The game is played by Drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red power bowl out of a drum 26 red balls (numbered 1-29) The jackpot is one by matching all five white balls in any order in the red Powerball.

The expected value for purchasing one ticket for the jackpot = $77.26

Step-by-step explanation:

We first compute the probability mass function for the problem.

Probability of winning the jackpot

One has to get all 5 white ball and the one red ball correctly. There are 69 white balls and 26 red balls.

5 white balls can be selected from 69 with order not important, and 1 red ball selected from 26 red balls in

⁶⁹C₅ × ²⁶C₁ ways = 292,201,338 ways

And there are (5! × 1) different combinations of those winning numbers = 120 combinations (since order isn't important for the 5 numbers of the white balls)

Required Probability of winning

= (120 ÷ 292,201,338) = 0.0000004107

= (4.107 × 10⁻⁷)

To win, one would buy a $2 ticket, and win $193 million.

Amount of winnings = 193,000,000 - 2 = $192,999,998

Probability of losing = 1 - (Probability of winning) = 1 - (4.107 × 10⁻⁷) = 1

To lose, one would buy a $2 ticket and win nothing.

Amount of winnings = 0 - 2 = -$2

So, the probability mass function

X | 192,999,998 | -2

p | (4.107 × 10⁻⁷) | 1

Expected value = E(X) = Σ xᵢpᵢ

E(X) = [(192,999,998) × (4.107 × 10⁻⁷)] + (-2)(1)

E(X) = 79.26 - 2 = $77.26

Hope this Helps!!!

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

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°