The lines are coincident when the determinant of the coefficients is zero, leading to k = 0.

The nature of the intersection can be determined by the slopes, which indicate that the angle is obtuse.

The angle can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes derived from the equation.

The sum of the slopes of the lines is given by -b/a, which is 0 in this case.

The nature of the roots can be determined by the discriminant of the quadratic equation.

The lines are not perpendicular as the condition for perpendicularity is not satisfied.

The condition for the lines to be real and distinct is that the discriminant D must be greater than 0.

For the lines to be perpendicular, the condition a + b = 0 must hold.

For the lines to be coincident, the constant term must be zero.

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.

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.

New mode = 2 (as 4 is removed, 2 is the next most frequent).

Mode is the number that appears most frequently. Here, 4 appears 3 times.

Mode = 3 (most frequent value).

Removing 5 leaves 2, 3, 4, 4, 6. The new mode is 4.

Mode is the value that appears most frequently. Here, 5 appears 3 times.

Removing mode 6 leaves 3, 4, 4, 5, 7. New mode = 4.

Mode is the most frequent value. Here, 7 appears most frequently.

Removing mode 4 leaves {1, 2, 2, 3, 5}. New mode = 2.

Mode is the number that appears most frequently. Here, 3 appears 3 times.

a_4 = 4^2 + 4 = 16 + 4 = 20.