h(2)=-2²+6(2) the question has to be 20 characters long so I'm just adding this
2 answers:
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*see attachment below for the box plots that is being referred to
Answer:
*The median weight for shelter A is greater than that for shelter B
*The data for shelter B are a symmetric data set
Step-by-step explanation:
Let's take each stated option and examine the box plot to see which is TRUE or NOT.
OPTION 1: "The median weight for shelter A is greater than that for shelter B."
The median for shelter A = 21,
Median for shelter B = 18
Median weight for shelter A (21) is greater than that for shelter B.
This statement in this option is TRUE.
OPTION 2: "The median weight for shelter B is greater than that for shelter A."
Median for B (18) < median of A (21)
This statement in option is NOT TRUE.
OPTION 3: "The data for shelter A are a symmetric data set."
This is NOT TRUE because the length of both whiskers are unequal and also, the box is not divided equally. One side is longer than the other.
OPTION 4: "The data for shelter B are a symmetric data set."
This is TRUE because the length of both whiskers are relatively equal, and also, the rectangular box is divided equally.
OPTION 5: "The interquartile range for shelter A is 8"
This is NOT TRUE.
IQR = Q3-Q1
IQR for shelter A is approximately = 28-17 = 11
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