 5}.

The complement of A, denoted A', includes all elements in U that are not in A. Thus, A' = {3, 4, 5}.

Using the principle of inclusion-exclusion, the number of elements in either A or B is: (A + B - Both) = 40 + 30 - 10 = 60. Therefore, elements in neither = U - (A ∪ B) = 100 - 60 = 40.

Doubling one resistance will change the ratio, thus making the bridge unbalanced.

Increasing one resistance will generally cause the bridge to become unbalanced.

Using Raoult's Law, P_solution = X_solvent * P_pure_solvent; 60 mmHg = X_solvent * 80 mmHg; X_solvent = 60/80 = 0.75.

Using Raoult's Law, P_solution = X_solvent * P_solvent^0; 80 = X_solvent * 120; X_solvent = 80/120 = 0.67.

Using Raoult's Law, P_solution = X_A * P_A^0 = 0.6 * 100 mmHg = 60 mmHg.

According to Raoult's Law, P_solution = X_A * P_A^0 = 0.5 * 100 mmHg = 50 mmHg.

According to Raoult's Law, the vapor pressure of the solution is 0.5 * 100 mmHg = 50 mmHg.

Using Raoult's Law: P_solution = X_solvent * P_solvent. X_solvent = P_solution / P_solvent = 80/100 = 0.8, thus X_solute = 1 - X_solvent = 0.2.

Relative lowering of vapor pressure = (P° - P) / P° = (100 - 80) / 100 = 0.2.

Using Raoult's Law, the vapor pressure of the solution is P_solution = P_solvent * X_solvent = 120 * (1/(1+0.2)) = 120 * (1/1.2) = 100 mmHg.

Using Raoult's Law, P_solution = X_solvent * P_solvent^0 = 0.75 * 80 mmHg = 60 mmHg.

Using Raoult's law, the vapor pressure lowering is calculated considering the van 't Hoff factor for NaCl.

Standard deviation = √16 = 4. If the minimum is 0, the maximum can be 4, thus range = 4 - 0 = 4.

Standard deviation = √variance = √16 = 4.

Standard deviation is the square root of variance. Therefore, SD = √16 = 4.

Standard deviation = √25 = 5.

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Cosine of angle = (A · B) / (|A| |B|) = (1*2 + 2*1) / (√5 * √5) = 4/5, angle = cos^(-1)(4/5).

cos(θ) = (a · b) / (|a| |b|). a · b = 1*3 + 2*4 = 11, |a| = √(1^2 + 2^2) = √5, |b| = √(3^2 + 4^2) = 5. Thus, cos(θ) = 11 / (√5 * 5) = 11 / (5√5), θ = 60 degrees.

a + b = (2 + 1, -1 + 3) = (3, 2)

Cross product in 2D = a1*b2 - a2*b1 = 2*3 - (-1)*1 = 6 + 1 = 7

Angle = cos⁻¹((a·b) / (|a||b|)) = cos⁻¹(0) = 90 degrees

Scaled vector = 3 * a = 3 * (2, 2) = (6, 6)

Cross product a × b = 2*1 - 3*4 = 2 - 12 = -10.

Resultant vector a + b = (2+4, 3+1) = (6, 4).

Resulting vector = 2 * A = 2 * (2, 3) = (4, 6).