MIT

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question:Queenie earns 150 a day as a part-time clerk. She earns an additional 5 per hour as overtime pay. Queenie will receive 770 for working 5 days with x hours overtime. 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 hours of overtime Queenie worked. Let's break down the information given: Queenie earns 150 a day as a part-time clerk. Queenie earns an additional 5 per hour as overtime pay. Queenie worked 5 days. Total earnings for working 5 days with x hours overtime: 770 We can set up the equation as follows: Total earnings from part-time work + Total earnings from overtime work = Total earnings 150 * 5 + 5 * x = 770 Let's simplify and solve for x: 750 + 5x = 770 To isolate x, we subtract 750 from both sides of the equation: 750 + 5x - 750 = 770 - 750 5x = 20 To solve for x, we divide both sides of the equation by 5: x = 20 / 5 x = 4 The value of x is 4. Queenie worked 4 hours of overtime. 4 The answer is: 4

question:f the lengths of two sides of a right triangle are 5 and 12 units, what is the least possible length, in units, of the third side? Express your answer in simplest radical form.

answer:Since the triangle is a right triangle, we can use the Pythagorean theorem to find the length of the third side. Let c be the length of the third side. By the Pythagorean theorem, we have c^2 = 12^2 - 5^2 = 144 - 25 = 119. Taking the square root of both sides, we find c = sqrt{119}. Therefore, the least possible length of the third side is boxed{sqrt{119}} units.The answer is: sqrt{119}

question:f Carly collected 7 starfish, each with 5 arms, and one seastar with 14 arms, what is the total number of arms on the animals she collected?

answer:Carly collected 7 starfish, each with 5 arms, so the total number of arms on the starfish is 7 * 5 = 35 arms. She also collected one seastar with 14 arms. Therefore, the total number of arms on the animals she collected is 35 + 14 = 49 arms. 49 The answer is: 49

question:Jack goes hunting 6 times a month. The hunting season lasts for 1 quarter of the year. He catches 2 deers each time he goes hunting and they weigh 600 pounds each. He keeps half the weight of deer a year. How much deer does he keep in pounds?

answer:The hunting season lasts for 1/4 of the year, so Jack goes hunting for 12/4 = 3 months. He goes hunting 6 times a month, so in 3 months he goes hunting 6 x 3 = 18 times. He catches 2 deer each time he goes hunting, so in 18 hunts he catches 18 x 2 = 36 deer. Each deer weighs 600 pounds, so the total weight of the deer he catches is 36 x 600 = 21,600 pounds. He keeps half the weight of the deer, so he keeps 21,600 / 2 = 10,800 pounds of deer. 10800 The answer is: 10800