answer:Let's denote the amount of apples Dana has as D. According to the problem, Charlie has 75% more apples than Dana, and Bella has 50% more apples than Dana. We can express the amounts of apples Charlie and Bella have in terms of D. 1. **Calculate the amount of apples Charlie has:** Charlie has 75% more apples than Dana. This can be expressed as: [ C = D + 0.75D = 1.75D ] 2. **Calculate the amount of apples Bella has:** Bella has 50% more apples than Dana. This can be expressed as: [ B = D + 0.50D = 1.50D ] 3. **Find the relationship between the amounts of apples Charlie and Bella have:** To find how much more apples Charlie has compared to Bella, we calculate the difference and then find what percentage this difference is of Bella's amount: [ C - B = 1.75D - 1.50D = 0.25D ] To find this as a percentage of Bella's amount: [ text{Percentage} = left(frac{0.25D}{1.50D}right) times 100% = frac{0.25}{1.50} times 100% = frac{1}{6} times 100% approx 16.67% ] Thus, Charlie has approximately 16.67% more apples than Bella. Therefore, the correct answer is textbf{(B)}. The final answer is boxed{textbf{(B)}}

answer:To calculate the equivalent overall percentage reduction for each bicycle, we need to apply each discount consecutively and then determine the overall percentage reduction from the original price. Let's start with Bicycle A: 1. Bicycle A (600 original price): - First reduction: 20% of 600 = 120, so the new price is 600 - 120 = 480. - Second reduction: 15% of 480 = 72, so the new price is 480 - 72 = 408. - Third reduction: 10% of 408 = 40.80, so the final price is 408 - 40.80 = 367.20. The overall reduction for Bicycle A is 600 - 367.20 = 232.80. The equivalent overall percentage reduction is (232.80 / 600) * 100% = 38.8%. Now, Bicycle B: 2. Bicycle B (800 original price): - First reduction: 25% of 800 = 200, so the new price is 800 - 200 = 600. - Second reduction: 20% of 600 = 120, so the new price is 600 - 120 = 480. - Third reduction: 5% of 480 = 24, so the final price is 480 - 24 = 456. The overall reduction for Bicycle B is 800 - 456 = 344. The equivalent overall percentage reduction is (344 / 800) * 100% = 43%. Finally, Bicycle C: 3. Bicycle C (1000 original price): - First reduction: 30% of 1000 = 300, so the new price is 1000 - 300 = 700. - Second reduction: 10% of 700 = 70, so the new price is 700 - 70 = 630. - Third reduction: 25% of 630 = 157.50, so the final price is 630 - 157.50 = 472.50. The overall reduction for Bicycle C is 1000 - 472.50 = 527.50. The equivalent overall percentage reduction is (527.50 / 1000) * 100% = 52.75%. So, the equivalent overall percentage reductions for each bicycle are: - Bicycle A: 38.8% - Bicycle B: 43% - Bicycle C: boxed{52.75%}

answer:(I) To simplify f(α), we first rewrite the trigonometric functions using angle identities: f(α)= frac{sin (π-α)tan (-α-π)}{sin (π+α)cos (2π-α)tan (-α)} Since α is in the second quadrant, we know that sin α > 0 and cos α < 0. Using the identities sin(π-α) = sin α, tan(-α-π) = -tan α, sin(π+α) = -sin α, cos(2π-α) = cos α, and tan(-α) = -tan α, we can simplify the expression: f(α)= frac{sin α(-tan α)}{-sin αcos α(-tan α)} Now, cancel out the common factors: require{cancel}f(α)=frac{cancel{sin α}(-cancel{tan α})}{-cancel{sin α}cos α(-cancel{tan α})}=-frac{1}{cos α} (II) Given that cos (α- frac{3π}{2})=-frac{1}{3}, we first use the cofunction identity cos(α- frac{3π}{2}) = sin α: sin α = -frac{1}{3} However, since α is an angle in the second quadrant, we know that sin α > 0. Therefore, there is a sign error in the given solution. The correct identity should be: cos left(frac{3π}{2} - αright) = sin α Now we can correctly find the value of sin α: sin α = frac{1}{3} Next, we find the value of cos α using the Pythagorean identity: cos α = -sqrt{1-sin^2 α} = -sqrt{1-left(frac{1}{3}right)^2} = -frac{2sqrt{2}}{3} Finally, we substitute the value of cos α in the simplified expression for f(α): f(α)=-frac{1}{cos α}=-frac{1}{-frac{2sqrt{2}}{3}}=boxed{frac{3sqrt{2}}{4}}

answer:Solution: The circumference of the circle: 3.14 times 2 times 2 = 3.14 times 4 = 12.56 (CM); The area of the circle: 3.14 times 2^2 = 3.14 times 4 = 12.56 (CM^2); Therefore, the numerical values are equal, but the units are different. Hence, the correct option is: boxed{C}. This can be determined by calculating based on the formulas for the circumference and area of a circle. This tests the formula for the circumference of a circle: C = 2pi r. It also tests the formula for the area of a circle: S = pi r^2.