The common difference can be found by calculating S_n - S_(n-1). Here, S_n = 3n^2 + 2n and S_(n-1) = 3(n-1)^2 + 2(n-1). The difference simplifies to 4.

'a' represents the first term of the arithmetic series.

Let the first term be a. The sum of the first three terms is a + 2a + 4a = 7a. Setting 7a = 14 gives a = 2.

Let the integers be x, x+1, and x+2. Their sum is x + (x + 1) + (x + 2) = 3x + 3 = 72. Solving gives 3x = 69, so x = 23.

All pairs listed are multiples of 7 that sum to 56.

The reciprocals are 1, 4, and 9. The common difference is 4 - 1 = 3.

The reciprocals of the terms are 1/3, 1/6, and 1/x. Since they form an arithmetic progression, we can set up the equation: 1/6 - 1/3 = 1/x - 1/6, solving gives x = 12.

The complement of set A consists of elements in the universal set U that are not in set A. Therefore, the complement is {1, 3, 5}.

Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 degrees.

If two angles are equal and their sum is 180 degrees, they are straight angles, each measuring 90 degrees.

The centers of two intersecting circles are equidistant from the points of intersection.

Circles that intersect at two points are said to be secant to each other.

The combinations that give a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), totaling 6 combinations. The total outcomes are 36, so the probability is 6/36 = 1/6.

Two lines are parallel if their slopes are equal, which occurs when a/d = b/e.

Both lines have the same slope (2) but different y-intercepts, indicating they are parallel.

Both alternate interior angles and corresponding angles are equal when two parallel lines are cut by a transversal.

When two parallel lines are cut by a transversal, alternate interior angles and corresponding angles are equal, while consecutive interior angles are supplementary. Therefore, the correct answer is 'All of the above'.

Typically, partners who contribute more capital may negotiate for a larger share of profits.

To find x, subtract 3 from both sides: x = 7 - 3, which gives x = 4.

We have x = 8 and y = 4. Thus, x/y = 8/4 = 2.

Using the method of successive substitutions or the Chinese Remainder Theorem, the smallest solution is x = 26.

x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.

'10' in base 3 is 3 and '11' is 4. Their product is 12, which is '110' in base 3.

'132' in base 4 is calculated as 1*4^2 + 3*4^1 + 2*4^0 = 16 + 12 + 2 = 30.

In base-5, '34' is 3*5 + 4 = 19 and '21' is 2*5 + 1 = 11. Their sum is 30, which is '100' in base-5.

The base-5 number 243 converts to decimal as 2*5^2 + 4*5^1 + 3*5^0 = 50 + 20 + 3 = 73.

In a base-5 numeral system, valid digits are 0, 1, 2, 3, and 4; thus, 5 is not valid.

'12' in base-6 is 1*6 + 2 = 8. '3' is 3. Their product is 8*3 = 24, which is '42' in base-6.

The probability that both are smokers is 0.3 * 0.3 = 0.09.

The probability that it does not rain = 1 - P(rain) = 1 - 0.1 = 0.9.