1
For how many ordered pairs of positive integers (π₯, π¦) is π₯ + 2π¦ = 100?
49
Which of the following is a factor of π2 β π2 + 6π + 4π + 5?
π β π + 5
The ratio of the supplements of two angles is 9:8 and the ratio of their complements is 3:2. Find the sum of the degree measures of the original angles.
105
Four dice are rolled. Given that no more than one of them rolled a 6, what is the probability that none of them rolled a 6?
5/9
Mu Lu tosses a fair coin, after which Wiggie throws a fair die. They continue this pattern until Mu Lu gets a tail and wins or Wiggie throws a 5 and wins. What is the probability that Mu Lu wins?
6/7
Each of two beakers contains 100mL of 20% acid solution. Some amount of pure acid is added to the first beaker, and some amount of water is evaporated from the second beaker. Both actions result in doubling the concentration. Which of the following is the closest to the amount of acid solution in the end? (That is, in both beakers combined, measured in mL.)
186
Not counting just 2019 itself as β1 consecutive integerβ, the least number of consecutive integers whose sum is 2019 is 2, since 1009 + 1010 = 2019. What is the largest number of consecutive integers whose sum is 2019?
4038
Compute the area of the hexagon when the 6 roots of π₯6 = 8 are connected in the complex plane.
3 root 3
Find the sum of the x and y coordinates of the point that is equidistant from (-2,5), (6,7), and (8,5).
5
The functions π(π₯) = π₯2 + 1 and π(π₯) = βπ₯2 share a common tangent line of positive slope. What is its equation?
y = root 2 + 0.5