A magician has 20 coins in his pocket. Twelve of these coins are normal fair coins (with one head and one tail) and eight are defective coins with heads on both sides. The magician randomly draws a coin from his pocket and flips it. Given that the flipped coin shows a head, what is the probability that it is defective?

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°