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190415
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The radius of $$O_1$$ is R. The radius of $$O_2$$ is r. These two circles are tangent to each other and they are tangent to the quadrilateral ABCD. BD =?
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200301
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A square has two circles, one big and one small, which are tangent to each other and are all tangent to the square. The radius is R and r respectively. What is the length of the diagonal of the square?
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Magoosh
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If A is the initial amount put into an account, R is the annual percentage of interest written as a decimal, and the interest compounds annually, then which of the following would be an expression, in terms of A and R, for the interest accrued in three years?
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PREP07 Test 1
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A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?
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Magoosh
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If the retail price of a shirt is R dollars, and the price including sales tax is T dollars then the sales tax, as a percent, is
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Magoosh
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Consider the three points in the x-y plane: P = (8, 4), Q = (6, 7), and R = (9, 0). Rank these three points from closest to the origin, (0, 0), to furthest from the origin.
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OG18 OG19 OG20 OG2022
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In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
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190124
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The radius of a balloon was x. After air letting out, the volume was reduced by 27.1%. If the balloon is always sphere. What's the functional relationship between the radius r after leaking and the original radius x?
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190310
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The radius of a balloon was x. After air letting out, the volume was reduced by 48.8%. If the balloon is always sphere. What's the functional relationship between the radius r after leaking and the original radius x?
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PREP07 Test 1
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If r and s are integers and rs + r is odd, which of the following must be even?
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Magoosh
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In Ophiuchus Corporation, 60% of the total revenue R is devoted to the advertising budget. Five-sixths of this advertising budget was spent on television advertising. Which of the following represents the dollar amount spent on television advertising?
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Over a period of 5 academic years from Fall 1999 through Spring 2004, the number of faculty at a certain college increased despite a decrease in student enrollment from 5,500 students in Fall 1999. In the given expressions, F and S represent the percent change in the number of faculty and students, respectively, over the 5 academic years, and R represents the number of students per faculty member in Fall 1999. The percent change in a quantity X is calculated using the formula $${\frac{X_{new}-X_o{ld}}{{x}_{o}{ld}}}(100)$$Select the expression that represents the number of faculty in Fall 1999, and select the expression that represents the number of students per faculty member in Spring 2004. Make only two selections, one in each column.
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Over a period of 5 academic years from Fall 1999 through Spring 2004, the number of faculty at a certain college increased despite a decrease in student enrollment from 5,500 students in Fall 1999.In the given expressions, F and S represent the percent change in the number of faculty and students, respectively, over the 5 academic years,and R represents the number of students per faculty member in Fall 1999. The percent change in a quantity X is calculated using the formula$${\frac{X_{new}-X_o{ld}}{{x}_{o}{ld}}}(100)$$Select the expression that represents the number of faculty in Fall 1999, and select the expression that represents the number of students per faculty member in Spring 2004. Make only two selections, one in each column.
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OG18 OG19 OG20 OG2022
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If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?
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200301
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As shown in the figure, the four circles are tangent to each other, and the radius is r, so what is the area of the shaded part?
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OG12
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If r = 0.345, s = $$({0.345})^{2}$$, and t =$$\sqrt{0.345}$$, which of the following is the correct ordering of r, s, and t ?
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PREP07 Test 2
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$$R=\frac{24\frac{F}{N}}{P+\frac{A}{12}}$$ A certain bank uses the formula above to approximate the annual percentage rate R of a monthly installment loan. Which of the following is an equivalent form of the formula?
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PREP07 Test 2
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An athlete runs R miles in H hours, then rides a bicycle Q miles in the same number of hours. Which of the following represents the athlete's average speed, in miles per hour, for these two activities combined?
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PREP07 Test 2
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 The figure shows the top side of a circular medallion made of a circular piece of colored glass surrounded by a metal frame, represented by the shaded region. If the radius of the medallion is r centimeters and the width of the metal frame is s centimeters, then in terms of s and r, what is the area of the metal frame, in square centimeters?
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191222
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As shown in the figure, the circle has radius r, which is the inscribed circle of an equilateral triangle. What is the length of the side of the equilateral triangle？（represented by r）
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