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A point on the rim of a wheel with a radius of 80 meters travels 50 meters in 30 seconds. How many degrees per second does the wheel rotate?

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A pool is enclosed between two concentric circles with radii of 10 and 15 meters and has a depth of 3 meters. If the pool is empty at 2:00 PM and is filled at a rate of 5 cubic meters per minute, at what time, to the nearest minute, will the pool first be full?

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A merry-go-round with a radius of 50 feet rotates at a speed of 3 degrees per second. How many feet does a point on the edge of the merry-go-round, farthest from the center, travel in 2 minutes?

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What fraction of a 12-inch pie contains the same amount of filling as a slice of a 14-inch pie cut into 10 equal slices, assuming both pies have the same thickness?

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In the following figure, each circle is tangent to the other two circles, and the two shaded circles are identical to each other. What is the ratio of the shaded region to the nonshaded region?

$\"\"$

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Liam and his friend Noah were racing on a 400-meter track. Noah started running first, and Liam didn’t start until Noah had completed half a lap. Liam passed Noah at the exact moment they both finished their seventh lap. If both ran at constant speeds, with Liam running 3 meters per second faster than Noah, what was Noah\\'s speed in meters per second?

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There are $$300$$ students at Greenwood High, where the ratio of sophomores to seniors is $$5:7$$. There are $$200$$ students at Lincoln High, where the ratio of sophomores to seniors is $$3:2$$. The two schools hold a combined event, and all the sophomores and seniors from both schools attend. What fraction of the students at the event are seniors?

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Lisa and John are working together to review $$72$$ reports. Lisa can review $$4$$ reports per hour, and John can review $$5$$ reports per hour. If Lisa starts reviewing first and John joins her three hours later, how many reports will John have reviewed by the time they finish?

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The ratio of the side lengths of a triangle is exactly $$5:8:10$$. In a second triangle similar to the first, the shortest side is $$15$$ inches long. To the nearest tenth of an inch, what is the length of the longest side of the second triangle?

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Let $$a$$ and $$b$$ be numbers such that $$a$$ and $$b$$ are both nonzero and $$a>b$$. If one-third of $$a$$ is equal to forty percent of the positive difference between $$a$$ and $$b$$, then what is the ratio of $$a$$ to $$b$$?

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A box contains apples that are either red or yellow. The ratio of red apples to yellow apples in the box is $$5:4$$. When $$6$$ red apples and $$6$$ yellow apples are removed, the ratio becomes $$4:3$$. How many yellow apples were originally in the box?

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The time $$T$$ a pendulum takes to complete one full oscillation is directly proportional to the square root of its length $$L$$ and inversely proportional to the square root of the acceleration due to gravity $$g$$. If $$k$$ represents the constant of proportionality, which of the following expressions represents the time $$T$$ for a pendulum of length $$L$$ when the acceleration due to gravity is $$g$$?

","type_question":"QCM","explication":"","points":1,"temps_limite":"$undefined","reponses":[]},{"id":"cml0m82vb05nyv2ak7xxe6whu","texte_question":"

Lucas is designing a decorative hanging ornament composed of 3 circular metal plates of different sizes. The smallest circle has a diameter of 10 inches, and the diameters of the three circles are in the ratio $$1:3:5$$. To stabilize the ornament, Lucas will attach a straight metal rod from the center of the smallest circle, through the center of the middle circle, to the center of the largest circle. What is the total length, in inches, of the metal rod?

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A factory hires workers to assemble and pack smartphones. Each worker assigned to assembly can produce $$20$$ smartphones per hour. Each worker assigned to packaging can pack $$4$$ smartphones every $$10$$ minutes. The factory currently has $$10$$ workers, all assigned to assembly. How many additional workers should be hired and assigned to packaging so that the number of smartphones assembled and packaged are equal per hour?

","type_question":"QCM","explication":"","points":1,"temps_limite":"$undefined","reponses":[]},{"id":"cml0m82vb05o8v2akii3c2gax","texte_question":"

Lena deposits $$800$$ into a savings account that earns $$4\\\\%$$ interest compounded quarterly.
After $$1.5$$ years, she withdraws $$250$$. How much money does she have after $$2$$ years?

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