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In a sequence, $$r_{1}=1$$, $$r_{n}=(\frac{1}{5})*r_{n-1}$$ , where n is any integer greater than 1.

Quantity A

$$r_{5}$$

Quantity B

$$625*r_{10}$$


In a sequence, $$a_{1}=2$$, $$a_{2}=4$$, $$a_{3}=14$$, $$a_{4}=64$$, $$a_{n}= d*a_{n-1}-c$$ What is the value of c+d?
In a sequence, $$a_{1}$$=1, for any integer n greater than 1, $$a_{n}$$ is 12 times the square of its preceding term. If $$a_{5}$$=$$12^{n}$$, then what is the value of n?
In a sequence, $$S_{1}$$=1, for any integer n greater than 1, $$S_{n}=6nS_{1}$$, what is the value of $$S_{1}+ S_{2}$$ + ...+ 300?
$$a_{1}=6$$
$$a_{n}=a_{n-1}+2$$, where n is an even integer
$$a_{n}=a_{n-1}-8$$, where n is an odd integer

Quantity A

$$a_{7}$$

Quantity B

-12


Quantity A: 4!
Quantity B: 5!-4!
n and k are integers, n > k > 1

Quantity A

n!-k!

Quantity B

(n-k)!




How many positive divisors of 210 are product of two primes?
Six identical balls need to be put into four different bottles. If at least one ball should be included in each bottle, then how many ways can these balls be arranged?
What is the probability that a number whose tens digit is no more than 3 and units digit is no more than 4 is selected when selecting a number from 100 to 159 (inclusive)?
Give your answer as a fraction.
What is the probability that A and B are both selected when you randomly select 40 people out of a pool of 100 people (A and B included)?
Give your answer as a fraction.
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?
Positive integers from 1 to 9, inclusive, are written on 9 pieces of paper respectively and then put into 9 boxes. Someone randomly selects a number from the box for three times without replacement and uses these three numbers as the hundreds digit, tens digit and units digit of a three-digit integer.

Quantity A

The probability that the three-digit number is greater than 600

Quantity B

$$\frac{4}{9}$$


Each of 10 balls has an integer 0 to 9, inclusive, painted on the side. Shane randomly pick on each time without replacement.

Quantity A

The probability that 5 is picked at the first time

Quantity B

The probability that 5 is picked not until the second time


P, Q, and R are three points in a plane that are not all on the same line. Which of the following describes the set of all points in the plane that are equally distant from points P, Q and R?

If the area of the region is 5880, then what is the perimeter of the region? (All the angles shown above are right angles)

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