Vertically opposite angles are equal. Therefore, if one angle measures 120 degrees, the other angle also measures 120 degrees.

The total resistance in parallel is given by 1/R_total = 1/R1 + 1/R2. Thus, 1/R_total = 1/6 + 1/3 = 1/2, so R_total = 2 ohms.

In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.

Area = base * height = 8 * 5 = 40 cm²

Votes for ruling party = 40% of 1000 = 0.4 * 1000 = 400.

Total days = 20 sessions * 10 days/session = 200 days.

Prevalence rate = (Number of infected / Total population) = 50 / 1000 = 0.05 or 5%.

Total prize money = 1000 + 500 + 250 = $1750.

Speed = Distance / Time = 400 meters / 50 seconds = 8 m/s.

2H2 + O2 → 2H2O. 1 mole of water weighs 18 g, so 2 moles produce 36 g. Thus, 18 g of water is produced from 1 mole of O2.

2 moles of H2 and 1 mole of O2 produce 2 moles of H2O. The molar mass of water is 18 g/mol, so 2 moles produce 36 g.

The side opposite to the 30-degree angle is half the hypotenuse, so it is 10/2 = 5 cm.

In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees angles are in the ratio 1:√3.

In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees are in the ratio 1:√3.

Total resistance R_total = R1 + R2 = 4 Ω + 8 Ω = 12 Ω. Using Ohm's Law, I = V/R = 12 V / 12 Ω = 1 A.

Expected male patients = 70% of 400 = 0.7 * 400 = 280.

Number of people preferring tea = 70% of 200 = 0.7 * 200 = 140.

The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.

Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180, so 9x = 180, x = 20. The largest angle is 4x = 80 degrees.

The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.

Total points scored = 25 points/set * 4 sets = 100 points.

In an adiabatic process, as the temperature decreases, the pressure also decreases due to the ideal gas law.

The coefficient of x^3 in (2x - 3)^4 is given by 4C1 * (2)^3 * (-3)^1 = 4 * 8 * (-3) = -96. The coefficient is -108.

Using the binomial theorem, the coefficient of x^5 in (3x - 4)^7 is given by 7C5 * (3)^5 * (-4)^2 = 21 * 243 * 16 = 21 * 3888 = 81588.

Using the binomial theorem, the coefficient of x^4 in (x + 3)^6 is given by 6C4 * (3)^2 = 15 * 9 = 135.

To find x, subtract 5 from both sides: 3x = 20 - 5 = 15. Then divide by 3: x = 15 / 3 = 5.

From 2 moles of Fe, 2 moles of FeCl3 are produced. Therefore, from 4 moles of Fe, 4 moles of FeCl3 are produced.

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

The longest side of triangle GHI is GI, which measures 26 cm.