Substituting x = 2: 2(2) + 3y = 12 => 4 + 3y = 12 => 3y = 8 => y = 8/3 ≈ 2.67, closest is 3.

Substituting x = 0 in 2(0) + 3y = 6 gives 3y = 6, so y = 2.

Substituting x = 0: 3(0) + 4y = 12 => 4y = 12 => y = 3.

Slope = (6-2)/(4-1) = 4/3.

Slope = (7-3)/(4-2) = 4/2 = 2.

Length = √[(1-7)² + (2-2)²] = √[36] = 6.

Cost per kg = 200 / 5 = 40. Cost of 8 kg = 40 * 8 = 320.

Cost per kg = 200 / 5 = 40. Cost of 8 kg = 40 * 8 = 320.

The numbers are already in order. Since there are 6 numbers, the median is the average of the 3rd and 4th numbers: (6 + 8) / 2 = 7.

The mode is 10, as it appears most frequently (three times) in the data set.

Mean = (2 + 4 + 4 + 4 + 5 + 5 + 7 + 9) / 8 = 5. 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 = 4.

All values are the same, so variance = 0.

Mean = (5 + 7 + 9 + 11) / 4 = 8. Variance = [(5-8)² + (7-8)² + (9-8)² + (11-8)²] / 4 = 5.

Volume = Width x Depth x Length. Increase in volume = Width x 2 m x 100 m. Assuming width = 1 m, Volume = 1 m x 2 m x 100 m = 200 m³.

Volume = Length × Width × Depth. If width is constant, Volume increase = 1000 m × Width × 2 m = 2000 m³.

Area = (d1 * d2) / 2 = (8 * 6) / 2 = 48 cm²

Area = π * (radius)² = π * (5)² = 25π cm²

Circumference = πd = π(12) = 12π cm.

The circumference of a circle is given by C = πd, where d is the diameter. Here, C = π * 14 cm ≈ 44 cm.

Circumference = πd = π(20) = 20π cm.

If diameter increases by 50%, radius increases by 25%. Area increases by (new area - old area)/old area = (1.25² - 1) × 100% = 56.25%.

Circumference = π * diameter = π * 10.0 cm ≈ 31.4 cm. Uncertainty in circumference = π * 0.1 cm ≈ 0.314 cm.

The volume of a sphere is given by V = (4/3)πr³. The radius r = diameter/2 = 5 cm. Thus, V = (4/3)π(5)³ = (4/3)π(125) = 500/3 π cm³.

The product of the roots is given by c/a. Here, c = 6 and a = 1, so αβ = 6.

The discriminant must be negative for no real roots: 5^2 - 4*1*k < 0, which simplifies to 25 - 4k < 0, or k > 25.

For both roots to be negative, the sum of the roots (which is -5) must be negative, and the product (k) must be positive. Thus, k > 0.

The number of terms in the expansion of (x + y)^n is n + 1. Therefore, n + 1 = 15, which gives n = 14.

Power P = 1/f (in meters). Thus, P = 1/0.25 = +4 D.

The distance from the focus to the directrix is 4, so the equation is x^2 = 8y.

The numbers are already in order. The median is the average of the 5th and 6th numbers: (5 + 6) / 2 = 5.5.