The arithmetic mean of the numbers 8, 7, 12, x, 5, and 3 is 8. Find the value of x.
Find the equation of the line shown in the graph.
A. \( y = -\frac{2}{3}x \)
B. \( y = \frac{2}{3}x \)
C. \( y = -x \)
D. \( y = -1.5x \)
The interior angles of a convex pentagon are 100°, 90°, 135°, 135°, and $x$. Find the value of x.
Options:
A. 80°
B. 81°
C. 90°
D. 106°
If the number \( 4542x \) is divisible by 4, find the possible value(s) of x.
Find the probability that a randomly selected letter from the word "Улаанбаатар" (Ulaanbaatar) is a vowel.
A book was sold for 1210 tugriks, resulting in a 10% profit. What was the original cost (cost price) of the book?
A square ABCD has vertices at A(2, -2), B(4, -2), C(4, -4), and D(2, -4). The square is translated (shifted) according to the vector (-6, 6).
Draw the translated square on the coordinate plane and find its area. Which of the following represents the new coordinates and the area?
Options:
A. New vertices: A'(-4, 4), B'(-2, 4), C'(-2, 2), D'(-4, 2); Area = 4
B. New vertices: A'(-8, 8), B'(-10, 8), C'(-10, 6), D'(-8, 6); Area = 4
C. New vertices: A'(4, -4), B'(6, -4), C'(6, -6), D'(4, -6); Area = 16
D. New vertices: A'(-4, 4), B'(-2, 4), C'(-2, 2), D'(-4, 2); Area = 16
Students from two classes (6a and 6b) took a 10-point test. The results are shown in the frequency tables below.
Class 6a
| Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequency | 3 | 2 | 4 | 4 | 5 | 3 | 3 | 2 | 2 | 2 |
Class 6b
| Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Frequency | 6 | 6 | 5 | 4 | 7 | 1 | 1 | 1 | 0 | 0 |
Tasks:
A. How many students are there in both classes combined?
B. Which class performed better overall?
Solve the following equation for x:
Two trains start from the same point and travel around a circular track of equal length. The first train completes one lap in 16 minutes, and the second train completes one lap in 12 minutes.
If both trains start together at 07:00 AM, when will they next arrive at the starting point at the same time?
How many times will they arrive together at the starting point between 07:00 and 12:00?