Answer:
A = 27π units²
Step-by-step explanation:
Note that a central angle of 120 degrees corresponds to 1/3 of a full circle.
The area of the full circle is A = πr², or A = π(9 units)² = 81π units², and so
the area of the sector in question is 1/3 of that, or A = 27π units²
Answer:
it is b because I did the problem yes it is b
First, substitute the given radius and given height of the cone into the formula for the volume of a cone.
Volume of a cone: (1/3) pi r^2 h
In this case, the cone volume is (1/3) pi (12 cm)^2 (12 cm) = 576 cm^3
Vol. of a rt. cylinder: pi r^2 h
In this case, the vol. of the rt. cyl. is pi (8 cm)^2 h.
The two different shapes have the same volume. Therefore, set the two formulas (above) equal to each other:
576 pi cm^3 = pi (8cm)^2 h. This becomes
576 pi cm^3 = pi (64 cm^2) h. "pi" cancels out, leaving us with
576 cm^3
------------- = h. This is the height of the cylinder, in cm.
64 cm^2
Answer:
3u - 2v + w = 69i + 19j.
8u - 6v = 184i + 60j.
7v - 4w = -128i + 62j.
u - 5w = -9i + 37j.
Step-by-step explanation:
Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it
. This explanation uses both representations.
.
.
.
There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,
.
So is the case when the constant is negative:
.
When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,
.
Apply the two rules for the four vector operations.
<h3>1.</h3>

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.
.
<h3>2.</h3>
.
<h3>3.</h3>
.
<h3>4.</h3>
.
Answer: The test statistic value is -0.95.
Step-by-step explanation:
Since we have given that

Here, n = 4000
x = 170
So, 
So, Test statistic value would be

Hence, the test statistic value is -0.95.