We know to begin with that for x candy bards:

x / 10 = 0.89; x = 8.90

We are trying to ascertain how many bars (y) must be added to this to amount to have an average of 0.80.  This is represented:

(8.9 + 0.72y) / (10 + y) = 0.8

8.9 + 0.72y = 0.8 (10 + y)

8.9 + 0.72y = 8 + 0.8y

8.9 – 8 = 0.8y - 0.72y

0.9 = 0.08y

y = 0.9 / 0.08 = 11.25

However, since we cannot have a partial amount of candy bars, we will have to buy 12.

To find the answer, we need to know the total words and the total number of hours involved.  

The first is easy: 15000 + 200000 + 10000 = 225000 words

To ascertain the number of hours, we have to look at each translator separately. Although there are several ways to do this, let's consider it this way:

Translator 1 can translate at 500 words per 20 minutes OR 1500 words per hour.

Translator 2 can translate at 1250 words per half hour OR 2500 words per hour.

Translator 3 can translate at 250 words per 15 minutes OR 1000 words per hour.

Therefore, we know each translator took the following amount of time:

Translator 1: 15000 / 1500 = 10 hours

Translator 2: 200000 / 2500 = 80 hours

Translator 3: 10000 / 1000 = 10 hours

The total number of hours was therefore 10 + 80 + 10 = 100 hours.

The average rate was 225000 words/100 hours, or 2250 words per hour.

To find the mean or expected value, we multiply each value by its corresponding probability and add them up.  So the mean = 1(1/2) + 2(1/3) + 3(1/6) = 5/3.

The answer is f = g < j = h.

First rearrange the number set in a convenient form:

{2, 6, 7, 8, 9, 11, 12, 12, 14}

f = 9

g = 9 

h = 12

j = 12

There are 4 aces in the 52-card deck so the probability of dealing an ace is 4/52 = 1/13. In a 5-card hand, each card is equally likely to be an ace with probability 1/13. So together, the expected number of aces in a 5-card hand is 5 * 1/13 = 5/13.

We know the formula here is average = sum / number of values.  Plugging in the values we have, 72 = sum / 5.  Then the sum = 72 * 5 = 360, so Quantity A is greater.

To find the expected value, we multiply the number by its corresponding probability.  

expected value = 2(0.1) + 4(0.2) + 6(0.3) + 8(0.4) = 6

sum for all 7 tests = 85 * 7 = 595

sum for first 6 tests = 87 * 6 = 522

score on 7th test = 595 – 522 = 73

Let's assume that the three numbers that average 20 are x, y, and z.  That means that the sum of x, y and z has to be 60. The average (in this case 20) is the sum of the numbers divided by the quantity of numbers (in this case 3). Thus the sum of the numbers must equal the average (in this case 20) times the number of numbers (in this case 3). Similarly the sum of x, y, z, and the fourth number have to equal 100. If x + y + z = 60 and x + y + z + 4th number = 100 then 4th number has to be 40 which is greater than Option B at 35.

We know average = sum / number of students.  Rearranging this formula gives sum = average * number of students. So to find the total average, we need to add up the four groups' sums and divide by the total number of students.

average = (15 * 162 + 20 * 148 + 10 * 153 + 18 * 140) / (15 + 20 + 10 + 18) = 150