answer:Let's denote the original number of students in the class as ( N ) and the total age of all the students before the new students joined as ( T ). The average age of the original class is 40 years, so we can write the total age of the original class as: [ T = 40N ] When the 12 new students join, the total number of students becomes ( N + 12 ), and the new average age becomes ( 40 - 4 = 36 ) years. The total age of the new students is ( 12 times 32 ), so the new total age of the class is: [ T + 12 times 32 ] The new average age of the class is 36 years, so we can write the equation for the new total age as: [ T + 12 times 32 = 36(N + 12) ] Now we can substitute the value of ( T ) from the first equation into the second equation: [ 40N + 12 times 32 = 36N + 36 times 12 ] Solving for ( N ): [ 40N + 384 = 36N + 432 ] [ 40N - 36N = 432 - 384 ] [ 4N = 48 ] [ N = frac{48}{4} ] [ N = 12 ] So, the original strength of the class was boxed{12} students.

answer:The opposite of a number is the number with its sign changed. For positive numbers, the opposite is the same number but negative. Therefore, for 2023, its opposite is obtained by changing its sign from positive to negative. This can be represented as: [2023 to -2023] Thus, the opposite of 2023 is -2023. Matching this with the given options: A: frac{1}{{2023}} (This is the reciprocal, not the opposite) B: -frac{1}{{2023}} (This is the negative reciprocal, not the opposite) C: 2023 (This is the same number, not its opposite) D: -2023 (This matches our calculation) Therefore, the correct answer is boxed{D}.

answer:From the properties of the sum of the first n terms of an arithmetic sequence {a_n}, we know that S_5, S_{10}-S_5, and S_{15}-S_{10} also form an arithmetic sequence. Thus, we have the following equation: 2(S_{10}-S_5)=S_{15}-S_{10}+S_5, which simplifies to: 2times(20-8)=S_{15}-20+8, Solving for S_{15}, we get: S_{15}=boxed{36}. Therefore, the correct answer is C.

answer:First, let's calculate the value of x by summing a, b, and c and then rounding the result to the tenths place. a = 5.45 b = 2.95 c = 3.74 Sum of a, b, and c: x = a + b + c x = 5.45 + 2.95 + 3.74 x = 12.14 Now, we round x to the tenths place: x ≈ 12.1 Next, let's calculate the value of y by first rounding a, b, and c to the tenths place and then summing the resulting values. Rounded values: a ≈ 5.5 (rounded from 5.45) b ≈ 3.0 (rounded from 2.95) c ≈ 3.7 (rounded from 3.74) Sum of the rounded values: y = a + b + c y = 5.5 + 3.0 + 3.7 y = 12.2 Now, we find the difference between y and x: y - x = 12.2 - 12.1 y - x = 0.1 Therefore, y - x is boxed{0.1} .