15 hours from 9 o'clock is calculated as (9 + 15) mod 12 = 24 mod 12 = 0, which is 12 o'clock.

Reflecting a point across the x-axis changes the sign of the y-coordinate. Thus, A(2, 3) becomes (2, -3).

Reflecting a point (x, y) over the x-axis results in (x, -y). Therefore, A(2, 3) becomes (2, -3).

In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.

The coefficient 'a' in a quadratic function determines whether the parabola opens upwards (a > 0) or downwards (a < 0).

The function has critical points where the first derivative is zero, which can be analyzed to find both local maxima and minima.

The probability of losing all 4 games is (0.75)^4 = 0.3164. Therefore, the probability of winning at least once is 1 - 0.3164 = 0.6836, approximately 0.84.

The nth term of a GP is given by a * r^(n-1). Here, a = 3, r = 2, and n = 5. Thus, the 5th term = 3 * 2^(5-1) = 3 * 16 = 48.

The sum of the first n terms of a GP is given by S_n = a(1 - r^n)/(1 - r) for r ≠ 1.

The nth term of a geometric series is given by ar^(n-1). Here, a = 4, r = 2, n = 6. So, 4 * 2^(6-1) = 4 * 32 = 128.

The sum of the first n terms of a geometric series is a(1 - r^n) / (1 - r). Here, a = 4, r = 2, n = 5. So, 4(1 - 2^5) / (1 - 2) = 4(1 - 32) / -1 = 124.

The first four terms are 5, 2.5, 1.25, and 0.625. Their sum is 5 + 2.5 + 1.25 + 0.625 = 9.375.

The number of people who like at least one sport is 90 + 60 - 30 = 120, so those who like neither is 150 - 120 = 30.

The number of people who like only football is 120 - 50 = 70.

The first term is 1, the second term is 1/2, and the third term can be calculated as 1/(1 + 1/2) = 2/3. The sum is 1 + 1/2 + 2/3 = 2.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of 2 and 3 are 1/2 and 1/3. The common difference is 1/3 - 1/2 = -1/6. The third term's reciprocal will be 1/3 - 1/6 = 1/6, so the third term is 6.

In a harmonic progression, the reciprocals of the terms form an arithmetic progression. The reciprocals of the first two terms are 1/2 and 3/4. The common difference is 1/4, so the reciprocal of the third term is 1/2 + 1/4 = 3/4. Therefore, the third term is 1/(3/4) = 4/3.

The reciprocals of the terms are 1/4 and 1/2. The common difference is 1/2 - 1/4 = 1/4.

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8. The third term's reciprocal will be 1/8 - 1/8 = 0, hence the third term is 16.

The reciprocals are 1/4 and 1/8. The common difference is 1/8 - 1/4 = -1/8, which means the common difference of the corresponding arithmetic progression is 1/8.

The nth term of a harmonic progression can be expressed as 1/(1/a + (n-1)d) where d is the common difference of the corresponding arithmetic progression.

A premise is a statement or proposition that provides the basis for a conclusion in a logical argument.

P(winning at least once) = 1 - P(not winning) = 1 - (0.95^10) ≈ 0.4013.

Using the binomial probability formula, P(X=1) = C(10,1) * (0.05)^1 * (0.95)^9 = 10 * 0.05 * 0.630 = 0.315, approximately 0.2.

An algorithm is defined as a step-by-step procedure for calculations, widely used in various fields of mathematics and computer science.

The total parts in the mixture = 3 + 2 = 5. The fraction of A = 3/5.

Overall alcohol = (25% + 75%) / 2 = 50%.

Overall purity = (60% + 80%) / 2 = 70%.

Cost of mixture = (2*5 + 3*7) / (2 + 3) = (10 + 21) / 5 = 31 / 5 = $6.20.

To find x, we calculate 7 mod 5, which is 2. Therefore, x = 2.