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In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?
The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If∠ABC=90°, what is the area of triangle ABC?
The figure shows the graph of the equation $$y=k-x^{2}$$, where k is a constant. If the area of triangle ABC is $$\frac{1}{8}$$, what is the value of k?

Give your answer to the nearest 0.01_____
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If k is the greatest positive integer such that $$3^k$$?is a divisor of 15! then k =
In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?
Sid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type?
How many multiples of 5 are there between 81 and 358?
A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?
How many three-digit numbers are there such that all three digits are different and the first digit is not zero?
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
Kim is taking a math class, and the teacher gives a multiple choice test consisting of 8 questions. If each question has 5 answer choices, and Kim answers every question, in how many different ways can she complete the test?
In how many ways can 16 different gifts be divided among four children such that each child receives exactly four gifts?
N equals the number of positive 3-digit numbers that contain odd digits only.

Quantity A

N

Quantity B

125


Main course: Chicken, Beef, Tofu

Side dish: Rice, Salad, Soup, Pasta

Dessert: Pie, Cake

A meal at a certain restaurant consists of 1 main course, 2 different side dishes and 1 dessert.

Quantity A

Number of different meals possible

Quantity B

36




Quantity A

Number of different triangles possible using the given points as

Quantity B

42


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From a group of 8 people, it is possible to create 56 different k-person committees. Which of the following could be the value of k ?

Indicate all such values.
A knockoff website requires users to create a password using letters from the word MAGOSH. If each password must have at least 4 letters and no repeated letters are allowed, how many different passwords are possible?_____
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

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