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The tick marks shown on the number line are evenly spaced. Points D and E have coordinates of $$4^{10}$$ and $$4^{11}$$, respectively. The point that has a coordinate of $$4^{9}$$ is?


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?
There were 5 different new houses for sale in a certain town last month. This month the prices of 3 of these houses decreased by $45,000 each, while the prices of the other 2 houses remained the same.

Quantity A

The standard deviation of the original 5 prices

Quantity B

The standard deviation of the resulting 5 prices after the 3 prices decreased


If a set S has a total of 6 subsets that consist of 2 members each, then S consists of how many members?
What is the greatest prime divisor of $$3^{100}$$- $$3^{97}$$?
The number of points of intersection between an equilateral triangle and a square could be (such that none of the sides would be overlapping)?
Indicate all that is/are true.

The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

A survey of 5,500 book readers found that the number of books read per year was approximately normally distributed with mean 19.0 and standard deviation 2.0. Which of the following is the best description of the numbers of books read per year by the 880 book readers who read the most books?


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?
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.
z is a positive integer. When 17 is divided by z, the remainder is 2.

Quantity A

z

Quantity B

4


|x| < 1-x

Quantity A

x

Quantity B

0


The speed of light is $$3·10^{8}$$ meters per second, rounded to the nearest $$10^{8}$$ meters per second. A "light-hour" is the distance that light travels in an hour.



Quantity A

The number of kilometers in a light-hour

Quantity B

$$10^{10}$$




A tank initially contains g gallons of water. Beginning at 1 o'clock in the afternoon, water flows into the top of the tank at a constant rate of x gallons per minute and out of the bottom of the tank at a constant rate of y gallons per minute. If x < y, in how many minutes after 1 o'clock in the afternoon is the volume of water in the tank equal to $$\frac{1}{2}$$g, in terms of g, x, and y ?
x≠0

y≠0

x+y≠0

Quantity A

$$x^{-3}$$+$$y^{-3}$$

Quantity B

$$(x+y)^{-3}$$


On her walk today, Emma walked along a straight path between the entrance to her house, H, and the entrance to library, L, passing a crosswalk sign, J, and then a crosswalk sign, K. First Emma walked from H to J and then turned around and walked back from J to H. Then she walked directly from H to L, stopping briefly at J and K on her way. The total distance that Emma walked from H to J and back from J to H was $$\frac{2}{9}$$ of the distance that she walked directly from H to K and $$\frac{1}{6}$$ of the distance that she walked directly from H to L. If Emma walked a total of 420 meters during her walk today. what was the distance, in meters, that she walked from K to L?


The figure above represents six straight city streets that will be repaved. The figure shows only the centerlines of the streets, and all the streets have the same width. Four of the streets are parallel, with centerlines that are 200 meters apart from each other. If the cost to repair each street is estimated as $72,000 per kilometer of the length of its centerline, what is the total estimated cost to repave the six streets?

$_____


The area of square region ABIH equals the area of square region JDEF. Quadrilateral BJFI is a parallelogram. The area of squared region ACEG is 9 times the area of square region ABIH.

Quantity A

The area of ABIH

Quantity B

The area of BJFI




In the figure, ARD is an arc of a circle centered at point O, ABCD is a rectangle, and CD=$$\frac{a}{2}$$ . What is the area of the shaded region?

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