If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.

All pairs listed multiply to 48, hence they are valid pairs.

The other number is 72 divided by 8, which equals 9.

For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.

According to Vieta's formulas, the sum of the roots p and q is -b/a and the product is c/a.

For real roots, the discriminant must be non-negative: k^2 - 4*1*16 >= 0, leading to k^2 >= 64.

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0, leading to k = 4.

For the equation to have one real root, the discriminant must be zero. Thus, k must equal 4.

Factoring the equation gives (x - 2)(x - 3) = 0, thus the roots are 2 and 3.

The area of a circle is given by A = πr². If the radius is increased by 50%, the new radius is 1.5r. The new area is A' = π(1.5r)² = 2.25πr². The increase in area is (2.25 - 1) = 1.25 times the original area, which is a 125% increase.

If the radius increases by 50%, the new radius is 1.5r, and the area becomes (1.5r)² = 2.25r², which is a 125% increase.

Volume of a sphere = (4/3)πr³. If radius is halved, volume becomes (4/3)π(1/2)³ = (4/3)π(1/8) = (1/6)π, which is one-eighth of the original volume.

If E is added and ranks 3rd, C will drop to 4th position.

A constant ratio of consecutive terms indicates that the series is exponential.

The constant ratio of consecutive terms in a geometric series is called the common ratio.

The constant ratio of consecutive terms in a geometric series is called the common ratio.

Let A's age be 5x and B's age be 3x. Then, 5x + 3x = 64, which gives 8x = 64. Therefore, x = 8, and A's age is 5x = 40 years.

Let the lengths of the sides be 7x and 5x. Then, 7x + 5x = 48, which gives 12x = 48. Thus, x = 4, and the longer side is 7x = 28 cm.

The ratio of cats to dogs is 2:3. If there are 30 dogs, the number of cats can be calculated as (2/3) * 30 = 20 cats.

According to Vieta's formulas, the sum of the roots p + q is equal to -(-5) = 5.

According to Vieta's formulas, the sum of the roots p + q = -b/a and the product pq = c/a.

For both roots to be negative, the sum (p) must be positive and the product (q) must also be positive.

The sales increased to 350 units in Q2, which is a 75% increase from Q1.

The percentage increase from Q2 (200 units) to Q3 (300 units) is 50%.

Projected sales for Q4 would be 300 + (20% of 300) = 300 + 60 = 360 units.

If Product B sold 600 units in Q2, a 20% increase would result in 720 units in Q3.

If Product B sold 600 units in Q3, a 20% decrease would result in 480 units.

The total sales for Product B over the four quarters would be 1600 units (400 + 500 + 400 + 600).

Adding the projected Q4 sales of 600 to the previous quarters gives a total of 2200 units for the year.

The percentage increase from Q3 to Q4 is ((600 - 500) / 500) * 100 = 20%.