answer:Let's consider a circle representing the wheel with radius 2 text{ m}. The circumference of the circle is calculated by C = 2pi r = 2pi times 2 = 4pi text{ m}. For one complete revolution, the center of the wheel would travel a distance equal to the circumference of the wheel, which is 4pi text{ m}. However, the wheel is rolled for one and a quarter revolutions. Therefore, the total distance is: text{Total distance} = 1.25 times 4pi = 5pi text{ m} Hence, the center of the wheel traveled boxed{5pi} meters horizontally.

answer:Let's denote the original cost of each concert ticket as ( x ). Mr. Benson bought 12 tickets, so without any discount, he would have paid ( 12x ). However, he received a 5% discount for every ticket that exceeds 10. This means he received a discount on 2 tickets (since he bought 12 tickets and the first 10 are at full price). The discount on each ticket is ( 0.05x ) (which is 5% of the original cost ( x )). So the total discount he received is ( 2 times 0.05x = 0.1x ). The total amount he paid after the discount is ( 12x - 0.1x = 11.9x ). We know that Mr. Benson paid 476 in all, so we can set up the equation: ( 11.9x = 476 ) Now we can solve for ( x ): ( x = frac{476}{11.9} ) ( x = 40 ) Therefore, the original cost of each concert ticket is boxed{40} .

answer:According to the analytical expression of S, only increasing the value of a or c can increase the value of S. By using the method of special values, since 0<c<d<e<b<a, let's assign a=9, b=7, c=1, d=3, e=5. Then, S= frac {191}{105}. When a is increased by 1, S= frac {206}{105}, and the increase in the value of S is frac {15}{105}. When c is increased by 1, S= frac {226}{105}, and the increase in the value of S is frac {35}{105}. Therefore, when c is increased by 1, the value of S increases the most. Hence, the answer is boxed{c}. By using the method of special values, we assign a set of special values to a, b, c, d, e according to their order of magnitude and calculate the value of S. According to the analytical expression of S, only increasing the value of a or c can increase the value of S. We then compare the increase in the value of S when a is increased by 1 and when c is increased by 1. This problem examines the comparison of the sizes of several expressions under certain conditions, which can be approached by substituting special values.

answer:To find the gain percent, we use the formula: Gain Percent = (Gain / Cost Price) * 100 First, we need to calculate the gain, which is the difference between the selling price and the cost price. Gain = Selling Price - Cost Price Gain = 110 - 100 Gain = 10 Now we can calculate the gain percent: Gain Percent = (10 / 100) * 100 Gain Percent = 0.1 * 100 Gain Percent = 10% So, the gain percent is boxed{10%} .