f'(x) = 3x^2 - 3. Setting f'(x) = 0 gives x = ±1. f(1) = -2.

The solutions to z^2 = -1 are z = i and z = -i.

The determinant is 0 because the first column is repeated.

By definition, \( \tan(\tan^{-1}(x)) = x \). Therefore, \( \tan(\tan^{-1}(3)) = 3 \).

The determinant is \( 0*0 - 1*1 = 0 - 1 = -1 \).

|z| = √((-3)^2 + (4)^2) = √(9 + 16) = √25 = 5.

|z| = √(4^2 + (-3)^2) = √(16 + 9) = √25 = 5.

The modulus |z| = 4, as it is the coefficient in the polar form.

|z|^2 = 4^2 + (-3)^2 = 16 + 9 = 25.

Na2SO4 dissociates into 3 ions (2 Na⁺ and 1 SO4²⁻), so i = 3.

NaCl dissociates into two ions (Na+ and Cl-), so the van 't Hoff factor (i) is 2.

The van 't Hoff factor (i) is equal to the number of particles the solute dissociates into. For a strong electrolyte that dissociates into 3 ions, i = 3.

The van 't Hoff factor (i) for glucose is 1, as it does not dissociate in solution.

For a non-electrolyte solute, the van 't Hoff factor (i) is 1, as it does not dissociate into ions.

Vapor pressure = P°_solvent * (n_solvent / (n_solvent + n_solute)) = 23.76 * (55.5 / (55.5 + 0.1)) = 22.88 mmHg

Using Raoult's law, P_solution = X_solvent * P°_solvent = (9/10) * 100 mmHg = 90 mmHg.

Vapor pressure lowering = (moles of solute / total moles) * P0 = (1 / (1 + 3)) * P0 = 0.25 P0, so vapor pressure = P0 - 0.25 P0 = 0.75 P0.

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (10 / 11) * P0 = 0.909 P0.

Using Raoult's law, P_solution = X_solvent * P°_solvent. X_solvent = 3/(1+3) = 0.75, so P_solution = 0.75 * 100 mmHg = 75 mmHg.

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (3 / (3 + 1)) * P0 = 0.75 P0.

Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (9 / 10) * P0 = 0.9 P0.

The vapor pressure of a solution containing a non-volatile solute is lower than that of the pure solvent due to the presence of solute particles.

Mean = 5.2; Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²] / 5 = 2.56.

Mean = 3. Variance = [(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 = 2.

Mean = 5.0; Variance = [(2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2] / 8 = 2.5.

Mean = 7.8, Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²] / 5 = 3.

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

The vertex form of a parabola is y = a(x - h)^2 + k. Here, h = 1 and k = 4, so the vertex is (1, 4).

The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.