A point P has coordinates (-8, -2). what are its new coordinates after reflection point P across the x -axis
1 answer:
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Answer:
Lower Quartile = 25.5
Upper Quartile = 61.5
IQR = 36
Step-by-step explanation:
Given data is:
5, 12, 17, 23, 28, 31, 37, 41, 42, 49, 54, 58, 65, 68, 73, 71
The lower quartile is the first quartile and upper quartile is the third quartile.
A median divides the data set in two equal halves.
Lower quartile also known as first quartile is the middle value in the first half.
The first half is:
5, 12, 17, 23, 28, 31, 37, 41
As the number of values is even, the quartile will be the average of two middle values
Upper quartile is the average of middle two values in the second half when the number of values is even.
42, 49, 54, 58, 65, 68, 73, 71
Interquartile range is the difference of third quartile and first quartile
Hence,
Lower Quartile = 25.5
Upper Quartile = 61.5
IQR = 36
Answer:
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
---------------------------------------------------------------
cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - cosx -
sinx
squaring to obtain cos² (120 + x)
= cos²x +
sinxcosx +
sin²x
--------------------------------------------------------------------
cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - cosx +
sinx
squaring to obtain cos²(120 - x)
= cos²x -
sinxcosx +
sin²x
--------------------------------------------------------------------------
Putting it all together
cos²x + cos²x +
sinxcosx +
sin²x +
cos²x -
sinxcosx +
sin²x
= cos²x + cos²x +
sin²x
= cos²x +
sin²x
= (cos²x + sin²x) =