What is the amplitude, period, and phase shift of f(x) = −4 sin(2x + π) − 5? .

Amplitude = 4; period = π; phase shift: x = negative pi over two

Step-by-step explanation:

In this problem you have to use the form a sin (bx-c)+d to find the amplitude, period, and phase shift.

Amplitude:4

Period : π

Phase shift:

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1.) 0.54 ; 0.46

2.) 0.50 ; 0.40 ; 0.05 ; 0.85 ; 0.15

Step-by-step explanation:

A = feel guilty about wasting food ; P(A) = 0.39

B = feel guilty leaving lights on ; P(B) = 0.27

Probability of feeling guilty for doing both = 0.12

P(AnB) = 0.12

1a.) What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?

P(AuB) = P(A) + P(B) - P(AnB)

= 0.39 + 0.27 - 0.12

= 0.54

1b.) What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?

P(AuB)' = 1 - P(AuB)

P(AuB)' = 1 - 0.54

P(AuB)' = 0.46

2.)

n(ACC) = 10

n(SEC) = 8

n(total) = 20

n(ACC n SEC) = 1

a. What is the probability the ACC will have a team in the championship game (to 2 decimals)?

n(ACC) / n(Total) = 10 /20 = 0.50

b. What is the probability the SEC will have a team in the championship game (to 2 decimals)?

n(SEC) / n(Total) = 8/20 = 0.40

c. What is the probability the ACC and SEC will both have teams in the championship game (to 2 decimals)?

1 /20 = 0.05

d.)

P(AuB) = P(A) + P(B) - P(AnB)

= 0.50 + 0.40 - 0.05

= 0.85

e.)

P(AuB)' = 1 - P(AuB)

P(AuB)' = 1 - 0.85

= 0.15