answer:It takes 2.5 hours to groom a dog, so it takes 2.5 * 60 = 150 minutes to groom a dog. It takes x hours to groom a cat, so it takes x * 60 = 60x minutes to groom a cat. To find the total number of minutes it takes to groom 5 dogs and 3 cats, we can multiply the number of minutes it takes to groom a dog by 5 and the number of minutes it takes to groom a cat by 3, and then add the two results: 150 * 5 + 60x * 3 = 750 + 180x. We are given that the total number of minutes it takes to groom 5 dogs and 3 cats is 840, so we can write: 750 + 180x = 840. Solving for x, we get: 180x = 90. Dividing both sides by 180, we get: x = 0.5. The value of x is 0.5. 0.5 The answer is: 0.5

answer:To solve this problem, we need to determine the value of x, which represents the maximum value of each digit in the code chosen by Reckha. We know that our code is 023, so Reckha cannot choose a code that is the same as ours in two or more of the three digit-positions, nor can she choose a code that is the same as ours except for switching the positions of two digits. There are 969 codes available for Reckha. Let's break down the information given: Number of possible codes: 969 First digit can be any number from 0 to x. Second digit can be any number from 0 to x, excluding the first digit of our code (0). Third digit can be any number from 0 to x, excluding the first two digits of our code (0 and 2). We can set up the equation as follows: Number of possible codes = (Number of choices for the first digit) * (Number of choices for the second digit) * (Number of choices for the third digit) 969 = (x + 1) * (x - 1) * (x - 2) Let's simplify and solve for x: 969 = (x + 1) * (x - 1) * (x - 2) 969 = (x^2 - 1) * (x - 2) 969 = x^3 - 3x^2 + 2x + 2 To find the value of x, we can use trial and error or a calculator. We find that x = 9 is a solution to the equation. Therefore, the value of the unknown variable x is 9. The answer is: 9

answer:To solve this problem, we need to determine the value of x, which represents the number of toes each Neglart has on each of their 5 hands. Let's break down the information given: Number of toes on each Hoopit hand: 3 Number of Hoopit students: 7 Number of toes on each Neglart hand: x Number of Neglart students: 8 Total number of toes on the Popton school bus: 164 We can set up the equation as follows: (Number of toes on each Hoopit hand * Number of Hoopit students * Number of hands) + (Number of toes on each Neglart hand * Number of Neglart students * Number of hands) = Total number of toes on the Popton school bus (3 * 7 * 4) + (x * 8 * 5) = 164 Let's simplify and solve for x: 84 + 40x = 164 To isolate x, we subtract 84 from both sides of the equation: 84 + 40x - 84 = 164 - 84 40x = 80 To solve for x, we divide both sides of the equation by 40: x = 80 / 40 x = 2 The value of x is 2. 2 The answer is: 2

answer:To solve this problem, we need to determine the value of x, which represents the unknown variable in the equation log_{10} 40 +log_{10} X = 3. Let's simplify the equation: log_{10} 40 +log_{10} X = 3 We can combine the logarithms using the product rule: log_{10} (40X) = 3 To convert the equation into exponential form, we can rewrite it as: 10^3 = 40X Simplifying further, we have: 1000 = 40X To solve for X, we divide both sides of the equation by 40: 1000/40 = X 25 = X Therefore, the value of the unknown variable x is 25. The answer is: 25