Point `O` is the origin and point `A = (−3, 1)`. Point `A` is reflected over the x-axis to point `B`. Find the area of triangle `AOB`.
A circle has radius 4 and perpendicular diameters `bar (AC)` and `bar (BD)`. Find the area of the shaded region.
Point `M` is the midpoint of `OA` where `O` is the origin and `A = (2, 5)`. Point `P = (p, q)` is in the first quadrant and on the perpendicular bisector of `OA`. If `PM = AM`, find `p + q`.
Find the sum of the prime factors (with repeats if they occur) of 2018. Now find the sum of the prime factors of your answer. Continue this process until your number remains unchanged. What is that number?
A small country has exactly 15 cities, with no 3 cities on the same straight line. Straight roads joining each pair of cities are constructed. Find the number of roads.
The first term of an arithmetic sequence is 1 and the 4th term is 13. Find the 10th term.
Suppose `F(n)` represents the number of positive factors of the integer `n`. For example, `F(8) = 4`, since the factors of `8` are `1, 2, 4,` and `8`. Find `F(168)`.
Consider the following rule to determine terms of a sequence:
1. If a term, `x`, is even, then the next term is `1/2x`.
2. If a term, `x`, is odd, then the next term is `3x + 1`.
3. The first term is 20.
Find the 100 th term.
Let `X` be a 2-digit number and let `Y` be the number with the digits reversed. Find the 2-digit number if `3X − 4Y = 8`.
Evaluate `(−1)^(1!) + (−1)^(2!) + (−1)^(3!) + ⋯ + (−1)^(100!)`
A Mersenne prime number is one of the form `n=2^p − 1` where `n` is prime. The number `2^44497 − 1` is a Mersenne Prime. What is its units digit?
Alysha is training for a distance race and trains for 5 weeks. After keeping track of the number of hours for the 5 weeks, Alysha notices the following:
a. The first week she trained 2 more hours than the average for all 5 weeks.
b. On the second week, she trained for 36 hours.
c. On the 3rd week, she trained 7 more hours than the average of the first 2 weeks.
d. On the 4th week, she trained 8 hours less than the average of weeks two and three.
e. On the fifth week, she trained 2 hours less than the 4th week.
How many hours did Alysha train over the 5 weeks?