Agame is played as follows: a die numbered 1 to 6 is rolled. if the number 1 comes up, you get nothing. if the number 2, 3, or 5 comes up, you win $4. if the number 4 or 6 comes up, you lose $6. according to the expected value, this is a fair game. true false

So before I get to the steps to solving, we should first define what a fair game is. A fair game is a game where there is equal chance of win or loss, so for this to be a fair game, the expected value must be zero.

Now that we defined what a fair game is, let's get to solving! Firstly, we want to get all the possibilities and multiply their outcomes with their chance. In this case the possibilities are {1,2,3,4,5,6}, all have a 1/6 chance, and {1} outcome is 0, {2,3,5} outcome is 4 and {4,6} outcome is -6:

Next, take all the products and add them up:

Since the expected value is zero, it is true that this is a fair game.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

my guess would be b and d, but i didn’t actually get out the pen and paper. lol