For both roots to be negative, m must be greater than 0 and m² < 36. Thus, m must be in the range (-6, 0). The suitable value is -4.

The sum of the roots is 3 + 3 = 6, hence m = 6.

Using the sum of roots: 2 + (-2) = -p, hence p = 0.

For both roots to be negative, p must be greater than 0 and p² > 16. Thus, p < -4.

For both roots to be negative, p must be positive and p² > 4*9. Thus, p > 6, so p = -4 is valid.

The sum of the roots is 3 + 3 = 6, hence p = 6.

Gravitational potential energy increases as the distance from the center of the Earth increases.

Gravitational force is directly proportional to the product of the masses. Halving one mass halves the force.

The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.

Each digit can be any of the 10 digits (0-9), so the total number of PINs is 10^4 = 10000.

The number of 4-digit PINs is P(10, 4) = 5040.

The number of ways to choose 2 from 5 is C(5, 2) = 10.

The number of ways to arrange 5 people is 5! = 120.

The number of arrangements of 4 different colored balls is 4! = 24.

The number of ways to distribute 4 prizes among 10 students is 10P4 = 10! / (10-4)! = 5040.

The number of arrangements of 6 people is 6! = 720.

The number of arrangements of the letters in 'BOOK' is 4! / 2! = 12.

The number of arrangements of the letters in 'MATH' is 4! = 24.

Molar mass of C6H12O6 = 6*12 + 12*1 + 6*16 = 180 g/mol. Mass = 0.5 moles x 180 g/mol = 90 g.

Molar mass of KCl = 39 + 35.5 = 74.5 g/mol. Mass = 4 moles x 74.5 g/mol = 298 g.

Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 4 moles x 98 g/mol = 392 g.

Molarity = moles/volume(L). Moles = 0.5 mol/L * 0.5 L = 0.25 mol. Mass = moles * molar mass = 0.25 mol * 74.5 g/mol = 18.625 g.

Molar mass of KCl = 74.55 g/mol. Grams = Molarity * Volume (L) * Molar mass = 0.5 M * 0.25 L * 74.55 g/mol = 9.31 g.

Molar mass of KCl = 74.55 g/mol. Grams = moles × molar mass = 0.5 moles × 74.55 g/mol = 37.25 g.

Grams = moles × molar mass = (2 moles/L × 0.25 L) × 74.5 g/mol = 37.25 g.

Volume = moles / molarity = 1 mole / 0.5 M = 2 L.

Volume = moles / molarity = 2 moles / 0.5 M = 4 L

Volume = moles / molarity = 6 moles / 3 M = 2 L.

Number of molecules = moles x Avogadro's number = 0.1 moles x 6.022 x 10^23 molecules/mole = 6.022 x 10^22 molecules.

Number of molecules = moles x Avogadro's number = 0.25 moles x 6.022 x 10^23 molecules/mole = 1.5055 x 10^23 molecules.