1:30 PM is valid as it allows the conference to end by 4:30 PM, which is within the allowed time frame.

27 is a multiple of 3 and is less than 30, making it an element of the set.

The correct representation of the set is {1, 2, 3, 4, 5, 6, 7, 8, 9}, as it includes all natural numbers less than 10.

The valid representation of the set is {1, 2, 3, 4, 5} as it includes all integers within the specified range.

The letter 'A' is included in the set of vowels in the English alphabet.

The multiples of 3 less than 30 are 3, 6, 9, 12, 15, 18, 21, 24, 27, totaling 10 elements.

The number 31 is not an element of the set as it does not meet the constraints of being a multiple of 3 and less than 30.

The inequality x^2 < 4 implies that x must be between -2 and 2, hence the range is (-2, 2).

A winning percentage of 60% means the team won 60/100 * 30 = 18 matches.

Volume of a cube = side³. Therefore, side = ∛64 = 4 cm.

Total Price = 2 * 150 = 300. Discount = 10% of 300 = 30. Total Amount Paid = 300 - 30 = $270.

Total Price = $50 + $70 = $120. Discount = 20% of $120 = $24. Amount Paid = $120 - $24 = $96.

Total price = 50 + 50 = 100. Discount = 20% of 100 = 20. Final price = 100 - 20 = 80.

Total cost without discount = 2 * $50 = $100. Discount = 10% of $100 = $10. Total amount paid = $100 - $10 = $90.

Let the original price be x. After a 15% discount, the selling price is x - (0.15 * x) = 0.85x. Setting this equal to $85 gives 0.85x = $85, so x = $85 / 0.85 = $100.

Each match involves 2 teams, so the total number of matches is (16 teams * 4 matches) / 2 = 32.

The total number of matches is calculated using the formula n(n-1)/2, where n is the number of teams. Here, it is 16(15)/2 = 120.

To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.

In the linear function f(x) = mx + b, 'm' represents the slope, which is 2 in this case.

In the linear function f(x) = 2x + 3, the coefficient of x (which is 2) represents the slope of the graph.

In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 2.

Substituting x = 0 into the function gives f(0) = 2(0) + 3 = 3.

In the linear function f(x) = mx + b, 'm' represents the slope. Here, m = 2.

To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.

In the linear function f(x) = mx + b, m represents the slope. Here, m = 3, so the slope is 3.

In the linear function f(x) = mx + b, 'm' represents the slope, which is 3 in this case.

To find critical points, we take the derivative and set it to zero. The function has one local maximum and one local minimum based on the nature of cubic functions.

Critical points of a function can be local maxima, local minima, or points of inflection, depending on the behavior of the function around those points.

Substituting x = 4 into the function gives f(4) = 2(4) + 3 = 8 + 3 = 11.

In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 3.