5.5 / 1.5 = 3.6667

There are 3 even numbers (2, 4, 6) out of 6 possible outcomes, so the probability is 3/6 = 1/2.

Using sine, opposite = 12 * sin(30) = 12 * (1/2) = 6 meters.

sin(θ) = √(1 - cos²(θ)) = √(1 - 0.36) = √0.64 = 0.8

f(-1) = 4(-1)^2 + 3(-1) - 5 = 4 - 3 - 5 = -4.

g(1) = 1^3 - 2(1^2) + 1 - 2 = 1 - 2 + 1 - 2 = -2.

p(2) = 2^3 - 3(2^2) + 4 = 8 - 12 + 4 = 0.

Using the identity sin²(θ) + cos²(θ) = 1, we have cos²(θ) = 1 - 0.6² = 1 - 0.36 = 0.64. Thus, cos(θ) = √0.64 = 0.8.

Using the identity tan(θ) = sin(θ)/cos(θ), we can find sin(θ) = 3/5.

Area = πr²; 154 = (22/7) * r²; r² = 154 * (7/22) = 49; r = 7 m.

Area = πr², r² = 50.24/π ≈ 16, r ≈ 4 m.

New area = (2L) × (W/2) = L × W = original area; area doubles.

It is a right triangle because 9² + 12² = 15² (81 + 144 = 225).

The probability of the event not occurring is 1 - 0.2 = 0.8.

Substituting x = 1 gives 1^2 + 2*1 + k = 0 => 1 + 2 + k = 0 => k = -3.

Area = πr²; if radius is doubled, new area = π(2r)² = 4πr², so area increases by a factor of 4.

Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.

Using the sum of roots formula, p = -(4 + (-2)) = -2.

The sum of the roots a + b = -(-7) = 7.

10.5 - 4.5 = 6.0

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

The only outcome without a head is TT, so the probability of at least one head is 3/4.

3.5 * 2.5 = 8.75

3 + 2 = 5

Using the binomial formula: P(X=3) = C(5,3) * (0.5)^3 * (0.5)^(5-3) = 10 * 0.125 * 0.25 = 0.3125.

The sum of angles in a triangle is 180°. Third angle = 180° - 45° - 55° = 80°.

No, because the sum of the lengths of the two shorter sides (7 + 5 = 12) must be greater than the length of the longest side (10).

The maximum length of the third side is less than the sum of the other two sides: 7 + 24 = 31 cm.

Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 36; 12x = 36; x = 3. Longest side = 5x = 15 cm.

The roots can be found using the factorization method: (x-2)(x-3) = 0, hence x = 2 and x = 3.