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$$n$$ is a positive integer

$$x=n^{2}+7n+10$$

Quantity A

The remainder when $$x$$ is divided by $$2$$

Quantity B

$$1$$
n is a four-digit positive integer such that its four digits are all different and each digit is either 4, 7, 8, or 9.

Quantity A

The remainder when n is divided by 5

Quantity B

The remainder when n is divided by 9

Quantity A

The digit in the hundredths place in the the number 0.083

Quantity B

The digit in the hundreds place in number 1600


If the function $$f$$ is defined by $$f(x)=1-2^{x}$$ for all integers $$x$$, then $$-f(10)$$ is closest to which of the following?

Quantity A

(1.98)(81)(99)(1,249)

Quantity B

25,000,000
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 voter 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?


The figure shows two normal distributions, A and B, with means a and b, respectively.

Quantity A

The standard deviation of distribution A

Quantity B

The standard deviation of distribution B
Each day for 25 days, the number of people who used a certain library that day was recorded. The standard deviation of the 25 recorded numbers is 12.

Which of the following statements individually provide(s) sufficient additional information to determine the mean of the 25 recorded numbers?

Indicate all such statements.
The variance of n numerical data $$ x_{1}, x_{2}, x_{3}, ..., x_{n}$$, With mean $$\bar{x}$$ is equal to $$\sqrt{\frac{S}{n}}$$, where S is the sum of the squared differences $$(x_{i}-\bar{x})^{2}$$, for 1 ≤ i ≤ n.

Data set R consists of n values and data set T consists of 2n values, where n is a positive integer. The means of the values in R and T are the same, and the variances of the values in R and T are 16 and 100, respectively. What is the variance of the values in the data set that consists of the values in R and the values in T?

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