Appearance
question:Paul makes pencils, making x pencils a day five days a week. He started the week with 80 pencils in his stock, and during the week he sold 350 pencils. He had 230 pencils in his stock at the end of the week. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of pencils Paul makes a day. Let's break down the information given: Number of pencils Paul makes a day: x Number of days in a week: 5 Initial number of pencils in stock: 80 Number of pencils sold during the week: 350 Final number of pencils in stock: 230 We can set up the equation as follows: Initial number of pencils in stock + (Number of pencils made a day * Number of days in a week) - Number of pencils sold during the week = Final number of pencils in stock 80 + (x * 5) - 350 = 230 Let's simplify and solve for x: 5x - 270 = 230 To isolate x, we add 270 to both sides of the equation: 5x - 270 + 270 = 230 + 270 5x = 500 To solve for x, we divide both sides of the equation by 5: x = 500 / 5 x = 100 The value of x is 100. 100 The answer is: 100
question:On Monday, Jasmine had 2 paperclips. Each day after that, the number of paperclips she had tripled. On which day of the week did she first have more than 100 paperclips?
answer:On Monday, Jasmine had 2 paperclips. On Tuesday, she had 2 times 3 = 6 paperclips. On Wednesday, she had 6 times 3 = 18 paperclips. On Thursday, she had 18 times 3 = 54 paperclips. On Friday, she had 54 times 3 = 162 paperclips. Therefore, Jasmine first had more than 100 paperclips on boxed{text{Friday}}.The answer is: text{Friday}
question:Compute begin{pmatrix} -4 -1 end{pmatrix} cdot begin{pmatrix} 6 X end{pmatrix}. The answer is -32. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which is the unknown variable in the second vector. We are given that the dot product of the two vectors is -32. The dot product of two vectors is calculated by multiplying the corresponding components and adding them together. In this case, we have: (-4)(6) + (-1)(x) = -32 -24 - x = -32 To isolate x, we add x to both sides of the equation: -24 - x + x = -32 + x -24 = -32 + x To solve for x, we subtract -32 from both sides of the equation: -24 - (-32) = -32 - (-32) + x -24 + 32 = 0 + x 8 = x The value of x is 8. The answer is: 8
question:f all three digits on a suitcase lock have to be different, how many possible settings are there with the digits 0, 1, 2,..., 9 on each dial?
answer:For the first dial, we have 10 choices (0 through 9). For the second dial, we have 9 choices (any digit except the one already chosen on the first dial). And for the third dial, we have 8 choices (any digit except the two already chosen on the first and second dials). So the total number of possible settings is 10 times 9 times 8 = boxed{720}. The answer is: 720