Using inclusion-exclusion, the percentage of students who play either sport is 70% + 50% - 20% = 100%.

Using inclusion-exclusion, the percentage of students who play either sport is 70% + 50% - 20% = 100%.

7x + 1 ≥ 15 => 7x ≥ 14 => x ≥ 2

Subtracting 4x from both sides gives 3x - 3 = 6, then adding 3 gives 3x = 9, leading to x = 3.

Dividing both sides by 7 gives x = 3.

To solve 7x ≡ 3 (mod 5), we first reduce 7 mod 5 to get 2x ≡ 3 (mod 5). The solution is x ≡ 4 (mod 5), which corresponds to 2.

Since 49 can be expressed as 7^2, we have 7^(2x) = 7^2, thus 2x = 2, leading to x = 1.

Since 1/49 can be expressed as 7^(-2), we have 7^x = 7^(-2), thus x = -2.

49 = 7^2, so x = 2.

If 8 workers take 12 days, then 4 workers will take 12 * (8/4) = 24 days.

The percentage of people who like only sports is 80% - 30% = 50%.

Using inclusion-exclusion, the percentage liking at least one is 80% + 60% - 30% = 110%, which is capped at 100%.

8b + 16 = 48 => 8b = 32 => b = 4.

Dividing both sides by 4 gives 2x ≡ 1 (mod 3). The solution is x = 2.

64 = 8^2, so x = 2.

If A > B and B > C, then by transitive property, A > C is true.

Since A < B and B ≤ C, it follows that A < C.

The roots of the equation x^2 - 10x + 21 = 0 are found using the quadratic formula, yielding a = 3 and b = 7.

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we have 70 = 12^2 - 2ab. Thus, 70 = 144 - 2ab, leading to ab = 37.

a² + b² = (a + b)² - 2ab = 5² - 2*6 = 25 - 12 = 13.

Potential Energy (PE) = m * g * h = 10 kg * 9.8 m/s^2 * 20 m = 1960 J

Using v² = u² + 2gh, v = √(0 + 2 × 10 m/s² × 20 m) = √400 = 20 m/s.

Potential energy = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.

The force due to gravity is F = mg = 10 kg * 9.8 m/s² = 98 N, which rounds to 100 N.

Work done = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.

KE = 0.5 × m × v² = 0.5 × 10 kg × (2 m/s)² = 0.5 × 10 × 4 = 20 J.

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 10 * (4^2) = 80 J

Using F = ma, acceleration a = F/m = 30 N / 10 kg = 3 m/s².

Using F = ma, a = F/m = 50 N / 10 kg = 5 m/s².