Answer with Step-by-step explanation:
Volume of sphere is given by
V=
where r is the radius of sphere
Let d be the diameter then, r=d/2
d=18 cm
⇒ r=9 cm
V=
V=
V=972π cubic centimeters
When diameter is reduced to half
⇒radius is reduced to half
⇒ r'=r/2
⇒V'=
⇒ V'=
⇒ V'=V/8
Hence, If its diameter were reduced by half, its volume would be 1/8 of its original volume.
Answer:
Option D : $20
Step-by-step explanation:
The average total cost to produce 100 oatmeal cookie = $0.25 per cookie.
So, total cost for 100 cookies will be = dollars
The company’s marginal cost is constant at $0.10 for all oatmeal cookies produced.
When 50 cookies are produced, the marginal cost will be = dollars
The total cost to produce 50 oatmeal cookies = dollars
Hence, option D is correct.
Answer:
Option A and Option B are not equivalent to the given expression.
Step-by-step explanation:
We are given the following expression:
Applying properties of exponents and base:
A. Using the exponential property , we can write:
which is not equal to the given expression.
B. Using the exponential property , we can write:
which is not equal to the given expression.
C. First we convert the radical form into exponent form. Then by using the property of exponent, we can write the following:
which is equal to the given expression.
D. First we convert the radical form into exponent form. Then by using the property of exponent, we can write the following:
which is equal to the given expression.
Option D and Option C are equivalent to the given expression.
Any 1 of the following transformations will work. There are others that are also possible.
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
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We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.
