Joe owns a stock which has probability .5 of going up. This morning, he bought a ticket in a lottery game which gives him a probability .0001 of winning. What is the probability that Joe's stock will go up and he will win in the lottery? Your answer should keep 5 positions to the right of the decimal, like .43212

0.00005

Step-by-step explanation:

The probability of the stock going up and that of winning in the lottery are independent.

Hence, the probability of both = P(stock going up) × P(winning in the lottery) = 0.5 × 0.0001 = 0.00005

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°