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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 set of numbers include 1, a, 7 (a≥0)
a must be which of the following integer so that the standard deviation of the set of is the lowest?
The 8 items A, B, C, D, E, F, G, and H are to be displayed on a straight line. In how many ways can the items be displayed if item B must be placed in any position that is to the right of item A, and item C must be placed in any position that is to the right of B?

Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that they are arranged in both an odd row and an odd column?
Give your answer as a fraction.
Which of the following could be a factor of $$\frac{9!}{(6!*3!)}$$?

Indicate all such numbers.
A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?
x and y are positive integers

$$x^{2}$$+$$y^{2}$$=89

xy=40

Quantity A

|x-y|

Quantity B

3


A mixture of brown sugar and cinnamon in a bowl contains 20 percent cinnamon, by weight. To this mixture x ounces of cinnamon and 5x ounces of brown sugar will be added (x > 0).

Quantity A

The percent of cinnamon, by weight, in the bowl after the cinnamon and brown sugar are added

Quantity B

20%




In a hexagon, ∠X=115°

Quantity A

∠y

Quantity B

115°




A certain closed curve consists of n semicircles having the same radius of $$\frac{r}{n}$$ together with a larger semicircle having a radius of r. The n semicircles are aligned along the diameter of the larger semicircle as indicated in the figure for n=7. The area of the region enclosed by the curve, in terms of n, and r, is which of the following?


As shown in the figure, the centers of the two circles are respectively on the circumference of each other, and the radius is 3. What is the perimeter of this figure?
The sum of 101 consecutive even integers is 20,200.

Quantity A

The average (arithmetic mean) of the 101 integers

Quantity B

The median of the 101 integers


n is an even integer greater than 2

Quantity A

$$\frac{n!}{(\frac{n}{2})!}$$

Quantity B

2*($$\frac{n}{2}$$)!


Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?
Some norms governing authors` dedications of their works are (i)___________ to the norms governing ordinary speech (it may be wrong to lie, and thus wrong to lie in dedication), but other norms (ii)__________ dedications. For example, one ought not dedicate to a worthy recipient an object that one feels is devoid of value.
Although collisions between the largest planetesimal belt are _________, they can release large amounts of debris when they occur.
Although economics emerged as a discipline in Great Britain and France at the end of the eighteenth century, it has taken two centuries to become (i)____________ field of study: among early economists, intuition and opinion (ii)____________ facts and figures in economic thought, but the teaching of economics today is dominated by complex algorithms and mathematical models.
After the first monarch butterfly overwintering site was discovered in Mexico in 1975, the biologist Lincoln Brower (i) _____________ the (ii) _____________ of additional sites. The principal reason for Brower`s contention was that roosting in a very limited area would make the species highly vulnerable to wildfire.
Science is a seemingly inexhaustible source of _____________, yet paradoxically scientists have been portrayed in recent decades as rather conservative--resisting innovation in their discipline sometimes to the point of dogmatism.
The overall message of this book on neuroscience is (i) _____________: the brain is quite (ii) _____________, and therefore damaged brains can be healed, aging brains can be rejuvenated, and even ordinarily healthy brains can be made faster and better.

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