answer:The division of one polynomial by another polynomial follows the rule that the remainder has a degree less than the divisor. In this case, the divisor is 3x^3 - 4x^2 + x - 5, which has a degree of 3. Therefore, the possible degrees of the remainder are the integers less than 3. Therefore, the possible degrees of the remainder are: [ 0, 1, 2 ] This is because a polynomial remainder must have a degree smaller than the divisor. And since our divisor is a third-degree polynomial, the remainder must be of degree 0, 1, or 2. The final answer for the possible degrees of the remainder when a polynomial is divided by (3x^3 - 4x^2 + x - 5) is boxed{0, 1, 2}.

answer:We start with the equations: [ log(xy^4) = log x + 4log y = 1 ] [ log(x^3y) = 3log x + log y = 1 ] Let log x = a and log y = b. Then we have: [ a + 4b = 1 ] [ 3a + b = 1 ] Solving these equations, we first multiply the second equation by 4: [ 12a + 4b = 4 ] Subtracting the first equation from this result gives: [ 12a + 4b - (a + 4b) = 4 - 1 ] [ 11a = 3 quad Rightarrow quad a = frac{3}{11} ] Substitute a = frac{3}{11} into 3a + b = 1: [ 3left(frac{3}{11}right) + b = 1 quad Rightarrow quad b = 1 - frac{9}{11} = frac{2}{11} ] Now, compute log(x^2y^2): [ log(x^2y^2) = 2log x + 2log y = 2a + 2b = 2left(frac{3}{11} + frac{2}{11}right) = frac{10}{11} ] So, log(x^2y^2) = boxed{frac{10}{11}}.

answer:From the problem, we know that elements 1 and 2 must be included in set M, and we can choose from elements 3, 4, and 5. We can choose 0, 1, or 2 elements from 3, 4, and 5, so there are C_3^0 + C_3^1 + C_3^2 = 7 (sets). Therefore, the answer is boxed{text{C}}. It is important to note the difference between the symbols “subset” and “subseteq”. This problem mainly examines the judgment of the relationship between elements and sets, as well as the idea of discussing cases, making it a basic question.

answer:To solve this problem, we use the law of total probability to calculate the probability of selecting a strap mask from the factory. The law of total probability allows us to consider all possible ways in which an event can occur, in this case, selecting a strap mask from either regular medical masks or surgical masks. Given that the production ratios for regular medical masks and surgical masks are 80% and 20% respectively, and the proportions of strap masks within these categories are 10% and 20% respectively, we can calculate the overall probability of selecting a strap mask as follows: - The probability of selecting a strap mask from the regular medical masks is the product of the probability of selecting a regular medical mask and the probability that it is a strap mask, which is 0.8 times 0.1. - Similarly, the probability of selecting a strap mask from the surgical masks is the product of the probability of selecting a surgical mask and the probability that it is a strap mask, which is 0.2 times 0.2. Therefore, the total probability of selecting a strap mask from the factory is the sum of these two probabilities: [P = (0.8 times 0.1) + (0.2 times 0.2)] [P = 0.08 + 0.04] [P = 0.12] Thus, the probability of selecting a strap mask from this factory is 0.12. Therefore, the correct answer is boxed{text{A}}.