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In a box, the probability that the red ball is selected is $$\frac{5}{8}$$. 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 $$\frac{2}{3}$$. What is the probability that Mark get at least one red ball?(Another version: What is the probability that the first or the second ball selected will be red?)
Give your answer as a fraction.
In seven continuous tosses, Event X or Event Y appears randomly each time. If Event X appear first, then the probability that Event X appears the next time is 0.3. If Event Y appears first, then the probability that Event Y appears the next time is 0.4. If Event X appears in the fifth time, then what is the probability that Event X appears in the seventh time?
Give your answer as a decimal.
0 < a < b < 1

c and d are positive integers such that c < d

Quantity A

$$a^{c-d}$$

Quantity B

$$b^{d-c}$$


In 1998, how many of the imported towels were not imported from China?
If the average (arithmetic mean) number of towels imported from China per month was the same for the last 3 months of 2000 as it was for the first 9 months of 2000, approximately how many million dozen towels were imported from China during the 12 months of 2000?
In 1999, the ratio of the number of towels imported from China to the total number of towels imported from countries other than China was closets to which of the following?


The circle in the xy-plane shown has radius 5 and center O. Line l has a slope of $$\frac{1}{2}$$ and passes through the center of the circle. P is the point in the first quadrant at which l intersects the circle. Which of the following represents the coordinates of point P?


In the figure, point A is the center of the circle and points B and D lies on the circle. The length of DC is one-half of the length of AD.

Quantity A

The area of sector ABD

Quantity B

The area of triangle ABC




△MNO is inscribed in semicircle MNO with radius r.

Quantity A

$$x^{2}$$+$$y^{2}$$

Quantity B

4$$r^{2}$$


S is the set of all numbers $$(k-n)^{2}$$, where k and n are integers such that 4 ≤ k < 7 < n ≤ 12. What is the range of the numbers in S?
For each value x in a list of values with mean m, the absolute deviation of x from the mean is defined as |x-m|.

A certain online course is offered once a month at a university. The number of people who register for the course each month is at least 5 and at most 30. For the past 6 months, the mean number of people who registered for the course per month was 20. For the numbers of people who registered for the course monthly for the past 6 months, which of the following values could be the sum of the absolute deviations from the mean?

Indicate all such values.
A certain truck takes 10 trips to transport 2,000 cartons from warehouse A to warehouse B. For each trip except the 10th trip, the truck is loaded to its full carrying capacity of x cartons. On the 10th trip, the truck is loaded with the remaining cartons.

Quantity A

x

Quantity B

210


Dr. Bradley treated a different number of patients on each of the 5 working days last week, and the least number of patients treated on any of the days was 20. No patient was treated on more than one day.

Quantity A

The least possible total number of patients that Dr. Bradley treated on the 5 working days last week

Quantity B

110


$$a_1$$ , $$a_2$$ , $$a_3$$ , ...... , $$a_{99}$$

In the sequence shown, each term after the first is 1 greater than the preceding term. If the sum of all the 99 terms of the sequence is 99, then what is the value of the first term of the sequence?

Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


Quantity A

The number of odd integers between $$\sqrt{12}$$ and $$12^{2}$$

Quantity B

70


Which of the following could be a factor of $$\frac{9!}{(6!*3!)}$$?

Indicate all such numbers.
If $$2^{n}$$ is the highest power of 2 that is a divisor of the product ($$10^{2}$$) ($$12^{5}$$) ($$18^{6}$$), then n=
n is a positive even integer

Quantity A

The greatest possible value of x such that $$2^{x}$$ is a factor of n(n+2)(n+4)(n+6)

Quantity B

The greatest possible value of y such that $$2^{y}$$ is a factor of n(n+2)(n+4)(n+6) + 360


Quantity A

The number of positive divisors of 16,000

Quantity B

The number of positive divisors of 18,000


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