MathDB

4

Part of 2021 BMT

Problems(5)

BMT Discrete #4 - Basketball Teams Pick Captains

Source:

11/29/2021
Derek and Julia are two of 64 players at a casual basketball tournament. The players split up into 8 teams of 8 players at random. Each team then randomly selects 2 captains among their players. What is the probability that both Derek and Julia are captains?
probabilityBmt
BMT 2021 Guts Round p4

Source:

10/7/2022
Compute the sum of all real solutions to 4x−2021⋅2x+1024=04^x - 2021 \cdot 2^x + 1024 = 0.
algebra
BMT 2021 Geometry #4

Source:

8/12/2023
An equilateral polygon has unit side length and alternating interior angle measures of 15o15^o and 300o300^o. Compute the area of this polygon.
geometry
BMT 2021 General p4

Source:

9/27/2023
Moor and Samantha are drinking tea at a constant rate. If Moor starts drinking tea at 8:008:00 am, he will finish drinking 77 cups of tea by 12:0012:00 pm. If Samantha joins Moor at 10:0010:00 am, they will finish drinking the 77 cups of tea by 11:1511:15 am. How many hours would it take Samantha to drink 11 cup of tea?
algebra
2021 BMT Algebra #4

Source:

3/10/2024
Let θ\theta be a real number such that 1+sin⁡2θ−(12sin⁡2θ)2=01 + \sin 2\theta -\left(\frac12 \sin 2\theta\right)^2= 0. Compute the maximum value of (1+sin⁡θ)(1+cos⁡θ)(1 + \sin \theta )(1 + \cos \theta).
algebratrigonometry