Mathematics Quiz: Various Topics

The combined price after discounts: 564 manats Price of suit after discount: 564 - (Price of shoes after discount) Price of shoes after discount = 0.7 x (Original price of shoes) Price of suit after discount = 0.8 x (Original price of suit) Therefore: 0.8 x (Original price of suit) + 0.7 x (Original price of shoes) = 564 Original price of suit + Original price of shoes = 720 Solve the system of equations to get the original price of the suit.

Percentage increase = ((New population - Old population) / Old population) x 100% Percentage increase = ((74200 - 70000)/70000) x 100%

Modulus of a complex number: |z| = √(Real part² + Imaginary part²) Find z_2 by simplifying the given expression. Multiply z_1 and z_2 by their respective coefficients. Add all terms to get the complex number z. Find the modulus of z using the formula.

Length of AD can be determined using the Pythagorean theorem. AC and CD are radii of the circle, so AC = CD = 8. Apply the Pythagorean theorem to triangle ACD: AD² = AC² + CD² AD = √(AC² + CD²)

0.2(6) + 0.2 = (0.2 x 6) + 0.2 = 1.2 + 0.2 = 1.4

The projection of a line segment onto a plane is the line segment formed by drawing perpendicular lines from each endpoint of the line segment to the plane. Length of the projection: √(1² - (0.5 - 0.1)²) = √(1² - 0.4²) = √(0.84) cm

Probability = (Favorable outcomes) / (Total possible outcomes) Favorable outcomes: Even numbers divisible by 7 in the range of 1-50 are 14, 28, 42. Total possible outcomes: 50 Probability = 3/50

Multiply both sides of the inequality by 6 to eliminate fractions. Simplify and solve for k: 21 - 9k - 16k - 2 < 72 - 60k -25k + 19 < 72 - 60k 35k < 53 k < 53/35

The angle $

alpha$ is formed in the square, and it becomes the acute angle of a right triangle formed by dividing the square into 25 equal parts. The angle $

alpha$ is formed by the line segment between two adjacent points on the grid, so it represents the ratio of the side of the square to one part (i.e., 1/5).
The tangent of $

alpha$ can be found by dividing the opposite side of the triangle by the adjacent side (i.e., 1/4). The angle $

beta$ is also formed by the line segment between two points on the grid, and it represents the ratio of the side of the square to one part (i.e., 1/5). The cosine of $

beta$ can be found by dividing the adjacent side of the triangle by the hypotenuse (i.e., 4/√32). Therefore, the final answer is 1/4 + 4/√32

Degree of a polynomial is the highest power of its variable. Degree of a polynomial raised to a power is the degree of the polynomial multiplied by the exponent. Degree of $M_1 = 8 * 4 = 32$. Degree of $M_2 = 7 * 6 = 42$. Degree of $M_5 = 5 * 4 = 20$. Degree of $M_{11} = 11 * 4 = 44$. Degree of $M_{22} = 22 * 4 = 88$. Degree of $M_5

⋅ M_{11}

⋅ M_{22}$: 20 + 44 + 88 = 152