Answer:
Area of the regular dodecagon inscribed in a circle will be 27 square units.
Step-by-step explanation:
A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.
Since angle formed at the center by a polygon = 
Therefore, angle at the center of a dodecagon = 
= 30°
Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units
Now area of a small triangle = 
where a and b are the sides of the triangle and θ is the angle between them.
Now area of the small triangle = 
= 
Area of dodecagon = 12×area of the small triangle
= 12×
= 27 unit²
Therefore, area of the regular octagon is 27 square unit.
Answer:
The test hypothesis is
:
Step-by-step explanation:
Consider the provided information.
Null hypothesis refer the population parameter is equal to the claimed value.
If there is no statistical significance in the test then it is know as the null which is denoted by 
, otherwise it is known as alternative hypothesis which denoted by 
.
The historical average lifetime for cartridges produced by the current process is 1502.5 pages.
Hence, the test hypothesis is
:
Equations and Inequalities - Multiplication equations - First Glance. To solve a multiplication equation, use the inverse operation of division. Divide both sides by the same non-zero number. Click the equation to see how to solve it.
5m + 4m = 72
Combine like terms.
9m = 72
Divide both sides by 9.
m = 8
