In the following series, identify the number that needs to be changed to form the Fibonacci series.
1, 1, 2, 3, 6, 8, 13, 21, …
The real variables $x, y, z$, and the real constants $p, q, r$ satisfy
$\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$
Given that the denominators are non-zero, the value of $px + qy + rz$ is
Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4 probability of landing on any of the four rectangular faces. The label on the top face of the dice is the score of the throw.
If thrown together, what is the probability of getting the sum of the two long dice scores greater than 11?
A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.
What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?
