Answer: Choice A)
Set A is an exponential function and the values increase at a faster rate than Set B.
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Explanation:
Focus on Set A. Each time x goes up by 1, y goes up by a factor of 10. In other words, the y value is being multiplied by 10.
- 10*10 = 100
- 100*10 = 1,000
- 1,000*10 = 10,000
- 10,000*10 = 100,000
etc
This strongly implies that we're dealing with an exponential function. The equation for this function is y = 10^x.
Plug in x = 1 and you should get y = 10. Repeat for x = 2 and it should lead to y = 100. This helps confirm we have the correct function.
On the other hand, Set B deals with a linear equation which is y = 50x+950. The slope 50 is the amount we're increasing y each time x goes up by 1. If you plug x = 1 into this, you should get y = 1000. Plug in x = 2 and it leads to y = 1050, and so on.
When comparing exponential growth rates versus linear growth rates, the exponential will be faster. This is true even if you have a very small exponential growth rate. At some point, the exponential will overtake the linear. The linear growth rate is some constant value that never changes. The exponential growth rate increases over time. Think about simple interest versus compound interest and that may be a good example to go over.
Whether the events are dependent or not, the rule for conditional probability applies:
P(a|b) = P(a∩b)/P(b)
P(a|b)×P(b) = P(a∩b)
0.25×0.4 = P(a∩b) = 0.1
The appropriate choice is
C. 0.1
We are given the following function:
f(x) = 4/(x+2) - 2
We are asked to determine the inverse of this function. To do that we will first change the "f(x)" for "y":
Now we will switch "x" and "y", like this:
Now we will solve for "y", first by adding 2 to both sides:
Now we multiply both sides by "y+2":
Now we divide both sides by "x+2":
Now we subtract 2 to both sides:
Now we change "y" for the inverse of f(x), that is:
And thus we found the inverse. A similar procedure can be used for function 2.
Answer:
Step-by-step explanation:
It is a result that a matrix 
is orthogonally diagonalizable if and only if is a symmetric matrix. According with the data you provided the matrix should be
We know that its eigenvalues are 
, where 
has multiplicity two.
So if we calculate the corresponding eigenspaces for each eigenvalue we have
,
.
With this in mind we can form the matrices 
that diagonalizes the matrix so.
and
Observe that the rows of 
are the eigenvectors corresponding to the eigen values.
Now you only need to normalize each row of dividing by its norm, as a row vector.
The matrix you have to obtain is the matrix shown below
