Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Using Vieta's formulas, the sum of the roots is 7 and the product is k = 10.

Using Vieta's formulas, the sum of the roots is -b/a = -12/3 = -4.

Unit vector = A/|A| = (6i - 8j)/√(6^2 + (-8)^2) = (6i - 8j)/10 = 3/5 i - 4/5 j.

To find the vertex, use the formula x = -b/(2a). Here, a = 2, b = -4, so x = 1. Plugging x = 1 into the equation gives y = -1.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Possible outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 6 * 6 = 36. Probability = 6/36 = 1/6.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Perpendicular lines intersect at right angles, which measure 90 degrees.

Vertically opposite angles are equal. Therefore, the measure of the vertically opposite angle is also 70 degrees.

Adjacent angles formed by intersecting lines are supplementary. Therefore, 180 - 70 = 110 degrees.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.

The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.

The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.

The 4th term is given by C(6,3) * (3x)^3 * (2)^3 = 20 * 27x^3 * 8 = 4320x^3.

The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.

The absolute value of -12 is 12.

The absolute value of -7 is 7.

The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.

The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.

Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm²

Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².

Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².

Area = side² = 8² = 64 cm²

The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².

Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².

The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).