The mode is 5, as it appears 3 times, more than any other number.

The mode is 6, which appears 3 times in the data set.

The mode is 3, as it appears most frequently (three times) in the data set.

The order of a matrix is given by the number of rows followed by the number of columns. Therefore, a matrix with 3 rows and 4 columns is of order 3x4.

The perimeter of a rectangle is given by P = 2(length + width). Here, P = 2(10 + 5) = 30 cm.

The perimeter of an equilateral triangle is 3 times the length of one side. Therefore, perimeter = 3 * 8 = 24 cm.

There are 13 hearts in a deck of 52 cards. Probability = 13/52 = 1/4.

The first five prime numbers are 2, 3, 5, 7, and 11. Their product is 2 × 3 × 5 × 7 × 11 = 2310.

The product of the roots of the equation ax^2 + bx + c = 0 is given by c/a. Here, c = 6 and a = 2, so the product is 6/2 = 3.

The product of the roots is given by c/a = 3/1 = 3.

The product of the roots is given by c/a = 10/1 = 10.

The product of the roots is given by c/a = 9/3 = 3.

Using Vieta's formulas, the product of the roots is c/a = 10/1 = 10.

Projection = (A · B / |B|^2) * B = (11 / 5) * (1i + 2j) = 2.5.

Projection of A onto B = (A · B / |B|^2)B. A · B = 6, |B|^2 = 4. Projection = (6/4)(2i) = 3i.

Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.

Projection of A onto B = (A · B / |B|^2) * B = ((6*2 + 8*2) / (2^2 + 2^2)) * (2i + 2j) = (28/8)(2i + 2j) = 7i + 7j.

Range = Maximum - Minimum = 12 - 3 = 9

The rows of B are linearly dependent, hence the rank of B is 2.

The rows of D are linearly dependent, hence the rank of D is 2.

The rank of a matrix is the maximum number of linearly independent row vectors. Here, the first and third rows are independent, while the second row is zero. Thus, the rank is 2.

The rank of E is 2 because the rows are linearly dependent (the third row is a linear combination of the first two).

The real part of z is -2.

The real part of z is 3.

The real part of z = 4 + 5i is 4.

The real part of z is 4.

Corresponding angles are equal when two parallel lines are cut by a transversal.

When two lines intersect, the angles formed are supplementary, meaning they add up to 180 degrees.

In an equilateral triangle, all three angles are equal and measure 60 degrees each.

When two parallel lines are cut by a transversal, the corresponding angles are equal.