Function Operations and Probability Problems

The video tutorial covers solving various math problems, including finding the nth term in an arithmetic series, understanding function composition and evaluation, adding functions, and calculating probabilities in different scenarios. The instructor explains each problem step-by-step, providing insights into mathematical reasoning and problem-solving techniques.

What is the formula for the nth term of an arithmetic sequence where the first term is 3 and the common difference is 4?

• 3n + 4

• 4n - 1

• 3n - 4

• 4n + 1

In an arithmetic sequence, if the first term is 5 and the common difference is 3, what is the 4th term?

• 14

• 11

• 17

• 8

If f(x) = x^2 - 1 and g(x) = x + 3, what is f(g(x))?

• (x + 3)^2 - 1

• x^2 + 3x - 1

• x^2 - 1 + 3

• (x + 3)^2 + 1

For f(x) = x^2 - 2x and g(x) = x + 4, what is f(g(x))?

• (x + 4)^2 + 2

• x^2 - 2x + 4

• (x + 4)^2 - 2(x + 4)

• x^2 + 4x - 2

Given f(x) = 3x^2 - 4 and g(x) = 2x - 6, what is g(f(2))?

• 14

• 12

• 8

• 10

If f(x) = 2x^2 + 3 and g(x) = x - 1, what is g(f(3))?

• 21

• 19

• 15

• 17

If f(x) = x^2 + 2x + 1 and g(x) = 3(x + 1)^2, what is the simplified form of f(x) + g(x)?

• 6x^2 + 4x + 2

• 4x^2 + 8x + 4

• 3x^2 + 6x + 3

• x^2 + 2x + 1

What is the probability that the first ruler handed out has centimeter labels and the second does not, given 15 rulers with labels and 10 without?

• 1/4

• 1/5

• 1/3

• 1/2

If the chance of rain is 80% in San Francisco and 30% in Sydney, what is the probability it will not rain in either city?

• 20%

• 10%

• 14%

• 30%

What is the probability of drawing two rulers with labels consecutively from a set of 15 labeled and 10 unlabeled rulers?

• 7/24

• 5/8

• 3/5

• 1/4