answer:To calculate the percentage of profit Sahil made on the sale, we first need to determine the total cost of the machine including the purchase price, repair costs, and transportation charges. Total cost = Purchase price + Repair costs + Transportation charges Total cost = Rs 14,000 + Rs 5,000 + Rs 1,000 Total cost = Rs 20,000 Next, we calculate the profit by subtracting the total cost from the selling price. Profit = Selling price - Total cost Profit = Rs 30,000 - Rs 20,000 Profit = Rs 10,000 Now, to find the percentage of profit, we use the formula: Percentage of profit = (Profit / Total cost) x 100 Percentage of profit = (Rs 10,000 / Rs 20,000) x 100 Percentage of profit = 0.5 x 100 Percentage of profit = 50% Sahil made a boxed{50%} profit on the sale of the machine.

answer:To find the length of the train, we can use the formula: Distance = Speed × Time First, we need to convert the speed from kilometers per hour (kmph) to meters per second (m/s) because the time is given in seconds. We know that 1 km = 1000 meters and 1 hour = 3600 seconds. Speed in m/s = (Speed in kmph × 1000 meters/km) / 3600 seconds/hour Speed in m/s = (125 × 1000) / 3600 Speed in m/s = 125000 / 3600 Speed in m/s ≈ 34.7222 m/s Now, we can calculate the distance, which is the length of the train, using the time it takes to cross the pole: Distance = Speed × Time Distance = 34.7222 m/s × 7 s Distance ≈ 243.0554 meters Therefore, the length of the train is approximately boxed{243.0554} meters.

answer:1. **Analyze the distances**: - Using the condition that PA^2 + PB^2 = PC^2 given that triangle ABC is a right triangle at B: [ PA^2 + PB^2 = 5^2 + 13^2 = 25 + 169 = 194 neq 144 = 12^2 = PC^2. ] - Thus, triangle PAB is not right, and the hypothesis was incorrectly assumed. The problem instead suggests that triangle ABC is a right triangle at B. 2. **Determine AB and BC assuming triangle ABC is a right triangle**: - Since triangle ABC is a right triangle at B, use the Pythagorean theorem: [ AC^2 = AB^2 + BC^2. ] - Use the triangle inequality and given conditions to check possible values for AB and BC. Assume AB = PA + PC = 5 + 12 = 17, and BC = PB = 13. 3. **Calculate the area of triangle ABC**: [ text{Area of } triangle ABC = frac{1}{2} times AB times BC = frac{1}{2} times 17 times 13 = frac{221}{2} = 110.5. ] Conclusion and final answer: [ 110.5 ] The final answer is boxed{B}

answer:To solve this problem: 1. **Calculation of Combinations**: First, determine the number of ways to choose which 4 out of the 8 dice will show even numbers. This is given by binom{8}{4}. 2. **Probability of Each Die Rolling Even or Odd**: Since the dice are 8-sided, each die has 4 even and 4 odd outcomes. Thus, the probability that a single die shows an even or an odd number is frac{4}{8} = frac{1}{2}. 3. **Total Probability**: Each distinct arrangement where 4 dice show even numbers and 4 show odd numbers has a probability of left(frac{1}{2}right)^{!8} (since each die independently shows an even or odd number with probability frac{1}{2}). Therefore, the total probability is binom{8}{4}left(frac{1}{2}right)^{!8} = 70 cdot frac{1}{256} = frac{70}{256} = frac{35}{128}. Conclusion: Hence, the probability that exactly four of the eight dice show even numbers, and four show odd numbers, is boxed{frac{35}{128}}.