Q55. Find the area of a circle quickly T=14cm, Thank A=.

$$
\text{Total balls} = 5 (\text{red}) + 3 (\text{blue}) = 8
$$

$$
\text{Red balls} = 5
$$

$$
\text{Probability (Red)} = \frac{\text{Number of red balls}}{\text{Total number of balls}} = \frac{5}{8}
$$
The answer is $\boxed{\frac{5}{8}}$.

$$
\text{Outcomes} = \{1, 2, 3, 4, 5, 6\}
$$
$$
\text{Total outcomes} = 6
$$

$$
\text{Even numbers} = \{2, 4, 6\}
$$
$$
\text{Number of even outcomes} = 3
$$

$$
\text{Probability (Even)} = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
$$
The answer is $\boxed{\frac{1}{2}}$.

$$
\text{Total apples} = 10
$$

$$
\text{Not rotten apples} = \text{Total apples} - \text{Rotten apples} = 10 - 3 = 7
$$

$$
\text{Probability (Not rotten)} = \frac{\text{Number of not rotten apples}}{\text{Total apples}} = \frac{7}{10}
$$
The answer is $\boxed{\frac{7}{10}}$.

$$
\text{Outcomes} = \{\text{HH, HT, TH, TT}\}
$$
$$
\text{Total outcomes} = 4
$$

$$
\text{Two heads} = \{\text{HH}\}
$$
$$
\text{Number of two heads outcomes} = 1
$$

$$
\text{Probability (Two heads)} = \frac{\text{Number of two heads outcomes}}{\text{Total outcomes}} = \frac{1}{4}
$$
The answer is $\boxed{\frac{1}{4}}$.

$$
s^2 = 36 \text{ cm}^2
$$
$$
s = \sqrt{36} \text{ cm} = 6 \text{ cm}
$$

$$
P = 4 \times 6 \text{ cm} = 24 \text{ cm}
$$
The answer is $\boxed{\text{24 cm}}$.

$$
A = 10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2
$$
The answer is $\boxed{\text{50 cm}^2}$.

$$
C = 2 \times \frac{22}{7} \times 7 \text{ cm}
$$

$$
C = 2 \times 22 \text{ cm} = 44 \text{ cm}
$$
The answer is $\boxed{\text{44 cm}}$.

$$
\text{Speed} = \frac{180 \text{ km}}{3 \text{ hours}}
$$

$$
\text{Speed} = 60 \text{ km/h}
$$
The answer is $\boxed{\text{60 km/h}}$.

$$\text{John's share} = 2 \text{ parts} = \$40$$
$$1 \text{ part} = \frac{\$40}{2} = \$20$$

$$\text{Mary's share} = 3 \text{ parts} = 3 \times \$20 = \$60$$
The answer is $\boxed{\$60}$.

$$
x = \frac{30}{0.15}
$$
$$
x = \frac{30}{\frac{15}{100}} = \frac{30 \times 100}{15}
$$
$$
x = 2 \times 100 = 200
$$
The answer is $\boxed{\text{200}}$.

$$
A = \frac{22}{7} \times (7 \text{ cm})^2
$$

$$
A = \frac{22}{7} \times 49 \text{ cm}^2 = 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2
$$
The answer is $\boxed{\text{154 cm}^2}$.

$$
\text{Back bearing} = 045^\circ + 180^\circ = 225^\circ
$$
The answer is $\boxed{225^\circ}$.

$$
\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}
$$

$$
\sin \theta = \frac{3}{5}
$$
The answer is $\boxed{\frac{3}{5}}$.