Appearance
question:Solve for n, if 9^ncdot9^ncdot9^ncdot9^n=81^4.
answer:We rewrite 81^4 as (9^2)^4 = 9^{2 cdot 4} = 9^8. So, we have 9^n cdot 9^n cdot 9^n cdot 9^n = 9^8. By applying the property of exponents, we can combine the terms on the left side of the equation to get 9^{4n} = 9^8. Since the bases are the same, we can equate the exponents: 4n = 8. Dividing both sides of the equation by 4, we find that n = boxed{2}. The answer is: 2
question:After receiving the 2000 stimulus check, Mr. Eithan decided to share the amount with his family. He gave 2/5 of the amount to his wife, 2/5 of the remaining amount to his first son, 40% of the remaining amount to his second son, and kept the remaining in their family savings account. Calculate the total amount he kept in the family's savings account.
answer:Mr. Eithan gave 2/5 of 2000 to his wife, which is (2/5) * 2000 = 800. The remaining amount after giving 800 to his wife is 2000 - 800 = 1200. He then gave 2/5 of 1200 to his first son, which is (2/5) * 1200 = 480. The remaining amount after giving 480 to his first son is 1200 - 480 = 720. He then gave 40% of 720 to his second son, which is 0.40 * 720 = 288. The remaining amount after giving 288 to his second son is 720 - 288 = 432. Therefore, Mr. Eithan kept 432 in their family's savings account. 432 The answer is: 432
question:The endpoints of a line segment are (2, 3) and (8, 15). What is the sum of the coordinates of the midpoint of the segment?
answer:The midpoint of a line segment with endpoints (x_1, y_1) and (x_2, y_2) is left(frac{x_1 + x_2}{2}, frac{y_1 + y_2}{2}right). In this case, the midpoint is left(frac{2 + 8}{2}, frac{3 + 15}{2}right) = (5, 9). The sum of the coordinates of the midpoint is 5 + 9 = boxed{14}. The answer is: 14
question:Carly recently graduated and is looking for work in a field she studied for. She sent 200 job applications to companies in her state, and twice that number to companies in other states. Calculate the total number of job applications she has sent so far.
answer:Carly sent 200 job applications to companies in her state. She sent twice that number to companies in other states, so she sent 2 * 200 = 400 job applications to companies in other states. In total, Carly has sent 200 + 400 = 600 job applications. 600 The answer is: 600