Answer:
Step-by-step explanation:
Given that X is the number of months between successive payments
Cumulative distribution function of X is
a) PMF of x would be
b)
Help me with this problem please
1 answer:
It makes more sense to start with parts (c) and (d), then answer parts (a) and (b).
(c) The plot is below.
(d) Mixtures that are the same color have the same ratio of blue to yellow. They fall on the same line.
(a) There are two (2) different shades of paint mixtures.
(b) Shades A and C are the bluest. Their ratio of blue to yellow is the highest. (The slope of the line connecting their dots to the origin is the steepest.)
(c) The plot is below.
(d) Mixtures that are the same color have the same ratio of blue to yellow. They fall on the same line.
(a) There are two (2) different shades of paint mixtures.
(b) Shades A and C are the bluest. Their ratio of blue to yellow is the highest. (The slope of the line connecting their dots to the origin is the steepest.)
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Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A