Gravitational potential energy U = mgh, so if mass is tripled, U also triples.

Gravitational potential energy is directly proportional to mass, so it triples.

Using F = G * (m1 * m2) / r^2, F = (6.67 x 10^-11) * (6 x 10^24 * 1) / (6.4 x 10^6)^2 = 9.8 N.

Using g = G * M / R², where G = 6.67 x 10^-11 N m²/kg², M = 6 x 10^24 kg, and R = 6.4 x 10^6 m, we find g ≈ 9.8 m/s².

g = G * M / R² = (6.67 × 10^-11) * (6 × 10^24) / (6.4 × 10^6)² = 9.81 m/s²

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

The gravitational acceleration at the surface of the Earth is given by g = GM/R^2.

The gravitational force F acting on a satellite at height h is given by F = GmM/(R+h)^2, where G is the gravitational constant.

Gravitational acceleration is directly proportional to mass, so if the mass doubles, g also doubles.

Gravitational acceleration is directly proportional to mass; thus, if the mass doubles, g also doubles.

Weight is proportional to mass; thus, if the Earth's mass doubles, the weight of an object on its surface also doubles.

If the mass of the Earth doubles, the gravitational force on an object at its surface would also double.

F = G * (m1 * m2) / r², doubling the mass of Earth doubles the force.

F ∝ M; if M doubles, F also doubles.

Weight is directly proportional to mass. If the Earth's mass doubles, the weight of the object also doubles.

If the mass of the Earth increases, the gravitational force experienced by an object on its surface would increase.

Total sum = Mean * Number of values = 12 * 8 = 96.

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (4 / 20) * 100 = 20%.

Total sum = Mean * Number of values = 30 * 10 = 300.

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (10 / 50) * 100 = 20%.

Total sum = Mean * Number of values = 50 * 10 = 500.

Relative error = (Absolute error / Measured value) = 0.5 / 20 = 0.025 or 2.5%

Absolute error = Relative error * Measured value = 0.02 * 100 = 2.

Relative error = Absolute error / True value. Let true value be x. 0.04 = |75 - x| / x. Solving gives x = 78.

For median to be 7, x must be 7 or less, hence x = 7.

Median = (4 + 5) / 2 = 9 / 2 = 4.5.

Sorted data set: {1, 2, 3, 4, 5}. Median = 3.

Area = (4/3) * √[m1 * m2 * m3] = (4/3) * √[6 * 8 * 10] = 48 cm².

Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s = (6 + 8 + 10)/2 = 12. Area = (4/3) * √(12 * 6 * 4 * 2) = 48.

Mode is the value that appears most frequently in a data set.