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question:The function f(x) is defined by f(x)=x^{2}-x. What is the value of f(4)?
answer:To find f(4), we substitute x=4 into the expression for f(x). We have f(4)=4^{2}-4=16-4=boxed{12}. The answer is: 12
question:Rookie police officers have to buy duty shoes at the full price of x, but officers who have served at least a year get a 20% discount. Officers who have served at least three years get an additional 25% off the discounted price. How much does an officer who has served at least three years have to pay for shoes? If we know the answer to the above question is 51, what is the value of unknown variable x?
answer:An officer who has served at least a year gets a 20% discount, which means they have to pay 80% of the full price. An officer who has served at least three years gets an additional 25% off the discounted price, which means they have to pay 75% of the discounted price. So, the total price they have to pay is 75% of 80% of the full price: 0.75 * 0.8 * x. We are given that the officer has to pay 51, so we can write: 0.75 * 0.8 * x = 51. Dividing both sides by 0.6, we get: x = 85. The value of x is 85. 85 The answer is: 85
question:f Karen bakes 50 chocolate chip cookies, keeps 10 for herself, and gives 8 to her grandparents, how many cookies can she give to each person in her class if there are 16 people in her class?
answer:Karen bakes 50 cookies. She keeps 10 for herself and gives 8 to her grandparents, so she has 50 - 10 - 8 = 32 cookies left. Karen wants to give these cookies to the people in her class, and there are 16 people in her class. To find out how many cookies she can give to each person, we divide the number of cookies left by the number of people in her class: 32 cookies / 16 people = 2 cookies per person. So Karen can give 2 cookies to each person in her class. 2 The answer is: 2
question:Mary is trying to count the animals in the petting zoo, but they kept moving around so she double-counts 7 sheep and forgets to count 3 pigs. If Mary thinks there are x animals, There are 56 of them really. What is the value of unknown variable x? 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 animals that Mary thinks are in the petting zoo. Let's break down the information given: Number of animals that Mary double-counted: 7 sheep Number of animals that Mary forgot to count: 3 pigs Total number of animals in reality: 56 We can set up the equation as follows: Number of animals that Mary thinks are in the petting zoo - Number of animals that Mary double-counted + Number of animals that Mary forgot to count = Total number of animals in reality x - 7 + 3 = 56 Let's simplify and solve for x: x - 4 = 56 To isolate x, we add 4 to both sides of the equation: x - 4 + 4 = 56 + 4 x = 60 The value of x is 60. 60 The answer is: 60