Answer:
132 mm^2
Step-by-step explanation:
The line added to the figure in the attachment shows it can be divided into two figures whose area is easily calculated.
1. A parallelogram of base length 20 mm and height 4 mm:
A = bh = (20 mm)(4 mm) = 80 mm^2
2. A trapezoid with bases 32 mm and 20 mm, and height 2 mm:
A = (1/2)(b1 +b2)h = (1/2)(32 mm +20 mm)(2 mm) = 52 mm^2
The total area of the figure is then ...
80 mm^2 +52 mm^2 = 132 mm^2
Answer:
On a unit circle, the point that corresponds to an angle of is at position
.
The point that corresponds to an angle of is at position
.
Step-by-step explanation:
On a cartesian plane, a unit circle is
The circle crosses the x- and y-axis at four points:
Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.
When the angle is equal to , the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be
.
To locate the point with a angle, rotate the
segment counter-clockwise by
. The segment would land on the positive y-axis. In other words, the
-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be
.
A suitable probability calculator can tell you the probability is about 6.7%.
_____
The standard deviation of the distribution of sample means is the population standard deviation (6) divided by the square root of the sample size (√144=12). Thus, your threshold is about (19.25-20)/(6/12) = -1.5 standard deviations from the mean.
