Appearance
question:A cat spends its time hunting birds. The cat catches 8 birds during the day and twice this many at night. In total, how many birds did the cat catch?
answer:During the day, the cat catches 8 birds. At night, the cat catches twice as many birds, so 2 * 8 = 16 birds. In total, the cat catches 8 + 16 = 24 birds. 24 The answer is: 24
question:Gwen received a x bonus at work and decided to invest this money in the stock market. She spent one-third of her bonus on stock A, one-third on stock B, and the remaining one-third on stock C. After one year, stock A and stock B had doubled in value, while stock C had lost half of its value. At the end of the year, how much were Gwen's stocks worth, In dollars, it is 1350. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the amount of Gwen's bonus. Let's break down the information given: Amount of bonus spent on stock A: 1/3x Amount of bonus spent on stock B: 1/3x Amount of bonus spent on stock C: 1/3x Value of stock A after one year: 2 * 1/3x = 2/3x Value of stock B after one year: 2 * 1/3x = 2/3x Value of stock C after one year: 1/2 * 1/3x = 1/6x Total value of Gwen's stocks after one year: (2/3x) + (2/3x) + (1/6x) = 1350 Let's simplify and solve for x: (4/3x) + (1/6x) = 1350 To add fractions, we need a common denominator. In this case, the common denominator is 6: (8/6x) + (1/6x) = 1350 To combine the fractions, we add the numerators: 9/6x = 1350 To isolate x, we multiply both sides of the equation by 6/9: (9/6x) * (6/9) = 1350 * (6/9) x = 1350 * (6/9) x = 900 The value of x is 900. 900 The answer is: 900
question:Add X + 163_7. Express your answer in base 7. If we know the answer to the above question is 203_7, what is the value of unknown variable X?
answer:We are given that X + 163_7 = 203_7. To find the value of X, we need to subtract 163_7 from both sides of the equation: X = 203_7 - 163_7 To subtract the numbers in base 7, we need to borrow from the next place value. In this case, we need to borrow 1 from the 7's place, which becomes 6 in the units place. Then we can subtract: X = 203_7 - 163_7 = 040_7 Therefore, the value of X is 040_7. The answer is: 7
question:What is the period of y = cos frac{x}{2}?
answer:The period of the function y=cos left(frac{x}{2}right) is given by 2pi divided by the absolute value of the coefficient of x inside the cosine function. In this case, the coefficient of x is 1/2, so the period is 2pi/(1/2) = 4pi. Therefore, the period of the function is boxed{4pi}. The answer is: 4pi