Answer: A) reflection over the x-axis, plus a vertical translation
Step-by-step explanation:
Ok, when we have a function y = f(x)
> A reflection over the x-axis changes a point (x, y) to a point (x, -y), then for a function (x , y = f(x)) the point will change to (x, -y =- f(x))
then for a funtion g(x), this tranformation can be written as h(x) = -g(x).
> A vertical translation of A units (A positive) up for a function g(x) can be written as: h(x) = g(x) + A.
Then in this case we have:
y = g(x) = ln(x)
and the transformed function is h(x) = -ln(x) + 64
Then we can start with h(x) = g(x)
first do a reflection over the x-axis, and now we have:
h(x) = -g(x) = -ln(x)
And now we can do a vertical translation of 64 units up
h(x) = -g(x) + 64 = -ln(x) + 64
Then the correct option is:
A) reflection over the x-axis, plus a vertical translation
Standard deviation is: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
For example: To find the standard deviation, you have to add up all the numbers in the data set, then divide by how many numbers there are, and that will get you your answer.
Example, Say your data set is: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4.
The Mean is: 9 + 2 + 5 + 4 + 12 + 7 + 8 + 11 + 9 + 3 + 7 + 4 + 12 + 5 + 4 + 10+ 9 + 6 + 9 + 4. Over 20. That equals: 104 over 20 = 7.
So, the Standard Variance and Mean is: 7 for this problem.
Hope I helped!
- Debbie
Not too sure what you're asking, but...
3(x+2) is the expression
5,000 tens = (5,000 x 10)
To find out how many thousands are in it,
just divide:
(5,000 x 10) / (1,000) = (5 x 10) = 50 of them .
Answer:
A
Step-by-step explanation:
Sum the product of the components in the first row of A with the corresponding components of the first column in B
Repeat this with the components in the second row of A with the corresponding components of the second column in B, that is
AB
= ![\left[\begin{array}{ccc}2&1\\3&4\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%261%5C%5C3%264%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}3&1\\5&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%261%5C%5C5%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}2(3)+1(5)&2(1)+1(2)\\3(3)+4(5)&3(1)+4(2)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%283%29%2B1%285%29%262%281%29%2B1%282%29%5C%5C3%283%29%2B4%285%29%263%281%29%2B4%282%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}6+5&2+2\\9+20&3+8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%2B5%262%2B2%5C%5C9%2B20%263%2B8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}11&4\\29&11\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%264%5C%5C29%2611%5C%5C%5Cend%7Barray%7D%5Cright%5D)
→ A
