Answer:
1) 6 cm
2) 117°
Step-by-step explanation:
1) Draw a picture of the rhombus. The distance between opposite sides is the height of the rhombus. If we draw the height at the vertex, we get a right triangle. Using trigonometry:
sin 30° = h / 12
h = 12 sin 30°
h = 6 cm
2) Draw a picture of the rectangle.
∠KML is the angle the diagonal makes with the shorter side ML. This angle is 54°. ∠NKM is the angle the diagonal makes with the shorter side NK. ∠KML and ∠NKM are alternate interior angles, so m∠NKM = 54°.
The angle bisector of angle ∠NKM divides the angle into two equal parts and intersects the longer side NM at point P. So m∠PKM = 27°.
KLMN is a rectangle, so it has right angles. That means ∠KML and ∠KMN are complementary. So m∠KMN = 36°.
We now know the measures of two angles of triangle KPM. Since angles of a triangle add up to 180°, we can find the measure of the third angle:
m∠KPM + 36° + 27° = 180°
m∠KPM = 117°
The perimeter of the polygon will be given by:
Perimeter=distance around the figure
Thus the perimeter will be:
P=9.9+(9.9-5.9)+5.9+15.9+(15.9-4.6)+4.6
P=9.9+4+5.9+15.9+11.3+4.6
P=51.6
Answer: 51.6 units
Answer:
The minimum sample size that should be taken is 62.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
If we want to be 90% confident that the sample mean is within 1 word per minute of the true population mean, what is the minimum sample size that should be taken
This is n when 
. So
The minimum sample size that should be taken is 62.
Answer:
63.7 feet
Step-by-step explanation:
We can re-write the width and the length both as rational numbers:
- Width: 
- Length: 
So now we can find the area of the garden by multiplying width and length:
Step-by-step explanation:
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