MathDB

4

Part of 2019 BMT Spring

Problems(5)

This could be good to introduce someone to geo probability (BMT 2019 Algebra #4)

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5/5/2019
Two real numbers x x and y y are both chosen at random from the closed interval [−10,10] [-10, 10] . Find the probability that x2+y2<10 x^2 + y^2 < 10 . Express your answer as a common fraction in terms of π \pi .
probability
Pythagoras would be proud (BMT 2019 Geo #4)

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5/10/2019
The area of right triangle ABC ABC is 4, and the length of hypotenuse AB AB is 12. Compute the perimeter of △ABC \triangle ABC .
In honor of the great Dr. Rubinstein-Salzedo... (BMT 2019 Discrete #4)

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5/24/2019
There exists one pair of positive integers a,b a, b such that 100>a>b>0 100 > a > b > 0 and 1a+1b=235 \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{2}{35} . Find a+b a + b .
2019 BMT Team 4

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1/7/2022
Let C be the number of ways to arrange the letters of the word CATALYSIS, T be the number of ways to arrange the letters of the word TRANSPORT, S be the number of ways to arrange the letters of the word STRUCTURE, and M be the number of ways to arrange the letters of the word MOTION. What is C−T+SM\frac{C - T + S}{M} ?
combinatorics
2019 BMT Individual 4

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1/9/2022
Justin is being served two different types of chips, A-chips, and B-chips. If there are 33 B-chips and 55 A-chips, and if Justin randomly grabs 33 chips, what is the probability that none of them are A-chips?
probabilitycombinatorics