answer:We consider the same three cases as in the original problem: 1. **Exponent is 0**: Solve x^2 - 7x + 6 = 0. Factoring gives (x-6)(x-1) = 0, so x = 6 or x = 1. 2. **Base is 1**: Solve x^2 - 6x + 4 = 1. Simplifying, x^2 - 6x + 3 = 0. Factoring gives (x-3)(x-3) = 0, so x = 3 (a repeated root). 3. **Base is -1 and exponent is even**: Solve x^2 - 6x + 4 = -1. Simplifying, x^2 - 6x + 5 = 0. Factoring gives (x-5)(x-1) = 0, so x = 5 or x = 1. Check the parity of the exponent: for x = 5, x^2 - 7x + 6 = 25 - 35 + 6 = -4 (even); for x = 1, x^2 - 7x + 6 = 1 - 7 + 6 = 0 (even). Summing all distinct solutions: x = 1, 3, 5, 6. The sum is 1 + 3 + 5 + 6 = boxed{15}.

answer:Let's call the number you're looking for "x". According to the problem, when you multiply this number by 7 and then add 21.28, you get 50.68. We can write this as an equation: 7x + 21.28 = 50.68 Now, we want to solve for x. First, we'll subtract 21.28 from both sides of the equation to isolate the term with x: 7x + 21.28 - 21.28 = 50.68 - 21.28 7x = 29.40 Next, we'll divide both sides by 7 to solve for x: 7x / 7 = 29.40 / 7 x = 4.2 So the number you're looking for is boxed{4.2} .

answer:**Analysis** This question examines the application issues of linear regression analysis and independence test, which is a basic question. By analyzing and judging the correctness of the statements in the options based on the application issues of independence test and linear correlation, we can determine the answer. **Solution** For statement 1, the correlation relationship is an uncertain relationship, so statement 1 is incorrect; For statement 2, in the regression model, (x) is called the explanatory variable, (widehat{y}) is called the forecast variable, so statement 2 is correct; For statement 3, the closer (R^2) is to (1), the better the regression effect, so statement 3 is correct; For statement 4, in the independence test, the larger (|ad-bc|) is, the larger the observed value (K^2) is, indicating a stronger relationship between the two categorical variables; the smaller (|ad-bc|) is, the smaller (K^2) is, indicating a weaker relationship between the two categorical variables, so statement 4 is incorrect; For statement 5, if the residual points are evenly distributed in a horizontal band area, and the narrower the band area, the higher the prediction accuracy of the regression equation, so statement 5 is correct. In summary, the correct statements are 2, 3, and 5, totaling 3. Therefore, the correct option is boxed{C}.

answer:We consider two cases because if the first card is an Ace, it could be a diamondsuit or not be a diamondsuit. 1. There is a dfrac{1}{52} chance that the Ace of diamondsuit is drawn first, and a dfrac{12}{51} = dfrac{4}{17} chance that the second card drawn is one of the twelve remaining diamondsuit, which gives a probability of dfrac{1}{52} times dfrac{4}{17} = dfrac{1}{221} that this occurs. 2. There is a dfrac{3}{52} chance that a non-diamondsuit Ace is drawn first, and a dfrac{13}{51} chance that a diamondsuit is drawn second, giving a probability of dfrac{3}{52} times dfrac{13}{51} = dfrac{39}{2652} = dfrac{13}{884} that this occurs. 3. Adding these probabilities, we get dfrac{1}{221} + dfrac{13}{884} = dfrac{4}{884} + dfrac{13}{884} = dfrac{17}{884} = dfrac{1}{52}. Thus, the total probability is boxed{dfrac{1}{52}}.