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question:What is the coefficient of the x^2y^4 term in the expansion of (x+y)^6?
answer:The coefficient of the x^2y^4 term in the expansion of (x+y)^6 is given by the binomial coefficient binom{6}{2}. This can be calculated as frac{6!}{2!(6-2)!} = frac{6 cdot 5}{2 cdot 1} = boxed{15}.The answer is: 15
question:The equation y = -4.9t^2 + 23.8t describes the height (in meters) of a projectile launched from the ground at 23.8 meters per second. In how many seconds will the projectile first reach X meters in height? If we know the answer to the above question is 2, what is the value of unknown variable X?
answer:We are given the equation y = -4.9t^2 + 23.8t that describes the height of a projectile launched from the ground at 23.8 meters per second. To find the time it takes for the projectile to reach a certain height, we need to set up an equation using the given information. The equation can be written as: X = -4.9t^2 + 23.8t We are given that the time is 2 seconds, so we can substitute this value into the equation: X = -4.9(2)^2 + 23.8(2) Now we can solve for X. Simplifying the equation, we get: X = -4.9(4) + 23.8(2) X = -19.6 + 47.6 X = 28 The value of X is 28 meters. The answer is: 28
question:f Lyn donates 240 to a private organization each year where 1/3 of it goes to the community pantry project, 1/2 goes to the local crisis fund, 1/4 of the remaining goes to livelihood project funds, and the rest is for contingency funds. How much goes to contingency fund?
answer:Lyn donates 240 each year. 1/3 of 240 goes to the community pantry project, so that's 240 * 1/3 = 80. 1/2 of 240 goes to the local crisis fund, so that's 240 * 1/2 = 120. The remaining amount after the first two donations is 240 - 80 - 120 = 40. 1/4 of 40 goes to the livelihood project funds, so that's 40 * 1/4 = 10. The rest of the amount is for contingency funds, which is 40 - 10 = 30. So, 30 goes to the contingency fund. 30 The answer is: 30
question:Jillian, Savannah, and Clayton were collecting shells on the beach. Jillian collected 29, Savannah collected 17, and Clayton collected x. They decided that they wanted to give the shells to two of their friends who had just arrived. They put their shells together and distributed them evenly to each friend. How many shells did each friend get? If we know the answer to the above question is 27, what is the value of unknown variable x?
answer:Jillian collected 29 shells. Savannah collected 17 shells. Clayton collected x shells. The total number of shells they collected is the sum of the shells each person collected: 29 + 17 + x. They decided to distribute the shells evenly to each friend, so each friend gets (29 + 17 + x)/2 shells. We are given that each friend gets 27 shells, so we can write: (29 + 17 + x)/2 = 27. Multiplying both sides by 2, we get: 29 + 17 + x = 54. Simplifying the left side, we get: 46 + x = 54. Subtracting 46 from both sides, we get: x = 8. The value of x is 8. 8 The answer is: 8