Mathematics

Let the total number of votes polled be x. Valid votes = x - 68. The winner gets 52% of valid votes, and the loser gets 48%. The difference is 4% of valid votes, which equals 98 votes. So, 0.04(x - 68) = 98, solving gives x = 2382.

The sum of the known numbers is 6999 + 8888 + 777 = 16664. To find the missing number, subtract this sum from 19700: 19700 - 16664 = 3036. However, the options given (36, 16, 64, 26) do not include 3036. The question as stated is inconsistent with the options. The search results show a similar question but with 9999 instead of 6999, where the missing number is 36. Assuming the intended question was 9999 + 8888 + 777 + ? = 19700, the missing number is 36, which corresponds to option A. Therefore, the question and options should be corrected to use 9999 instead of 6999, making the correct answer A (36).

Revenue is calculated as Price × Quantity. When the price of TV sets is increased by 30%, the new price becomes 1.3 times the original price. When sales decrease by 20%, the quantity sold becomes 0.8 times the original quantity. Therefore, the new revenue is 1.3 × 0.8 = 1.04 times the original revenue, which means revenue increases by 4%. Hence, the effect on the revenue receipts of the shop is a 4% increase.

Total votes = 7500; invalid votes = 20% of 7500 = 1500; valid votes = 7500 - 1500 = 6000. One candidate got 55% of valid votes = 0.55 × 6000 = 3300. The other candidate got the remaining valid votes = 6000 - 3300 = 2700. However, 2700 is option A, but the question asks for the number of valid votes the other candidate got, which is 2700. The original correct_answer was A, which matches 2700, so the original answer is correct. The explanation was missing and is now provided. The difficulty is set to easy as it involves basic percentage calculations.

If the price increases by 20%, the new price is 120% of the original. To keep expenditure the same, consumption must be reduced to 100/120 = 5/6 of original, which is a reduction of (1 - 5/6) × 100% = 16.66%.

After 2 hours, the first plane travels 150 mph × 2 = 300 miles north, and the second plane travels 200 mph × 2 = 400 miles west. Using the Pythagorean theorem, the distance apart is √(300² + 400²) = √(90000 + 160000) = √250000 = 500 miles.

When the tax increases by 20%, the price becomes 120% of the original. Consumption decreases by 20%, so quantity is 80% of original. Expenditure = price × quantity = 1.2 × 0.8 = 0.96, which is a 4% decrease from the original expenditure.

When the price of sugar increases by 20%, the price factor becomes 1.20. When consumption decreases by 25%, the consumption factor becomes 0.75. The new expenditure is the product of these two factors: 1.20 × 0.75 = 0.90, which means the expenditure is 90% of the original expenditure. This is a 10% decrease in expenditure. Therefore, the family's expenditure on sugar decreases by 10%.

To find the number to add to 11.138 to make it divisible by 77, first find the remainder when 11,138 is divided by 77. 11,138 ÷ 77 gives a remainder of 69. Since 77 - 69 = 8, adding 8 to 11,138 makes it divisible by 77 exactly.

Each animal has one head, so hens + cows = 48. Hens have 2 feet and cows have 4 feet, so 2*hens + 4*cows = 140. Solving these equations gives hens = 24 and cows = 24.