**Solution:**

To find the final temperature of the mixture, we can use the principle of conservation of energy. The energy gained by the water should be equal to the energy lost by the ice.

Let's assume the final temperature of the mixture is T.

**Energy gained by water:**
The specific heat capacity of water is 4186 J/kg·K. The mass of water is 4.4 kg. The initial temperature of water is 30°C. So, the energy gained by water can be calculated using the formula:

Energy gained by water = mass of water × specific heat capacity of water × change in temperature

Energy gained by water = 4.4 kg × 4186 J/kg·K × (T - 30)

**Energy lost by ice:**
The specific heat capacity of ice is 2100 J/kg·K. The mass of ice is 1 kg. The initial temperature of ice is -10°C. So, the energy lost by ice can be calculated using the formula:

Energy lost by ice = mass of ice × specific heat capacity of ice × change in temperature

Energy lost by ice = 1 kg × 2100 J/kg·K × (T - (-10))

According to the principle of conservation of energy, the energy gained by water should be equal to the energy lost by ice. So, we can set up the following equation:

Energy gained by water = Energy lost by ice

4.4 kg × 4186 J/kg·K × (T - 30) = 1 kg × 2100 J/kg·K × (T - (-10))

Simplifying the equation:

4.4 × 4186 × (T - 30) = 1 × 2100 × (T + 10)

18516 × (T - 30) = 2100 × (T + 10)

18516T - 555480 = 2100T + 21000

18516T - 2100T = 21000 + 555480

16416T = 576480

T = 576480 / 16416

T ≈ 35.1°C

Therefore, the final temperature of the mixture is approximately 35.1°C.

Ans :- 10.55 C