A person has a 30 percent chance of winning on a scratch-off lottery ticket. What is the probability she first wins of the fifth
1 answer:
You might be interested in
Answer: 267.947 (or 267.95) inches^3
Step-by-step explanation:
The formula for the volume of a sphere is .
To find your radius (r), divide the diameter of 8 inches by 2. <em>The radius is 4 inches.</em>
Plug in your numbers to the volume equation to get . The first step is to cube 4 (4*4*4) to get <em>64</em>. Now your equation is
.
Multiply 3.14 and 64 to get <em>200.96</em>. The equation is now or
.
Multiply the numerators (4 * 200.96) and denominators (1 * 3) to get a final equation of .
Finally, divide 803.84 by 3 to get the final answer of 267.947 in^3.
Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
.
- There is an n×n matrix D such that AD=
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
- For each column vector b in
, the equation Ax=b has a unique solution.
- The columns of A span
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
The correct option is C.