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题目内容
The average (arithmetic mean) of the values of the homes in Town A is $100,000. The average of the values of the homes in Town B is $150,000. The number of homes in Town A is between 2 times and 3 times the number of homes in Town B. Which of the following values could be the average of the values of the homes in Town A and Town B combined?

Indicate all such values.
A's salary is 33$$\frac{1}{3}$$ percent greater than B, while B's salary is 75 percent of C.

Quantity A

A's salary

Quantity B

C's salary
x and y are nonnegative numbers.

Quantity A

$$\sqrt{xy}$$

Quantity B

$$\frac{x+y}{2}$$

Quantity A

The greatest prime factor of 50

Quantity B

The greatest prime factor of 60


In the above figure, ABCD, OAPD, OBQC are all squares, and the radius of the circle O is 1.

Quantity A

The length of the semicircle PQ

Quantity B

The sum of lengths of line segments PD, DC and CQ
The salaries of five employees A, B, C, D and E are all positive integers. If the median salary of all five employees is 2000, and the salary of C, D, and E is 2000, 4000, 5000, respectively. Which of the following could be the average salary of all five employees?

Indicate all such numbers.
An organization offers only three types of annual memberships. Basic memberships cost $50 each, standard memberships cost $70 each, and premium memberships cost $100 each. Last year, a total of 200 memberships were purchased at an average arithmetic mean) cost of $80 per membership.

Which of the following statements individually provide(s) sufficient additional information to determine the number of premium memberships purchased last year?

Indicate all such statements
$$x+\frac{1}{x}=2$$

Quantity A

$$x^{2}$$+$$\frac{1}{x^{2}}$$

Quantity B

$$x^{3}$$+$$\frac{1}{x^{3}}$$
$$k+\frac{1}{k}=3$$

Quantity A

$$k+\frac{1}{k^{2}}$$

Quantity B

$$k^{2}$$+$$\frac{1}{k^{3}}$$
$$y=x^{2}+2x-35$$ can be transformed into $$y=(x+m)(x-n)$$ where $$m$$ and $$n$$ are both integers.

Quantity A

$$m$$

Quantity B

$$n$$
What is the product of the two solutions of the equation $$3x^{2}+17x+10=0$$?
The function f is defined by f(x) =$$x^{2}$$-18x+56 for all numbers x. If r and t are two different numbers such that f(r) = f(t) = 0. What is the value of $$\frac{r+t}{2}$$?
An apple falls straight to the ground from a tree branch 8 meters above the ground. The apple's height above the ground, t seconds after it starts falling, is H meters, where H=8-4.9$$t^{2}$$ and t≥0. How many seconds after the apple starts falling does it hit the ground?

Give your answer to the nearest 0.1 second.
The electric power P in a resistor is directly proportional to the square of the electric current I flowing through the resistor. For a given resistor, if the power is 18 watts when the current is 3 amperes, what is the power, in watts, when the current is 4 amperes?
The operation ⭕️ is defined by x ⭕️ y=$$\frac{1}{x}$$+$$\frac{1}{y}$$ for all positive numbers x and y. Which of the following statements must be true for all positive numbers m and r?

Indicate all such statements.
In the xy-plane, the point (3p, 5p-1) lies on the line with equation y=-$$\frac{1}{2}$$x-$$\frac{5}{3}$$. What is the value of p?

Give your answer as a fraction.

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