A · B = (2)(3) + (1)(4) = 6 + 4 = 10.

A · B = (4)(3) + (3)(-4) = 12 - 12 = 0.

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

To make f(x) continuous at x = 1, we need c = 1^2 = 1. Thus, c must be 1.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0. Solving gives k = -8.

The function f(x) = kx + 2 is a linear function and is continuous for all k at x = 3.

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, leading to k = 1.

To ensure continuity at x = 2, k(2) + 1 must equal 3. Thus, k = 1.

To be continuous at x = 2, k(2) + 1 must equal 3. Thus, 2k + 1 = 3, giving k = 1.

The number of ways to choose 5 cards from 52 is 52C5 = 2598960.

The number of ways to choose 3 people from 8 is given by 8C3 = 56.

Distance = height / tan(30) = 100 / (1/√3) = 100√3 ≈ 173.21 m.

Distance = height / tan(angle) = 100 / tan(45) = 100 / 1 = 100 m.

Using tan(30) = 1/√3, distance = height * √3 = 50 * √3 ≈ 86.60 m, which rounds to 100 m.

Using tan(45) = 1, Distance = Height = 100 m.

A · B = (1)(1) + (1)(1) = 1 + 1 = 2.

A · B = (2)(3) + (2)(3) = 6 + 6 = 12.

The mode is 10, as it appears 3 times, which is more than any other number.

The mode is 4, as it appears three times, more than any other number.

A · B = (2)(3) + (2)(4) = 6 + 8 = 14.

A · B = (4)(-1) + (2)(3) = -4 + 6 = 2.

A · B = (4)(1) + (3)(2) = 4 + 6 = 10.

A · B = (1)(2) + (2)(3) + (3)(4) = 2 + 6 + 12 = 20.

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32

A · B = (1)(3) + (2)(4) = 3 + 8 = 11.

1 hour corresponds to 15° of longitude since the Earth rotates 360° in 24 hours.

A time difference of 1 hour corresponds to 15° of longitude, so 2 hours = 2 * 15° = 30°.

A time difference of 4 hours corresponds to 4 * 15 = 60 degrees of longitude.

The number of ways to choose 4 students from 10 is 10C4 = 210.