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题目内容
Eight students of different heights need to be arranged into two rows of seats. Each row has four seats. For each column, the student in the row ahead needs to be shorter than the student in the row behind. In how many ways can these students be arranged?
An urn contains 4 red balls, 8 green balls and 2 yellow balls. Five balls are randomly selected WITH replacement from the urn. What is the probability that 1 red ball, 2 green balls, and 2 yellow balls will be selected?

Give your answer as a fraction.
An eight-digit integer is formed by three "1" and five "2". How many different such integers can be formed?


The table above consists of 10 rows and 10 columns. Each entry in the table is either a zero or a one. A zero is to be selected at random from the table. What is the probability that the zero selected will be in a row with an odd number of zeros and in a column with an odd number of zeros?

Give your answer as a fraction.
Each time a certain coin is tossed, it lands either heads up or tails up. The coin has the property that the probability that it will land heads up when tossed 1 time is 0.6. If the coin is to be tossed 3 times, what is the probability that it will land heads up at least 2 times?
Event A and event B are independent event. If the probability that even A occurs is 0.4 and event B occurs is 0.3, what will be the probability that at least one event occurs?

Give your answer as a decimal.
Set A, B, and C are subsets of a universal set U, as represented by the circular regions in the following diagrams. The set $$\overline{B}$$ consists of the elements in U that are not in B, and the set $$\overline{C}$$ consists of the elements in U that are not in C. The set A∩((B∩$$\overline{C}$$)∪(C∩$$\overline{B}$$)) is represented by the shaded regions in which of the following diagrams?


The daily high temperature, in degrees Fahrenheit, in a certain city were recorded for 11 consecutive days. The table above shows the frequency distribution of the recorded temperatures. Which of the following statements are true?

Indicate all such statements.


Quantity A

AB

Quantity B

BC


The figure ABCDOE above consists of a large semicircle ABC with center O and two small semicircles AEO and ODC. If the area of figure ABCDOE is 48π, what is the length of diameter AC?


The circle on the left has radius r and center O, and the circle on the right has radius s and center P. The lengths of arcs ABC and DEF are both equal to 3, and r < s < 3.

Quantity A

x

Quantity B

y
A plot of land used to display flowers in a botanical garden was designed in the shape of a trapezoid in which the lengths of the two sides that are not parallel are equal. The length of the longer parallel side is 5 times the length of the shorter parallel side, and the distance between the two parallel sides is 3 times the length of the shorter parallel side. The perimeter of the plot is 135 meters. Approximately what is the length, in meters, of the shorter parallel side?


The figure above represents a pond and the nearby land that surrounds it. Lucia plans to measure the distance across the pond from point A to point B. First, she will measure the distance from a rock on land at point R to point D on line AR. Next, she will measure the distance, along a line parallel to line AB, from point D to point C, which lies on line BR. Of the following, which additional measurement will be sufficient to determine the distance from A to B?


Quantity A

RS

Quantity B

3


What's the height of the unknown altitude?

Give your answer as a fraction.


In an equilateral triangle ABC,three points P,Q and R are on the side AB,AC and BC, respectively.

Quantity A

The sum of any two interior angles in Δ ABC

Quantity B

The sum of any two interior angles in Δ PQR


Quantity A

a

Quantity B

b


Quantity A

x

Quantity B

90

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