We are asked to find out how much Tom would win on average.  Since Bob has a 75% chance to win, Tom must have a 25% chance to win.  The amount Tom will lose is given to us: $100.  We now need to find how much he will win.

The first day, Bob will only pay $1.  Similarly for the second day. The third day Bob will now have to pay $2.  The fourth day, $4.  We notice that each day we will be doubling how much he pays (since he is matching how much was paid previously).  Thus he is paying:

Now, there are a couple ways to deal with this series.  There are only 10 terms, so we can simply add them up to get our answer. Another method would be looking at it as a geometric series.  If you recall, the sum of a geometric series (series that have terms differentiated by a constant multiplier) is given by:  where  is the initial value,  is the ratio between any 2 terms, and is the number of terms.  Here we just have , since the first term is a 1.  Each term is half the previous term, so , and we have 9 terms ( to ) so .

Hence this would be: 

and our answer would be 

We now have that Bob will have to pay $512 if Tom wins, while Tom will have to pay $100 if Bob wins.  We finally take into account the odds of winning.  25% of the time, Tom will win $512.  75% of the time he will lose $100.  We can more easily interpret this with fractions: 1/4 chance to win, 3/4 chance to lose.

Now we simply keep in mind how averages work: The numerator is going to be the sum of all the cases, while the denominator is the number of cases.  In this situation, we have 4 cases.  3 of them Tom loses, 1 he wins.  Thus we have:

So on average, Tom will make $53 with this bet.  The closest answer to this is $50.

List the numbers in order to find the median:  {50, 54, 54, 58, 59, 61, 63, 66, 67, 68}.  The middle numbers are 59 and 61 so their average is 60 for the median of the data set making statement I true.  Add the list of numbers and divide by 10 to get a mean of 60, making statement II true.  There is a mode of 54 so statement III is false.

To find the average speed, add up the total distance traveled

 and divide by the total time (4.5 hours).

Distance = Rate * Time

We are solving for the rate. Susie was driving for a total of 3 hours. The distance she traveled was 100 miles in the first leg, plus 40 miles (40 miles per hour for one hour) in the second leg, or 140 miles total. Use the total distance and total time to solve for the rate.

140/3 = 46 2/3 miles per hour (roughly 47 miles per hour)

The mean will be equal to the sum of the given values, divided by the number of given values.

Use this equation to solve for .

Multiply both sides by 3.

Divide both sides by 9.

Thursday is 5 degrees hotter than Monday, so on Thursday it is:

Friday, Saturday, and Sunday are the same temperature as Tuesday, so they are all 64 degrees. Now we know all the necessary information to calculate the average.

The best answer choice is therefore 64.

One can simply add all the odd numbers from 7 to 21 and divide by the number of odd numbers there are. Or, moreover, one can see that 14 is halfway between 7 and 21.

We cannot just take the average of the ages 25 and 40, which is 32.5 years old.

Instead, we need to take a weighted average, taking into account the varying number of people in each group.

Take the average age of each group and multiply it by the number of people in that group and then take the sum. Next divide by the total number of people to get the weighted average age of the new group.

(20 * 25 + 10 * 40)/30  =  30

The arithmetic mean can be though of as (total number of points)/(total number of tests). The total number of points that Stacey earned is  for the first 4 tests, plus 100 for the final test.

Stacey's final grade is .

The average is the sum of the numbers divided by the total number of terms. Therefore, .

We can multiply each side by 5 leaving us with ,  or   .

We can simplify this equation to .

After subtracting 49 from both sides, we are left with .