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question:Marc bought 50 episodes of the show "Friends" online. Each day Marc watches 1/10 of the episodes he bought. How many days will Marc need to finish 50 episodes of the show he bought?
answer:If Marc bought 50 episodes of the show and watches 1/10 of the episodes each day, he will watch 50 * 1/10 = 5 episodes per day. To finish 50 episodes, Marc will need 50 / 5 = 10 days. 10 The answer is: 10
question:My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. There are 1120 ways to select the team to have 3 boys and X girls. 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 girls on the team. Let's break down the information given: Number of boys in the math club: 6 Number of girls in the math club: 8 Total number of ways to select the team: 1120 Number of boys on the team: 3 Number of girls on the team: x We can set up the equation as follows: Number of ways to select 3 boys * Number of ways to select x girls = Total number of ways to select the team C(6, 3) * C(8, x) = 1120 C(6, 3) represents the number of ways to choose 3 boys from a group of 6, which is equal to 20. C(8, x) represents the number of ways to choose x girls from a group of 8. Let's simplify and solve for x: 20 * C(8, x) = 1120 To isolate C(8, x), we divide both sides of the equation by 20: C(8, x) = 1120 / 20 C(8, x) = 56 To find the value of x, we need to determine the number of ways to choose x girls from a group of 8 that equals 56. By trial and error, we find that C(8, 3) = 56. Therefore, the value of x is 3. The value of x is 3. The answer is: 3
question:On Tuesday, Liza had x in her checking account. On Wednesday, she paid her rent, 450. On Thursday, she deposited her 1500 paycheck. On Friday, she paid her electricity and internet bills which were 117 and 100, respectively. Then on Saturday, she paid her phone bill, 70. How much money is left in Liza's account? If we know the answer to the above question is 1563, what is the value of unknown variable x?
answer:On Tuesday, Liza had x in her checking account. On Wednesday, she paid her rent, 450, which means she had x - 450 left. On Thursday, she deposited her 1500 paycheck, which means she had (x - 450) + 1500 = x + 1050. On Friday, she paid her electricity and internet bills, 117 and 100, respectively, which means she had (x + 1050) - 117 - 100 = x + 833 left. On Saturday, she paid her phone bill, 70, which means she had (x + 833) - 70 = x + 763 left. We are given that the amount of money left in Liza's account is 1563, so we can write: x + 763 = 1563. Subtracting 763 from both sides, we get: x = 800. The value of x is 800. 800 The answer is: 800
question:What is the minimum value of 5x^2-20x+1357?
answer:We can rewrite the expression as 5(x^2-4x)+1357. Completing the square inside the parentheses, we get 5(x^2-4x+4)+1357-5(4). Simplifying further, we have 5(x-2)^2+1337. Since (x-2)^2 is always nonnegative, the minimum value of 5(x-2)^2 is 0, which occurs when x=2. Therefore, the minimum value of 5(x^2-4x+1357) is 5(0)+1337=boxed{1337}. The answer is: 1337