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

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

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.

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%.

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.

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.

Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.

Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right triangle.

Set y = 0: 2x + 6 = 0; x = -3.

Setting x = 0 in the equation gives 3y = 12, thus y = 4. The point of intersection is (0, 4).

Rearranging gives y = (4/3)x + 4. The slope is -4/3, so a parallel line has the same slope.

Substituting (1, 2) gives 2 = 3(1) + c, so c = -1.

Using y = mx + c: 3 = 2(2) + c => c = -1.

Mean of 10 numbers = 50, so total sum = 500. Sum of last 5 numbers = 500 - 200 = 300. Mean of last 5 = 300 / 5 = 60.

The sum of the numbers is calculated as mean * number of items = 25 * 12 = 300.