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question:A 40-bead necklace is made up of three kinds of beads. There are seven amethyst beads and twice as many amber beads as amethysts. The third beads are turquoise. How many turquoise beads are in the necklace?
answer:There are 7 amethyst beads in the necklace. There are twice as many amber beads as amethysts, so there are 2 * 7 = 14 amber beads. The total number of amethyst and amber beads is 7 + 14 = 21 beads. The remaining beads are turquoise, so there are 40 - 21 = 19 turquoise beads. 19 The answer is: 19
question:Kendall is counting her change. She has a total of 4 in quarters, dimes, and nickels. If she has 10 quarters and 12 dimes, how many nickels does she have?
answer:Kendall has a total of 10 quarters, which is equal to 10 * 0.25 = 2.50. She also has 12 dimes, which is equal to 12 * 0.10 = 1.20. The total value of the quarters and dimes is 2.50 + 1.20 = 3.70. Since Kendall has a total of 4, the remaining change must be in nickels. The value of the remaining change is 4 - 3.70 = 0.30. Since each nickel is worth 0.05, Kendall must have 0.30 / 0.05 = 6 nickels. Therefore, Kendall has 6 nickels. 6 The answer is: 6
question:What is the value of f(g(5)) for the functions f(x) = x^2 + 1 and g(x) = 2x - 1?
answer:First, we need to find g(5). Plugging in x=5 into the function g(x), we get g(5) = 2(5) - 1 = 9. Next, we need to find f(g(5)). Plugging in x=9 into the function f(x), we get f(g(5)) = (9)^2 + 1 = 81 + 1 = boxed{82}. The answer is: 82
question:What are the coordinates of the center of the circle described by the equation x^2 - 2x + y^2 - 4y - 28 = 0?
answer:We rewrite the equation as (x^2-2x+1) + (y^2 - 4y + 4) = 28 + 1 + 4, or (x-1)^2 + (y-2)^2 = 33. This is the equation of a circle with center (1, 2) and radius sqrt{33}, so the coordinates of the center are boxed{(1, 2)}. The answer is: (1,2)