answer:Let's denote the selling price as ( SP ) and the cost price as ( CP ). The profit percentage is given as 5.263157894736842%, which means that the profit (( P )) is 5.263157894736842% of the selling price. The profit can also be expressed as the difference between the selling price and the cost price: [ P = SP - CP ] Since the profit is 5.263157894736842% of the selling price, we can write: [ P = frac{5.263157894736842}{100} times SP ] Substituting the expression for ( P ) from the first equation into the second equation, we get: [ SP - CP = frac{5.263157894736842}{100} times SP ] Now, we want to find the percentage of the cost price with respect to the selling price, which is: [ frac{CP}{SP} times 100 ] To find ( CP ), we can rearrange the equation: [ CP = SP - frac{5.263157894736842}{100} times SP ] [ CP = SP times left(1 - frac{5.263157894736842}{100}right) ] [ CP = SP times left(frac{100 - 5.263157894736842}{100}right) ] [ CP = SP times frac{94.73684210526316}{100} ] Now, we can express the cost price as a percentage of the selling price: [ frac{CP}{SP} times 100 = frac{94.73684210526316}{100} times 100 ] [ frac{CP}{SP} times 100 = 94.73684210526316 ] Therefore, the percentage of the cost price with respect to the selling price is boxed{94.73684210526316%} .

answer:Given that the line is perpendicular to y = -x + 2, its slope is the negative reciprocal of the slope of y = -x + 2. Since the slope of y = -x + 2 is -1, the slope of the perpendicular line is frac{1}{-(-1)} = 1. Using the point-slope form of a line, y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope, we substitute m = 1 and (x_1, y_1) = (0, 3) to get: y - 3 = 1(x - 0) Simplifying, we get: y - 3 = x Rearranging to get the standard form of a linear equation, Ax + By + C = 0, we have: x - y + 3 = 0 Therefore, the equation of the line is boxed{x - y + 3 = 0}.

answer:1. **Selection of Balls**: Since the balls are not replaced after being drawn, each draw reduces the number of options Joe has for the next draw. 2. **First Draw**: Joe can choose any of the 15 balls. 3. **Second Draw**: Only 14 balls remain, so he has 14 choices. 4. **Third Draw**: Now, 13 balls are left, giving him 13 choices. 5. **Fourth Draw**: Finally, 12 balls remain, providing 12 choices. 6. **Calculate Total Permutations**: Multiply the number of choices for each draw to find the total number of different lists possible. This is calculated as (15 times 14 times 13 times 12). [ 15 times 14 times 13 times 12 = 32760 ] [ boxed{32760} ] Conclusion: The total number of different lists possible, when balls are not replaced, is boxed{32760}.

answer:We can write (7^{106} = (10 - 3)^{106}). Using the Binomial Theorem: [ (10 - 3)^{106} = sum_{k=0}^{106} binom{106}{k} 10^{106-k} (-3)^k ] To find the last three digits, we only need to consider terms where (106-k leq 2). These terms are: - (k = 104) for (10^2) term: (binom{106}{104} 10^2 (-3)^{104}) - (k = 105) for (10^1) term: (binom{106}{105} 10^1 (-3)^{105}) - (k = 106) for (10^0) term: (binom{106}{106} (-3)^{106}) Calculating these: - (binom{106}{104} = frac{106 cdot 105}{2} = 5565), (10^2 cdot 5565 cdot 1 = 556500) - (binom{106}{105} = 106), (10 cdot 106 cdot (-3) = -3180) - (binom{106}{106} = 1), ((-3)^{106} = 1) Summing these: [ 556500 - 3180 + 1 = 553321 ] Thus, the last three digits are (boxed{321}).