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question:At a gym, the blue weights are 2 pounds each, and the green weights are 3 pounds each. Harry put 4 blue weights and 5 green weights onto a metal bar. The bar itself weighs 2 pounds. What is the total amount of weight, in pounds, of Harry's custom creation?

answer:The total weight of the blue weights is 4 blue weights * 2 pounds each = 8 pounds. The total weight of the green weights is 5 green weights * 3 pounds each = 15 pounds. The total weight of Harry's custom creation is the weight of the blue weights + the weight of the green weights + the weight of the metal bar = 8 pounds + 15 pounds + 2 pounds = 25 pounds. 25 The answer is: 25

question:Janet makes 20 per hour at work. She works 52 hours per week. Anything over 40 hours per week is considered overtime and is paid at 1.5 times the normal rate. She wants to purchase a 4640 car. How many weeks does she need to work to purchase the car?

answer:Janet works 40 hours per week at her normal rate of 20 per hour, so she earns 40 * 20 = 800 per week. She also works 12 hours of overtime per week (52 total hours - 40 regular hours), which is paid at 1.5 times her normal rate, so she earns an additional 12 * (20 * 1.5) = 360 per week for overtime. Therefore, she earns a total of 800 + 360 = 1160 per week. To purchase a 4640 car, she needs to work 4640 / 1160 = 4 weeks. 4 The answer is: 4

question:The pattern of Pascal's triangle is illustrated in the diagram shown. What is the fourth element in Row 15 of Pascal's triangle? begin{array}{ccccccccccccc}vspace{0.1in} textrm{Row 0}: & qquad & & & & & 1 & & & & & & vspace{0.1in} textrm{Row 1}: & qquad & & & & 1 & & 1 & & & & & vspace{0.1in} textrm{Row 2}: & qquad & & & 1 & & 2 & & 1 & & & & vspace{0.1in} textrm{Row 3}: & qquad & & 1 && 3 && 3 && 1&& vspace{0.1in} textrm{Row 4}: & qquad & 1&& 4 && 6 && 4 && 1 end{array}

answer:The fourth element in Row 15 corresponds to the coefficient of the x^3 term in the expansion of (x+1)^{15}. By the Binomial Theorem, this coefficient is binom{15}{3} = boxed{455}. The answer is: 455

question:What is the greatest possible value of x for the equation left(frac{4x-16}{3x-4}right)^2+left(frac{4x-16}{3x-4}right)=12?

answer:Let y=frac{4x-16}{3x-4}. Then, the given equation becomes y^2+y=12. Rearranging, we have y^2+y-12=0. Factoring, we get (y+4)(y-3)=0. So, y=-4 or y=3. Since y=frac{4x-16}{3x-4}, we have two cases to consider. Case 1: y=-4 Substituting into the equation, we get frac{4x-16}{3x-4}=-4. Cross multiplying, we have 4x-16=-4(3x-4). Expanding, we get 4x-16=-12x+16. Adding 12x and 16 to both sides, we get 16x=32. Dividing by 16, we have x=2. Case 2: y=3 Substituting into the equation, we get frac{4x-16}{3x-4}=3. Cross multiplying, we have 4x-16=3(3x-4). Expanding, we get 4x-16=9x-12. Subtracting 9x and 16 from both sides, we get -5x=-4. Dividing by -5, we have x=frac{4}{5}. Since we are looking for the greatest possible value of x, we choose the larger value of x, which is boxed{2}. The answer is: 2