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How many noncongruent triangles are there such that the length of each side of each triangle is an integer and the perimeter of each triangle is 15?


In the figure above, what is the perimeter of the shaded region?


Quantity A

y

Quantity B

1


List A consists of the 5 numbers x, x+ 1, x+ 1, x+ 1, and x+ 2, where x is a positive integer. List B is formed by adding 3 times the range of the numbers in list A to each number in list A. How much greater is the average (arithmetic mean) of the numbers in list B than the average of the numbers in list A?
One piece of candy is to be selected at random from each of 4 different boxes of assorted candies. For each of the boxes, the probability that the candy selected will be a chocolate candy is 1/10, and the 4 selections are to be made independently of each other.

Quantity A

The probability that none of the 4 pieces of candy selected will be a chocolate candy

Quantity B

$$\frac{4}{5}$$


To wake up in the morning, Doug sets two alarm clocks that operate independently of each other, in case one alarm clock fails to ring. If the probability that the first clock will ring is 0.95 and the probability that the second clock will ring is 0.90, what is the probability that neither alarm clock will ring?

Give your answer as a decimal.
A teacher will assign a group project to 2 or more of the 4 students James, Kalla, Lomi, and Michelle. To how many different groups of students can the teacher assign the project?
There are 10 students, including Ann, Bob, Clive, and Dora, who are seated in 10 adjacent chairs arranged in a row. There are 5 students seated between Ann and Bob, 8 students seated between Bob and Clive, and 5 students seated between Clive and Dora. If Ann and Clive switch seats with each other, how many students will be seated between Clive and Dora?
The units digit of 2!+4!+6!+8!+10! Is
k is an integer greater than 1.

Quantity A

$$\frac{(k+1)!}{(k-1)!}$$

Quantity B

(k)(k+1)


In a local election there are 2 candidates for mayor, 4 candidates for sheriff, and 5 candidates for dogcatcher on the ballot. In each of the three categories a voter may vote for exactly one candidate or none. How many different ways can a vote fill out the ballot?
A combination lock is set to open when the correct direction sequence is selected, either left-right-left or right-left-right, and when the correct three numbers from 1 to 60, inclusive, are selected in the correct order. If each number can be used only once, which of the following gives the number of different combinations that can be set to open the lock?

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