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An equilateral triangle that has an area of $${9}\sqrt{3}$$is inscribed in a circle. What is the area of the circle?
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Which of the following is equal to $$\frac{2^{12}-2^6} {2^6-2^3}$$?
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排列组合
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A company has assigned a distinct 3-digit code number to each of its 330 employees. Each code number was formed from the digits 2, 3, 4, 5, 6, 7, 8, 9 and no digit appears more than once in any one code number. How many unassigned code numbers are there?
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A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
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If each of the 12 teams participating in a certain tournament plays exactly one game with each of the other teams, how many games will be played?
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OG16 OG17 OG18 OG19 OG20 OG2022
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 The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length l and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?
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If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest possible value of z ?
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OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?
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Is xy + z = z, is |x-y|> 0 ?(1)x = 0(2)y = 0
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Color X ink is created by blending red, blue, green, and yellow inks in the ratio 6 : 5 : 2 : 2. What is the number of liters of green ink that was used to create a certain batch of color X ink?(1)The amount of red ink used to create the batch is 2 liters more than the amount of blue ink used to create the batch.(2)The batch consists of 30 liters of color X ink.
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If $$x$$ and $$y$$ are positive integers, what is the value of $$x$$?(1)$${3}^{x}{5}^{y}={1},{125}$$(2)$$y = 3$$
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PREP07 Test 2
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?(1)Two of the interior angles of ABCD are right angles.(2)The degree measure of angle ABC is twice the degree measure of angle BCD.
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$10,000 is deposited in a certain account that pays r percent annual interest compounded annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by $${D}({t})=10,000[1+(\frac r {100})]^{t}$$. What amount will the deposit grow to in 3 years?(1)$$D(1)=11,000$$(2)$$r =10$$
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If a and b are integers, is b even?(1)3a + 4b is even.(2)3a + 5b is even.
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The area of square S is equal to the area of rectangle R. What is the perimeter of square S?(1)The length of one of the sides of rectangle R is twice the length of a side of square S.(2)The area of rectangle R is 36.
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OG18-数学分册
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Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other's point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?(1)At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.(2)Train Q averaged a speed of 55 miles per hour for the entire trip.
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What is the value of $${v}^{3}-{k}^{3}$$?(1)$$v k > 0$$(2)$$v - k = 6$$
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PREP07 Test 1
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An attorney charged a fee for estate planning services for a certain estate. The attorney's fee was what percent of the accessed value of the estate?(1)The accessed value of the estate was $1.2 million.(2)The attorney charged $2,400 for the estate planning services.
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Is the sum of the integers x and y a prime number?(1)x is an even prime number.(2)y is a prime number between 10 and 20.
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OG18-数学分册
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A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?(1)The units digit of the sum of the numbers on the remaining 35 cards is 6.(2)The sum of the numbers on the remaining 35 cards is 176.
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