Rithvik's Blog 11+

A box contains 5 red balls, 3 green balls, and 2 blue balls. If 2 balls are randomly drawn from the box without replacement, what is the probability that both balls are red?

The exterior angles of a regular polygon are given by (3x - 10) degrees and the interior angles are given by (4x + 5) degrees. Determine the number of sides of the polygon.

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is randomly selected from the bag, what is the probability of choosing a red or green marble?

The graph of the equation y = 2x^2 + 3x - 5 is a parabola. Determine the vertex (h, k) of the parabola

A geometric sequence has a common ratio of 3 and its third term is 81. Find the first term of the sequence.

A car rental company charges a fixed fee of £50 and an additional £30 per day for renting a car. Let's denote the total cost as C and the number of days as D. Write an equation to represent the total cost C in terms of the number of days D.

The ratio of boys to girls in a class is 5:3. If there are 48 students in total, how many boys and girls are in the class?

Solve the following simultaneous equations for x and y: 2x + 3y = 10 4x - 5y = 2

A triangle has side lengths of 8 cm, 12 cm, and 15 cm. Determine whether the triangle is a right triangle or not

The quadratic equation x^2 - 5x + k = 0 has roots p and q. Given that, p + q = 7 and pq = 10, find the value of k.

 A cylindrical water tank has a radius of 5 meters and a height of 12 meters. If the tank is filled to 80% of its capacity, calculate the volume of water in the tank, in cubic meters. Give your answer in terms of pi.

Solve the following equation for x: 3^(2x + 1) - 27 = 9^(x + 2)

Simplify the following: (4x^3y^2 - 2x^2y^3 + 6xy^4) / (2xy)

Simplify the following algebraic expression: 4x + 2y - (3x - y) A) x + 3y B) x - y C) x - y + 2 D) 7x + y   

Solve the following equation for x: 3x + 5 = 2x - 7