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question:At constant temperature, the pressure of a sample of gas is inversely proportional to its volume. I have some oxygen in a 2.28 liter container with a pressure of X kPa. If I move all of it to a 5.7 liter container at the same temperature, The new pressure will be 2 kPa. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the initial pressure of the oxygen in the 2.28 liter container. We know that pressure is inversely proportional to volume. This means that as the volume increases, the pressure decreases. Let's set up the equation using the formula for inverse proportionality: Initial pressure * Initial volume = New pressure * New volume X kPa * 2.28 liters = 2 kPa * 5.7 liters Let's simplify and solve for x: 2.28X = 11.4 To isolate x, we divide both sides of the equation by 2.28: 2.28X / 2.28 = 11.4 / 2.28 X = 5 The value of x is 5 kPa. The answer is: 5
question:Using the digits 1, 2, 3, 4, X, 40 even three-digit numbers less than 500 can be formed if each digit can be used more than once. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the missing digit. We know that the three-digit numbers formed must be even and less than 500. Let's break down the information given: Digits available: 1, 2, 3, 4, X Number of even three-digit numbers less than 500 that can be formed: 40 To form an even three-digit number, the units digit must be even. So it can be either 2 or 4. If the units digit is 2, the hundreds digit can be any of the available digits except 2. If the units digit is 4, the hundreds digit can be any of the available digits except 4. Since we need to form 40 even three-digit numbers, we can have 20 numbers with units digit 2 and 20 numbers with units digit 4. Let's consider the case when the units digit is 2: Number of available digits for the hundreds digit: 4 (1, 3, 4, X) Number of available digits for the tens digit: 5 (1, 2, 3, 4, X) So, the total number of three-digit numbers with units digit 2 is 4 * 5 = 20. Now let's consider the case when the units digit is 4: Number of available digits for the hundreds digit: 3 (1, 2, 3) Number of available digits for the tens digit: 5 (1, 2, 3, X, 4) So, the total number of three-digit numbers with units digit 4 is 3 * 5 = 15. Adding the numbers from both cases, we get 20 + 15 = 35 three-digit numbers. Since we need 40 three-digit numbers, there must be 5 more numbers that can be formed. To form these 5 numbers, we need to use the available digits (1, 2, 3, 4, X) as the hundreds digit. So, the value of unknown variable x must be 5. The value of x is 5. The answer is: 5
question:Trisha needed to buy some groceries for herself and her dog. She spent 17 on meat, 22 on chicken, x on all the veggies, 5 on the eggs, and finally 45 on her dog’s food. When she left the store, she had only 35 left. How much money did she bring with her at the beginning? If we know the answer to the above question is 167, what is the value of unknown variable x?
answer:Trisha spent 17 on meat, 22 on chicken, x on veggies, 5 on eggs, and 45 on her dog's food. The total amount of money she spent is: 17 + 22 + x + 5 + 45 = 89 + x. When she left the store, she had 35 left. So, the amount of money she brought with her at the beginning is: 89 + x + 35 = 124 + x. We are given that the amount of money she brought with her at the beginning is 167, so we can write: 124 + x = 167. Solving for x, we get: x = 167 - 124 = 43. The value of x is 43. 43 The answer is: 43
question:There are 8 loads of laundry that need to be washed. Each load of laundry takes around 45 minutes to complete in the wash cycle and 1 hour in the dry cycle. How long, in hours, will it take to complete the entire set of laundry?
answer:To complete one load of laundry, it takes 45 minutes in the wash cycle and 1 hour in the dry cycle, so a total of 45 minutes + 60 minutes = 105 minutes. Since there are 8 loads of laundry, it will take a total of 8 loads x 105 minutes per load = 840 minutes. To convert minutes to hours, we divide by 60, so it will take 840 minutes / 60 minutes per hour = 14 hours. 14 The answer is: 14