Set A: 

Set B: 

In Set A, there are five consonants out of a total of seven letters, so the probability of drawing a consonant from Set A is .

In Set B, there are three consonants out of a total of six letters, so the probability of drawing a consonant from Set B is .

The question asks for the probability of drawing at least one consonant, which can be interpreted as a union of events. To calculate the probability of a union, sum the probability of each event and subtract the intersection:

The interesection is:

So, we can find the probability of drawing at least one consonant:

Set A: 

Set B: 

Between Set A and Set B, there are two potential matching pairs of letters: AA and XX. The amount of possible combinations is the number of values in Set A, multiplied by the number of values in Set B, .

Therefore, the probability of drawing a matching set is:

First calculate the number of students:

The probability of drawing an honors student will then be the total number of honors students divided by the total number of students attending the school:

First calculate the number of students:

The percentage of seniors that do not attend honors classes is:

Therefore, the probability of selecting a student who is a senior and one who does not attend honors classes is:

Possible numbers 5,6,7,8,9,10,11,12,13,14,15 (11 total numbers)

Prime numbers are 5,7,11,13 (4 total prime numbers)

totalnumber of prime numbers/ total numbers in box

Answer = 4/11

Consider first all of the possible ways the men may be arranged, which is

Now, consider all of the ways that Aaron and Gary could be seated beside each other; it may be easier to visualize by drawing it out:

1. A G _ _
2. G A _ _
3. _ A G _
4. _ G A _
5. _ _ A G
6. _ _ G A

As seen, there are six possibilities.

Finally, for each of these cases, Craige and Boone could be seated in one of two ways.

So the probability that Aaron and Gary will be seated beside each other is:

Let x be the number of 10-person tables, and y be the number of 20-person tables. Since there are 40 tables in the cafeteria, x + y = 40. 10x represents the number of people sitting at 10-person tables, and 20y represents the number of people sitting at 20-person tables. Since the cafeteria can seat 600 people, 10x + 20y = 600. Now we have 2 equations and 2 unknowns, and can solve the system. To do this, multiply the first equation by 10 and subtract it from the second equation. This yields 0x + 10y = 200; solving for y tells us there are 20 tables that seat 20 people. Since x + y = 40, x = 20, so there are 20 tables that seat 10 people. The ratio of x:y is therefore 1:1.

The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.

We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.

Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.