answer:To find the least number that must be subtracted from 7538 to make it divisible by 14, we need to find the remainder when 7538 is divided by 14. The number that must be subtracted will be equal to this remainder. Let's perform the division: 7538 ÷ 14 = 538 with a remainder of 6. This means that when 7538 is divided by 14, there is a remainder of 6. To make 7538 divisible by 14, we need to subtract this remainder from it. Therefore, the least number that must be subtracted from 7538 to make it divisible by 14 is boxed{6} .

answer:1. **Center square remains unchanged**: The center 4 squares (positions (2,2), (2,3), (3,2), (3,3) in a 4 times 4 grid) remain unchanged after rotation. For the entire grid to be black, each of these center squares must start as black. The probability for one square to be black is frac{1}{3}, so for all four center squares, the probability is: [ left(frac{1}{3}right)^4 = frac{1}{81} ] 2. **Consider rotation effect on other squares**: The other 12 squares are affected by rotation. Each square must either start black or turn black due to a white square rotating into a black square. 3. **Calculation for edge and corner squares**: Separately, consider the first row's four squares. For simplicity, since the grid is symmetric and colored at random, each square in the first row behaves identically to corresponding squares in the other rows and columns. - Probability each is initially black: frac{1}{3} - Probability each starts white and rotates into a black square (i.e., the corresponding initial square in the last column must be black): frac{1}{3} times frac{1}{3} = frac{1}{9} - Thus, the probability that each square in the first row ends up black is frac{1}{3} + frac{1}{9} - (frac{1}{3} times frac{1}{9}) (to correct for double counting the scenario where both squares are initially black): [ frac{1}{3} + frac{1}{9} - frac{1}{27} = frac{9}{27} + frac{3}{27} - frac{1}{27} = frac{11}{27} ] 4. **Combine probabilities**: Multiply the probability for the center squares with the probability that each of the 12 rotating squares turns black: [ frac{1}{81} times left(frac{11}{27}right)^{12} ] 5. **Conclusion**: The overall probability that the grid is entirely black after the operation is: [ frac{1{81} times left(frac{11}{27}right)^{12}} ] The final answer is boxed{A}

answer:If Shara is 10 years old, twice her age would be 2 * 10 = 20 years. Since Jaymee is 2 years older than twice Shara's age, we add 2 to 20. So, Jaymee is 20 + 2 = boxed{22} years old.

answer:1. Calculate the expressions under the square roots: [ 64 + 81 = 145 quad text{and} quad 49 - 36 = 13 ] 2. Calculate the square roots: [ sqrt{145} quad text{and} quad sqrt{13} ] 3. Subtract the second square root from the first: [ sqrt{145} - sqrt{13} ] Since we are not required to provide decimal approximations, we leave the answer in a simplified exact form: [ boxed{sqrt{145} - sqrt{13}} ]