answer:To solve the given expression step-by-step, we start with the original expression: [(-frac{1}{2})^{-2}+(pi -3.14)^{0}+4cos 45^{circ}-|1-sqrt{2}|] First, we simplify each term individually: 1. (-frac{1}{2})^{-2} simplifies to 4 because raising a fraction to the power of -2 inverts the fraction and squares it, thus (-frac{1}{2})^{-2} = left(frac{1}{-frac{1}{2}}right)^2 = (-2)^2 = 4. 2. (pi -3.14)^{0} simplifies to 1 because any non-zero number raised to the power of 0 is 1. 3. 4cos 45^{circ} simplifies to 4times frac{sqrt{2}}{2} because cos 45^{circ} = frac{sqrt{2}}{2}. Therefore, 4cos 45^{circ} = 4times frac{sqrt{2}}{2} = 2sqrt{2}. 4. |1-sqrt{2}| simplifies to |sqrt{2}-1| because 1-sqrt{2} is negative, and taking the absolute value flips the sign, resulting in sqrt{2}-1. Putting it all together, we have: [4 + 1 + 2sqrt{2} - (sqrt{2}-1)] [= 4 + 1 + 2sqrt{2} - sqrt{2} + 1] [= 4 + 1 + sqrt{2} + 1] [= 6 + sqrt{2}] Therefore, the final answer is boxed{sqrt{2} + 6}.

answer:Miss Quick eats cereal at a rate of frac{1}{15} pound per minute, Mr. Fat eats at frac{1}{20} pound per minute, and Mr. Thin eats at frac{1}{30} pound per minute. Together, they eat at a combined rate of frac{1}{15} + frac{1}{20} + frac{1}{30}. To find the combined rate, find a common denominator for the fractions: [ frac{1}{15}=frac{4}{60}, , frac{1}{20}=frac{3}{60}, , frac{1}{30}=frac{2}{60} ] Therefore, the combined rate is: [ frac{4}{60}+frac{3}{60}+frac{2}{60}=frac{9}{60}=frac{3}{20} text{ pounds per minute} ] At this rate, to eat four pounds of cereal: [ frac{4}{frac{3}{20}} = frac{4 times 20}{3} = frac{80}{3} approx 26.67 text{ minutes} ] Therefore, it will take them boxed{frac{80}{3}} minutes (or approximately 26.67 minutes) to eat 4 pounds of cereal.

answer:1. **Understanding the problem requirements**: - Leonid paints a rectangular grid by coloring every other column starting from the first column, and then colors every other row starting from the first row. - The problem is to find the possible number of painted cells given that 74 white cells remain. 2. **Examining the structure of the grid**: - Denote the number of rows by (2k+1) and the number of columns by (2l+1), both must be odd numbers. This is because he colors every other column and row starting from the first, ensuring that every even-numbered row and column remain unpainted. - Each white cell must lie in a position where both its row number and column number are even. 3. **Formulating the relationship**: - The number of unpainted (white) cells after grid is colored is given by: [ text{Number of unpainted cells} = k times l = 74 ] - Therefore, we need (k times l = 74). 4. **Finding possible values for (k) and (l)**: - The pairs ((k, l)) that satisfy (k times l = 74) are ((1, 74)) and ((2, 37)), because these are only factors of 74: [ k = 1, quad l = 74 quad text{(since (1 times 74 = 74))} ] [ k = 2, quad l = 37 quad text{(since (2 times 37 = 74))} ] 5. **Calculating the total number of cells and painted cells**: - The total number of cells in the rectangle is ((2k+1) times (2l+1)). - The number of painted cells is then given by subtracting the number of white cells from the total number of cells: [ text{Number of painted cells} = (2k+1) times (2l+1) - k times l ] 6. **Substituting the values**: - For (k = 1) and (l = 74): [ text{Total cells} = (2 times 1 + 1) times (2 times 74 + 1) = 3 times 149 = 447 ] [ text{Painted cells} = 447 - 74 = 373 ] - For (k = 2) and (l = 37): [ text{Total cells} = (2 times 2 + 1) times (2 times 37 + 1) = 5 times 75 = 375 ] [ text{Painted cells} = 375 - 74 = 301 ] Hence, the possible solutions are (373) and (301). # Conclusion: [ boxed{373 text{ or } 301} ]

answer:In June, Katy read 8 books. In July, she read twice as many as in June, so she read 8 * 2 = 16 books. In August, she read three fewer than in July, so she read 16 - 3 = 13 books. To find the total number of books she read during the summer, we add the books from each month together: 8 (June) + 16 (July) + 13 (August) = 37 books. Katy read boxed{37} books during the summer.