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

The number of people who like either dogs or cats is 30 + 25 - 10 = 45. Therefore, those who do not like either is 50 - 45 = 5.

The speed order is R > P > Q and S > T > P. Thus, T is the slowest.

The order of ages is B < A < C < D < E. Therefore, B is the youngest.

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, which means the common difference of the corresponding arithmetic progression is 1/8.

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 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.

If element X is found in both sets, it is classified as a common element, which is a key feature of hybrid sets.

The intersection of set P and set Q includes only the elements that are present in both sets, which are {b, c}.

If 'x' is present in both sets, it is part of the intersection, which is a key characteristic of hybrid sets.

The cardinality of the hybrid set will be at least the maximum of the two sets, which is 5, but could be more if there are common elements.

A hybrid set can be represented as the union of the sets A, B, and C, which combines all elements from each set.

The hybrid set includes all unique elements from both sets, which are {apple, banana, cherry}.

An empty intersection indicates that the two sets do not share any elements, confirming their disjoint nature.

In a knockout tournament, the number of matches required to determine a winner is always one less than the number of teams. Therefore, for 16 teams, 16 - 1 = 15 matches are needed.

Each team plays 4 other teams twice, so total matches = 5 * 4 / 2 * 2 = 20.

If X is at one end and Y at the other, there can be six people between them, making this statement true.

Since A is to the left of B and C is to the right of D, we cannot definitively place E without additional information. However, A being to the left of C is a possible arrangement.

Since P is to the left of Q and R is to the right of P, R must be to the left of Q.

R can be at one end, and P must be next to Q, making R, P, Q, S a valid arrangement.

If A is to the left of B, D cannot be to the left of A without contradicting the arrangement.

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.