MATH 4 - Final Exam Review #5

Front

What is the probability of drawing a red marble first and a blue marble second from a bag containing 8 red and 4 blue marbles without replacement?

Back

The probability is 8/33.

Front

What is the middle term in the expansion of (a + b)^6?

Back

The middle term is 20a^3b^3.

Front

Identify the amplitude, period, phase shift, and vertical shift of the function y = 3 cos (x + π) + 1.

Back

Amplitude = 3, Period = 2π, Phase Shift = π, Vertical Shift = 1.

Front

How do you calculate the area of a triangle?

Back

Area = 1/2 * base * height. For the given triangle, the area is 14529.96 m.

Front

Evaluate the piecewise function f(x) = { 2x + 8, if x ≤ -2; x^2, if x > -2 } for f(2), f(5), f(1), and f(27).

Back

f(2) = 12, f(5) = 25, f(1) = 1, f(27) = 144.

Front

What is the formula for the probability of an event?

Back

Probability = Number of favorable outcomes / Total number of outcomes.

Front

What is the binomial theorem?

Back

The binomial theorem describes the algebraic expansion of powers of a binomial. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Front

Define amplitude in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline of the graph to its peak or trough.

Front

What is the formula for the area of a triangle given its base and height?

Back

Area = 1/2 * base * height.

Front

How do you find the middle term in the expansion of (a + b)^n?

Back

For even n, the middle term is the (n/2 + 1)th term; for odd n, it is the ((n+1)/2)th term.