answer:First, we note the even and odd numbers in the set: - **Even:** (4, 6, 8, 12) - **Odd:** (3, 9) Given the constraint, we choose ({a, b, c}) with two even and one odd, and ({d, e, f}) with two odd (by repeating) and one even. 1. Let's choose ({a, b, c} = {6, 8, 3}) and ({d, e, f} = {12, 4, 9}) for maximizing the product. 2. Calculate ((a + b + c)) and ((d + e + f)): [ (6 + 8 + 3) = 17, quad (12 + 4 + 9) = 25 ] 3. The maximum sum is given by: [ 17 times 25 = 425 ] Conclusion: The largest possible sum of the nine entries is (boxed{425}).

answer:To find the rate of interest for the loan, we can use the formula for simple interest: Simple Interest (SI) = Principal (P) * Rate (R) * Time (T) In this case, we know the Simple Interest (SI) is 810 per year, and the Principal (P) is 9,000. We are looking for the Rate (R), and since the interest given is annual, the Time (T) is 1 year. Plugging in the values we have: 810 = 9,000 * R * 1 To solve for R, we divide both sides by 9,000: R = 810 / 9,000 R = 0.09 To express the rate as a percentage, we multiply by 100: R = 0.09 * 100 R = 9% Therefore, the rate of interest for the loan is boxed{9%} .

answer:Let's calculate the number of eggs each person collects: 1. Benjamin collects 6 dozen eggs. 2. Carla collects 3 times the number of eggs that Benjamin collects: Carla = 3 * Benjamin = 3 * 6 = 18 dozen eggs. 3. Trisha collects 4 dozen less than Benjamin: Trisha = Benjamin - 4 = 6 - 4 = 2 dozen eggs. 4. David collects twice the number of eggs that Trisha collects, but half the number that Carla collects. Since we know that David's collection is the same whether we double Trisha's or halve Carla's, we can calculate either way: David = 2 * Trisha = 2 * 2 = 4 dozen eggs. (We can also check: David = Carla / 2 = 18 / 2 = 9 dozen eggs, which is not correct based on the given information, so we'll stick with the first calculation.) 5. Emily collects 3/4 the amount of eggs that David collects: Emily = (3/4) * David = (3/4) * 4 = 3 dozen eggs. 6. Emily ends up with 50% more eggs than Trisha. Let's check if our calculation for Emily matches this information: 50% more than Trisha = Trisha + (1/2 * Trisha) = 2 + (1/2 * 2) = 2 + 1 = 3 dozen eggs. This matches our previous calculation for Emily, so it is correct. Now, let's add up the total number of dozen eggs collected by all five of them: Total = Benjamin + Carla + Trisha + David + Emily Total = 6 + 18 + 2 + 4 + 3 Total = 33 dozen eggs. Therefore, the five of them collect a total of boxed{33} dozen eggs.

answer:Let's denote the original number of employees in the company as E. Before hiring the additional male workers, 60% of the workforce was female. Therefore, the number of female employees was 0.60E. After hiring 24 additional male workers, the total number of employees became E + 24, which is given as 288. So we can write: E + 24 = 288 Now, let's solve for E: E = 288 - 24 E = 264 This means that before the new male workers were hired, there were 264 employees in the company. Since 60% of these were female, the number of female employees was: 0.60 * 264 = 158.4 Since the number of employees cannot be a fraction, we round this to the nearest whole number, which is 158 female employees. After hiring the 24 additional male workers, the total number of employees is 288, as given. The number of female employees remains the same (158), as the new hires were all male. To find the new percentage of female workers, we divide the number of female employees by the total number of employees and multiply by 100: (158 / 288) * 100 = 54.86% Rounded to two decimal places, the new percentage of female workers in the company is approximately boxed{54.86%} .