answer:Let ( y = sqrt{x - 2} ). Then ( y^2 = x - 2 ), and hence ( x = y^2 + 2 ). Therefore, the given expression transforms as: [ frac{x + 9}{sqrt{x - 2}} = frac{y^2 + 11}{y} = y + frac{11}{y}. ] By the arithmetic mean-geometric mean inequality (AM-GM), [ y + frac{11}{y} ge 2sqrt{y cdot frac{11}{y}} = 2sqrt{11}. ] Equality occurs when ( y = sqrt{11} ), or substituting back ( x = 11 + 2 = 13 ). For the maximum, note that the expression ( y + frac{11}{y} ) grows larger as ( y ) deviates further from ( sqrt{11} ), approaching infinity as ( y ) tends to either 0 or ( infty ). Therefore, the minimum value of the expression is ( 2sqrt{11} ), occurring at ( x = 13 ), and the maximum value is unbounded as ( x ) tends towards 2 or ( infty ). Conclusion: The minimum value of ( frac{x + 9}{sqrt{x - 2}} ) is ( boxed{2sqrt{11}} ) at ( x = 13 ), and the maximum value is unbounded.

answer:The coefficient of x should be negative to indicate a negative correlation, which eliminates options B and D. Considering the practical meaning, we know x > 0 and y > 0. In option C, the scatter plot would be in the fourth quadrant, which is meaningless. Therefore, the correct choice is boxed{text{A}}.

answer:To find out how many hours Jaydee will take to finish typing the research paper, we first need to calculate the total number of minutes it will take him to type 7125 words. Since Jaydee can type 32 words in a minute, we divide the total number of words by the number of words he can type per minute: 7125 words ÷ 32 words/minute = 222.65625 minutes Now, to convert minutes into hours, we divide the total number of minutes by 60 (since there are 60 minutes in an hour): 222.65625 minutes ÷ 60 minutes/hour = 3.7109375 hours Therefore, Jaydee will take approximately boxed{3.71} hours to finish typing the research paper.

answer:Let's assume the cost price (CP) of the articles is 100. The shopkeeper wants to earn a profit of 40%, so he labels the price (LP) of the articles as: LP = CP + (40% of CP) LP = 100 + (0.40 * 100) LP = 100 + 40 LP = 140 Now, the shopkeeper offers a discount of 5% on the labeled price. The selling price (SP) after the discount is: Discount = 5% of LP Discount = 0.05 * 140 Discount = 7 SP = LP - Discount SP = 140 - 7 SP = 133 The actual profit earned is the difference between the selling price and the cost price: Profit = SP - CP Profit = 133 - 100 Profit = 33 To find the actual percent profit, we use the formula: Percent Profit = (Profit / CP) * 100 Percent Profit = (33 / 100) * 100 Percent Profit = 0.33 * 100 Percent Profit = 33% So, the actual percent profit earned in the deal is boxed{33%} .