Order the number from greatest to least 16.4,1.64,1.6,16.099

16.4 > 16.099 >1.64 >1.6
Here, let me give you an explanation for how to this. First, you need to start with the greatest value, the tens place. Only two numbers in the set have a tens place, 16.4 and 16.099. Then since they both have the same tens place, we go to the one's place. The one's place is also the same, so we go to the tenths place. In the tenth's place, the value for 16.4 is 4 while 16.099 is 0. So we now know that 16.4 is the greatest number and 16.099 is right after it. Then we have to decide which is greater, 1.64 or 1.6. They both have the same one's place. However, for 1.6, the tenths place is 0 since there is no tenths place for it. So now we know that 1.64 is greater than 1.6.

Hope this helps!

Part (a)

If you win $12165, then you really net 12165-35 = 12130 dollars when you consider the ticket fee. So this is the true amount of money you win, or take home at the end of the day. This is before taxes.

Multiply 0.002 with 12,130 to get 0.002*12130 = 24.26

We'll use this later so let A = 24.26

The chances that you don't win are 1 - 0.002 = 0.998 which multiplies with -35 to indicate you lost $35 in playing the game. So we get B = 0.998*(-35) = -34.93

Lastly, add the values of A and B to get the expected value:

A+B = 24.26 + (-34.93) = -10.67 is the expected value.

On average, you expect to lose about $10.67 for any time you play the game.

 -10.67 dollars

Part (b)

0.125 is the probability of winning so 1-0.125 = 0.875 is the probability of losing.

Let's say you get really unlucky and lose 12 times in a row. Assuming each trial (aka case when you play the game) is independent, this would mean the probability of such an event is (0.875)^12 = 0.2014172, which is approximate.

Subtract that from 1 to get the probability of winning at least once

1 - (0.875)^12 = 1 - 0.2014172 = 0.7985828

which is also approximate. If we rounded to three decimal places, then it would be 0.799; I'm picking three decimals since 0.125 is to three decimal places. Round however you need to if otherwise.

 0.799 (approximate)