answer:The original price of each t-shirt is 20. The discount is 50%, which means James gets 20 x 50% = 10 off each t-shirt. So, each t-shirt is now priced at 20 - 10 = 10. James bought 6 t-shirts, so the total amount he paid is 10 x 6 = 60. 60 The answer is: 60

answer:The shaded region is the difference in area between the larger and smaller circles. The area of a circle is pi r^2, so the area of the shaded region is pi(29^2-19^2). We want to find the radius of a circle with the same area as the shaded region. Let's call this radius r_3. The area of this circle is pi r_3^2. Since the area of the shaded region is equal to the area of the third circle, we can set up the equation pi(29^2-19^2) = pi r_3^2. Simplifying, we have 29^2-19^2 = r_3^2. Using the difference of squares, we can further simplify the equation to (29+19)(29-19) = r_3^2. Calculating, we get 48 cdot 10 = r_3^2. Taking the square root of both sides, we find r_3 = sqrt{480}. Simplifying the radical, we have r_3 = boxed{4sqrt{30}}.The answer is: 4sqrt{30}

answer:By AM-GM, begin{align*} 4x^5 + 5x^{-4} &= x^5 + x^5 + x^5 + x^5 + x^{-4} + x^{-4} + x^{-4} + x^{-4} + x^{-4} &ge 9 sqrt[9]{x^{5+5+5+5+(-4)+(-4)+(-4)+(-4)+(-4)}} &= 9 sqrt[9]{x^5} &= 9x. end{align*}Equality occurs when x=1, so the minimum value is boxed{9}.The answer is: 9

answer:There were 9 seasons before the announcement, so there were 9 * 22 = 198 episodes. The last season is 4 episodes longer, so it has 22 + 4 = 26 episodes. In total, there will be 198 + 26 = 224 episodes to watch. If each episode is 0.5 hours, then it will take 224 * 0.5 = 112 hours to watch them all. 112 The answer is: 112