# While at a carnival, andrew comes across a game that involves rolling a die. according

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## Answers

he can expect to lose 0.5$

Step-by-step explanation:

To solve this problem we must calculate the expected value of the game.

If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:

[tex]E =\sum xP (x)[/tex]

When throwing a dice the possible values are:

x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12

The probability of obtaining any of these numbers is:

[tex]p=\frac{1}{6}[/tex]

The gain when obtaining an even number is twice the number.

The loss to get an odd number is $ 9

So the expected gain is:

[tex]E=-9*\frac{1}{6}-9*\frac{1}{6}-9*\frac{1}{6} + 4*\frac{1}{6} + 8*\frac{1}{6} + 12*\frac{1}{6}\\\\E =-27*\frac{1}{6} + 24*\frac{1}{6}\\\\E=-3*\frac{1}{6}\\\\E=-$0.5[/tex]

he can expect to lose 0.5$

Step-by-step explanation:

To solve this problem we must calculate the expected value of the game.

If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:

[tex]E =\sum xP (x)[/tex]

When throwing a dice the possible values are:

x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12

The probability of obtaining any of these numbers is:

[tex]p=\frac{1}{6}[/tex]

The gain when obtaining an even number is twice the number.

The loss to get an odd number is $ 9

So the expected gain is:

[tex]E=-9*\frac{1}{6}-9*\frac{1}{6}-9*\frac{1}{6} + 4*\frac{1}{6} + 8*\frac{1}{6} + 12*\frac{1}{6}\\\\E =-27*\frac{1}{6} + 24*\frac{1}{6}\\\\E=-3*\frac{1}{6}\\\\E=-$0.5[/tex]

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.

the distance y is the side opposite to angle x in the right triangle. use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

[tex]Hurry i need your (50 points) the moon forms a right triangle with the earth and the sun during one[/tex]your answer is a

step-by-step explanation:

4*4*4*4=256