answer:**Step 1: Calculate the diagonal of the rectangle (which is also the diameter of the circle).** Using the Pythagorean theorem, [ text{Diagonal} = sqrt{7^2 + 24^2} = sqrt{49 + 576} = sqrt{625} = 25 text{ cm}. ] **Step 2: Determine the circumference of the circle.** Given that the diameter is 25 cm, the circumference (C) of the circle can be calculated by: [ C = pi times (text{diameter}) = pi times 25 = 25pi text{ cm}. ] Thus, the circumference of the circle is boxed{25pi} centimeters. **Step 3: Calculate the area of the rectangle.** The area (A) of the rectangle is: [ A = text{length} times text{width} = 7 times 24 = 168 text{ square centimeters}. ] Thus, the area of the rectangle is boxed{168} square centimeters. Conclusion: The circumference of the circle is boxed{25pi} centimeters, and the area of the rectangle is boxed{168} square centimeters.

answer:First, express frac{5}{23} as a decimal using long division. Calculating manually or using a calculator, frac{5}{23} = 0.overline{217391304347826086956521739130}. This decimal has a repeating block of 23 digits: "217391304347826086956521". To find the 150th digit, consider the 149th digit after the initial decimal point, since the first digit counted does not include the 0 before the decimal point. We use modular arithmetic: [ 149 mod 23 = 16. ] Thus, the 150th digit corresponds to the 16th digit within the repeating cycle. Based on the repeating block "217391304347826086956521", the 16th digit is "1". Conclusion: The 150th digit after the decimal point in the decimal expansion of frac{5}{23} is boxed{1}.

answer:**Analysis** This problem examines the application of permutations. It is more convenient to use an indirect method than a direct analysis. By using the indirect method, we first calculate the number of situations where 4 out of 6 people are selected to visit the four pavilions, then analyze and calculate the number of situations that include person A and person B visiting the France Pavilion. From the relationship between events, we can calculate the answer. **Solution** According to the problem, by using the permutation formula, we first select 4 out of 6 people to visit the four pavilions, which gives us A_{6}^{4}=360 different situations. Among these, the situations that include person A visiting the France Pavilion are A_{5}^{3}=60, and the situations that include person B visiting the France Pavilion are also A_{5}^{3}=60. Therefore, if person A and person B do not visit the France Pavilion, the total number of different selection schemes is 360-60-60=240. Thus, the answer is boxed{240}.

answer:1. **Identify the pattern in the number of squares per row**: - The first row has 3 squares, and each subsequent row adds 3 squares compared to the previous row. 2. **Formulate the total number of squares in the n-th row**: - The total number of squares in the n-th row, N, is given by starting with 3 squares and adding 3 squares per subsequent row. - This implies N = 3 + 3(n-1) = 3n. 3. **Calculate the total number of squares in the 20th row**: - Substitute n = 20 into the formula: N = 3 times 20 = 60. - Therefore, there are 60 squares in the 20th row. 4. **Calculate the number of white squares**: - Given that both the first and last squares in every row are black, and squares alternate between black and white, if N (total squares in a row) is even, then exactly half of the squares will be white. - Calculation: Number of white squares = frac{60}{2} = 30. 5. **Conclusion**: - The number of white squares in the 20th row is 30. boxed{The correct answer is **(C)** 30.}