answer:Let's denote the number of dolls in each small box as ( x ). We know that there are 5 big boxes, each containing 7 dolls, so the total number of dolls in the big boxes is ( 5 times 7 ). There are 9 small boxes, each containing ( x ) dolls, so the total number of dolls in the small boxes is ( 9 times x ). The total number of dolls in all the boxes is 71. So, we can set up the following equation: [ 5 times 7 + 9 times x = 71 ] Now, let's solve for ( x ): [ 35 + 9x = 71 ] Subtract 35 from both sides: [ 9x = 71 - 35 ] [ 9x = 36 ] Now, divide both sides by 9: [ x = frac{36}{9} ] [ x = 4 ] So, there are boxed{4} dolls in each small box.

answer:First, let's calculate the number of French novels each person read: Jordan read 130 French novels. Alexandre read 1/10 of Jordan's French novels, so he read 130/10 = 13 French novels. Camille read twice as many French novels as Alexandre, so she read 2 * 13 = 26 French novels. Now let's calculate the number of Spanish novels each person read: Jordan read 20 Spanish novels. Alexandre read 3 times as many Spanish novels as Jordan, so he read 3 * 20 = 60 Spanish novels. Camille read half as many Spanish novels as Jordan, so she read 20/2 = 10 Spanish novels. Now let's calculate the total number of French novels read by Jordan, Alexandre, and Camille: Total French novels = Jordan's French novels + Alexandre's French novels + Camille's French novels Total French novels = 130 + 13 + 26 = 169 French novels Maxime read 5 less novels than half the total number of French novels read by Jordan, Alexandre, and Camille combined: Half of the total French novels = 169/2 = 84.5 (since we can't have half a novel, we'll consider it as 84) Maxime's French novels = 84 - 5 = 79 French novels Maxime read twice as many Spanish novels as Camille: Maxime's Spanish novels = 2 * Camille's Spanish novels = 2 * 10 = 20 Spanish novels Now let's calculate the total number of novels each person read: Jordan's total novels = French novels + Spanish novels = 130 + 20 = 150 novels Maxime's total novels = French novels + Spanish novels = 79 + 20 = 99 novels Finally, let's calculate how many more novels Jordan read compared to Maxime: More novels Jordan read = Jordan's total novels - Maxime's total novels = 150 - 99 = 51 novels Jordan read boxed{51} more novels in total compared to Maxime.

answer:1. We start with the series given in the problem: [ S = 2 + 4 + 6 + cdots + 2N ] This is an arithmetic series with the first term (2) and the common difference (2). 2. We recognize that the sum of the first (N) even numbers can be given by: [ S = 2 + 4 + 6 + cdots + 2N = 2(1 + 2 + 3 + dots + N) ] Here, we can use the formula for the sum of the first (N) positive integers: [ 1 + 2 + 3 + dots + N = frac{N(N+1)}{2} ] Substituting this in, we get: [ S = 2 left(frac{N(N+1)}{2}right) = N(N+1) ] 3. To satisfy the condition (S > 10^6), we need: [ N(N+1) > 10^6 ] This can be approximated as (N^2 approx 10^6): [ sqrt{N^2} approx sqrt{10^6} ] [ N approx 1000 ] 4. Next, we check the values for (N = 999) and (N = 1000): - For (N = 999): [ N(N+1) = 999 times 1000 = 999000 < 10^6 ] - For (N = 1000): [ N(N+1) = 1000 times 1001 = 1001000 > 10^6 ] Since (1001000) is greater than (10^6), the smallest integer (N) that satisfies (N(N+1) > 10^6) is (N = 1000). 5. The problem asks for the sum of the digits of (N): [ 1000 = 1 + 0 + 0 + 0 = 1 ] Conclusion: [ boxed{(E)} ]

answer:We begin by using the binomial theorem to find the general term of the expansion of ((x-2)^{6}). The general term is given by: T_{r+1} = C_{6}^{r} cdot (-2)^{r} cdot x^{6-r} To find the coefficient of the x^{2} term, we set 6 - r = 2, which gives us r = 4. Now, substitute r = 4 into the general term formula: T_{5} = C_{6}^{4} cdot (-2)^{4} cdot x^{2} = 240x^{2} Therefore, the coefficient of the x^{2} term in the expansion of ((x-2)^{6}) is boxed{240}.