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The diameters of the five circles all equals to 4. All the circles are tangent to each other and together inscribed in the rectangle. What is the area of the rectangle?
a=the greatest value of x such that $$5^{x}$$ is a factor of 1,500

b=the greatest value of y such that $$3^{y}$$ is a factor of 33,333,333

Which of the following statements must be true?

Indicate all such statements.
How many positive factors does 1,575 have?
If an integer greater than 100 and less than 1,000 is to be selected at random, what is the probability that the integer selected will be a multiple of 7?
Quantity A: The remainder when $$3^{100}$$ is divided by 8

Quantity B: 1
N= $$824^{x}$$, where x is a positive integer

Quantity A: The number of possible values the units digit of N

Quantity B: 4
n, k and r are all positive integers

If $$n^{k}$$=10r+3, then k could be?

Indicate all that are possible.
When a positive integer (less than 1,000) is divided by 5 and 6, the remainder is 2 and 3, respectively. What is the greatest possible number of such integers?
Someone needs to import a number of sets of bottles. Each bottle charges $12.04, and it also charges $4.8 for shipping each set (not single bottle but a whole set). The standard deviation of numbers of bottles in each set is 1.5. What is the standard deviation of the prices for each set?
What is the remainder when $$3^{283}$$ is divided by 5?
At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
In a box, the probability that the red ball is selected is 5/8. Mark randomly selects balls twice from the box without replacement. If he didn`t get a red ball in the first attempt, then the probability that he gets a red ball in the second attempt is 2/3. What is the probability that Mark get at least one red ball?
2< x< 5, 1/10< y< 1/5

Quantity A: x+y

Quantity B: (1/x) + (1/y)
A list contains 20 songs, Mike and Scott got the identical list. Mike marked 15 favorite songs, and Scott marked 12 songs. Which of the following cannot be the number of songs they both marked as favorite?
A teacher has 3 courses in total. The average number of students who sign up for these courses is 32. Among these students, 5 students sign up for 2 courses, 3 students sign up for all the 3 courses. How many different students sign up for these courses in total?


In how many ways can letter a b and c be assigned into a 3*3 nine palace such that no letter is used more than once in each line and each row?


If 7 white cubes and 20 red cubes, all of equal size, are fastened together to form one large cube as shown above, what is the greatest fractional part of the surface area of the large cube that could be red?
40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. How many ways can these DVDs be arranged?
If the probability for each cannon shoots the target is 0.6, then at least how many cannons shoot together can you ensure the overall probability of shooting the target reach 0.99?
The average(arithmetic mean) of the two numbers 3x and 3y is 48.

Quantity A

The average of the two numbers 2xand 2y

Quantity B

30

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