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A cookie jar contains 10 cookies of 3 types. There are 5 chocolate-chip cookies, 3 oatmeal-raisin cookies, and 2 sugar cookies. You reach into the jar and choose a cookie at random and then, without replacing the first cookie, reach into the jar and choose another cookie at random. What is the probability that both of the cookies you choose are the same type?
A cookie jar contains 10 cookies of 3 types. There are 5 chocolate-chip cookies, 3 oatmeal-raisin cookies, and 2 sugar cookies. You reach into the jar and choose a cookie at random and then, without replacing the first cookie, reach into the jar and choose another cookie at random. What is the probability that both of the cookies you choose are the same type?
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[Fermat Math Contest] If 2^11 x 6^5 = 4^x × 3^y for some positive integers x and y, then the value of x + y is (A) 10 (B) 11 (C) 12 (D) 13 (E) 14
[Fermat Math Contest] If 2^11 x 6^5 = 4^x × 3^y for some positive integers x and y, then the value of x + y is (A) 10 (B) 11 (C) 12 (D) 13 (E) 14
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Conor can throw a 360 g ball with a speed of 34 m/s. He moves his hand forward 1.1 m while doing so. (a) How much work does Conor do on the ball? (b) How much force, assumed to be constant, does Conor apply to the ball? (c) What is Conor's maximum power output as he throws the rock?
Conor can throw a 360 g ball with a speed of 34 m/s. He moves his hand forward 1.1 m while doing so. (a) How much work does Conor do on the ball? (b) How much force, assumed to be constant, does Conor apply to the ball? (c) What is Conor's maximum power output as he throws the rock?
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A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far as before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?
A spring-loaded toy dart gun is used to shoot a dart straight up in the air, and the dart reaches a maximum height of 24 m. The same dart is shot straight up a second time from the same gun, but this time the spring is compressed only half as far as before firing. How far up does the dart go this time, neglecting friction and assuming an ideal spring?
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