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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?
List A: 1, 5, 9, 13, 4

List B: 1, 5, 9, 13, 9

List C: 1, 5, 9, 13, 7

List D: 1, 5, 9, 13, 6

The standard deviation 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.

Which of the following shows lists A, B, C, and D in order from the list with the least standard deviation to the list with the greatest standard deviation?
The standard deviation of the five values 2, 4, 6, 8, 10 is σ. For which of the following lists is the standard deviation of the values in the list equals to σ?

Indicate all such lists.
List L consists of an odd number of consecutive integers. The median of the integers in L is 3. Which of the following statements must be true?

Indicate all such statements.


The figure shows three circles. A, B, and C, that are tangent to each other. The area of circle A is equal to 1/16 of the area of circle B. The circumference of citele C is equal to the sum of the circumferences of circle A and circle B. If circle C has an area of 100π. what is the radius of circle A?

Radius of circle A:__________


Quadrilateral ABCD is inscribed in the circle shown. What is the value of x+y?

(Note: The measure of an angle inscribed in a circle is equal to half of the measure of the central angle that subtends the same arc.)

Quantity A

The ones digit of $$208^{208}$$

Quantity B

7


If $$\frac{1}{x}$$+$$\frac{1}{y}$$=4.2 and $$\frac{1}{x}$$-$$\frac{1}{y}$$=3.5, what is the value of $$\frac{1}{x^{2}}$$-$$\frac{1}{y^{2}}$$?
If the length of each side of a regular hexagon is 6, what is the area of the regular hexagon?
Working alone at their respective constant rates, an outlet pump can empty a certain tank of water in 7 hours when the tank is initially full, and an inlet pump can fill the tank in 10 hours when the tank is initially empty. Beginning with a full tank, both pumps work simultaneously at their respective constant rates for 1 hour before the inlet pump is shut off. How many more hours would it take the outlet pump working alone to empty the tank?


In the figure, the line l and the x-axis are tangent to the circle at points P and S, respectively, and the line segment QS passed through center R of the circle. What is the slope of l?


The graph shows for each movie category the percent of a sample of middle school students who had watched at least one movie in that category within the last year. If 87 percent of the students in the sample had watched at least one movie in the comedy category and at least one movie in the drama category, what percent of the students in the sample had not watched any movies in either of these two categories?


In square PRSU shown, Q and T are midpoints of sides PR and SU, respectively, and the length of QS is √5. What is the area of quadrilateral PQST?

_____
For each set of three distinct nonzero digits, consider the sum of all positive three-digit integers that can be formed by the digits. For example, for the three digits 1, 2, and 3, the sum of all positive three-digit integers that can be formed by the digits is 123 + 132 + 213 + 231 + 312 + 321 = 1,332. How many different integers are equal to such a sum?


In the figure shown, what is the product of the lengths of line segments RU and RT?
x > y > 0

Quantity A

$$\frac{x}{y}+\frac{y}{x}$$

Quantity B

2


Of the students at a certain university, 40 percent are graduate students, and the rest are undergraduate students. If 15 percent of the graduate students and 30 percent of the undergraduate students are pursuing an engineering degree, what percent of the students pursuing an engineering degree are graduate students?

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