answer:First, let's calculate the original rate of interest using the initial information provided. The simple interest (SI) earned in 3 years when Rs. 800 becomes Rs. 956 is: SI = Final amount - Principal SI = Rs. 956 - Rs. 800 SI = Rs. 156 The formula for simple interest is: SI = P * R * T / 100 where P is the principal amount, R is the rate of interest per annum, and T is the time in years. We can rearrange the formula to solve for R: R = (SI * 100) / (P * T) Plugging in the values we have: R = (Rs. 156 * 100) / (Rs. 800 * 3) R = (15600) / (2400) R = 6.5% Now, let's calculate the new rate of interest when Rs. 800 becomes Rs. 1052 in 3 years. The new simple interest (SI_new) earned in 3 years is: SI_new = Final amount - Principal SI_new = Rs. 1052 - Rs. 800 SI_new = Rs. 252 Using the simple interest formula again: SI_new = P * R_new * T / 100 We can rearrange the formula to solve for R_new: R_new = (SI_new * 100) / (P * T) Plugging in the values we have: R_new = (Rs. 252 * 100) / (Rs. 800 * 3) R_new = (25200) / (2400) R_new = 10.5% Now we can calculate the percentage increase in the rate of interest: Percentage increase = ((R_new - R) / R) * 100 Percentage increase = ((10.5% - 6.5%) / 6.5%) * 100 Percentage increase = (4% / 6.5%) * 100 Percentage increase = (0.04 / 0.065) * 100 Percentage increase = 0.615384615 * 100 Percentage increase = 61.5384615% Therefore, the rate of interest is increased by approximately boxed{61.54%} .

answer:To find out how many muffins Mrs. MacAdams's class bakes, we need to subtract the number of muffins baked by Mrs. Brier's class and Mrs. Flannery's class from the total number of muffins baked by the first grade. Total muffins baked by first grade = 55 Muffins baked by Mrs. Brier's class = 18 Muffins baked by Mrs. Flannery's class = 17 Muffins baked by Mrs. MacAdams's class = Total muffins - (Muffins by Mrs. Brier's class + Muffins by Mrs. Flannery's class) Muffins baked by Mrs. MacAdams's class = 55 - (18 + 17) Muffins baked by Mrs. MacAdams's class = 55 - 35 Muffins baked by Mrs. MacAdams's class = 20 Mrs. MacAdams's class bakes boxed{20} muffins.

answer:Since a_{n+1}= begin{cases} frac{a_n}{2}, & a_n text{ is even} 3a_n+1, & a_n text{ is odd} end{cases}, and a_1=5, We have a_2=3a_1+1=3times5+1=16. Then, a_3= frac{a_2}{2}=8. Thus, a_1+a_2+a_3=5+8+16=29. Therefore, the correct answer is (A): boxed{29}.

answer:To solve this problem, we need to calculate the probability of selecting exactly one of "The Peony Pavilion" and "The Story of the Western Wing" from the five major classical Chinese operas. First, we determine the total number of ways to select any two operas from the five available. This can be calculated using the combination formula {C}_{n}^{r} = frac{n!}{r!(n-r)!}, where n is the total number of items, and r is the number of items to choose. For our case, n=5 and r=2, so the total number of ways to select two operas is: {C}_{5}^{2} = frac{5!}{2!(5-2)!} = frac{5 times 4}{2 times 1} = 10. Next, we calculate the number of ways to select exactly one of "The Peony Pavilion" and "The Story of the Western Wing", and one from the remaining three operas. This involves first choosing one opera from "The Peony Pavilion" and "The Story of the Western Wing", and then choosing one from the remaining three operas. The number of ways to choose one from "The Peony Pavilion" and "The Story of the Western Wing" is {C}_{2}^{1}, and the number of ways to choose one from the remaining three operas is {C}_{3}^{1}. Therefore, the total number of favorable outcomes is: {C}_{2}^{1} times {C}_{3}^{1} = 2 times 3 = 6. Finally, the probability of selecting exactly one of "The Peony Pavilion" and "The Story of the Western Wing" is the ratio of the number of favorable outcomes to the total number of outcomes: P(A) = frac{{C}_{2}^{1} times {C}_{3}^{1}}{{C}_{5}^{2}} = frac{6}{10} = frac{3}{5}. Therefore, the correct answer is boxed{text{C: }frac{3}{5}}.