answer:To find the smallest integer b for which 27^b > 3^24, we can use the fact that 27 is a power of 3. Specifically, 27 is equal to 3^3. So, we can rewrite 27^b as (3^3)^b, which simplifies to 3^(3b). Now we want to find the smallest integer b such that 3^(3b) > 3^24. Since the base is the same (3), we can compare the exponents directly. We want to find the smallest integer b such that 3b > 24. Divide both sides by 3 to solve for b: b > 24 / 3 b > 8 Since we are looking for the smallest integer b, and b must be greater than 8, the smallest integer that satisfies this inequality is b = 9. Therefore, the smallest integer b for which 27^b > 3^24 is b = boxed{9} .

answer:To solve this problem, we need to determine the value of x, which represents the number of inches in a foot. We know that Mr. Sanchez bought 6 feet of rope last week and 4 feet less than that this week. Last week: 6 feet This week: 6 - 4 = 2 feet Since there are x inches in a foot, we can calculate the total number of inches of ribbon Mr. Sanchez bought as follows: Total number of inches = (Number of feet last week + Number of feet this week) * Number of inches in a foot Total number of inches = (6 + 2) * x Total number of inches = 8x We are given that the total number of inches of ribbon Mr. Sanchez bought is 96. Therefore, we can set up the equation: 8x = 96 To solve for x, we divide both sides of the equation by 8: x = 96 / 8 x = 12 The value of x is 12. 12 The answer is: 12

answer:The area of a right triangle is given by the formula A = frac{1}{2}bh, where b and h are the lengths of the legs of the triangle. In this case, we are given that the leg length is 24 units, so we can substitute b = 24 into the formula. We can solve for h by rearranging the formula to get h = frac{2A}{b} = frac{2(120)}{24} = 10 units. Now we can use the Pythagorean theorem to find the length of the hypotenuse, c. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So, c^2 = 24^2 + 10^2 = 576 + 100 = 676. Taking the square root of both sides, we find that c = 26 units. Finally, we can find the perimeter of the triangle by adding up the lengths of all three sides: 24 + 10 + 26 = boxed{60} units. The answer is: 60

answer:From the given bio, we can gather the following details about Vladislav Naydenko: 1. Full name: Vladislav Andreyevich Naydenko 2. Date of birth: May 18, 1990 3. Nationality: Russian 4. Occupation: Football (soccer) player 5. Position: Defender 6. Last played for: FC Syzran-2003 Syzran (a Russian football club) 7. Debut: Made his debut in the Russian Second Division (now known as the Russian Football National League) for FC Syzran-2003 Syzran 8. Debut date: July 7, 2011 9. Debut match: Played against FC Khimik Dzerzhinsk in his debut match. This information provides a brief overview of Vladislav Naydenko's personal details, football career, and accomplishments.