Answer: The required lifetime value is 11.27.
Step-by-step explanation:
Since we have given that
Mean value = 11 hours
Standard deviation = 1 hour
The total lifetime of all batteries in a package exceeds that value for only 5% of all packages.
So, α = 0.95, z= 1.645
n = 9
So, the lifetime value would be

Hence, the required lifetime value is 11.27.
We need a system of equations to solve this. "Difference" is to subtract, and we are taking this difference of the 2 squared unknowns to be 20. That equation is

. Our "first number is x^2, so 3 times that is 3x^2. "Increased by" is adding to that first number. What we are adding is the second number. The second equation is

. Let's solve the first equation for x^2:

and sub that value for x^2 into the second equation.

and

. Subtract 60 from both sides and combine the y^2 terms to get

. Divide both sides by 4 to get y^2 = 16 and y = 4. Let's go back now and solve for x. We will use the fact that y^2 = 16 to solve for x^2 and then take the square root of it.

, x^2 = 4, so x = 2. Your solutions are x = 2 and y = 4. There you go!
Answer:
<em>Q'</em> = (-4, -2)
<em>R' </em>= (4, -2)
<em>S'</em> = (4, 2)
<em>T'</em> = (-4, 2)
Step-by-step explanation:
First, we can create a matrix to scale this rectangle by putting all the x coordinates in the top row and all the y coordinates in the bottom row and multiply it by 4.
Our initial matrix to multiply:
![4\left[\begin{array}{cccc}-1&1&1&-1\\-2&-2&-1&-1\end{array}\right]](https://tex.z-dn.net/?f=4%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%261%261%26-1%5C%5C-2%26-2%26-1%26-1%5Cend%7Barray%7D%5Cright%5D)
Moved to the origin:
![4\left[\begin{array}{cccc}-1&1&1&-1\\-0.5&-0.5&0.5&0.5\end{array}\right]](https://tex.z-dn.net/?f=4%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-1%261%261%26-1%5C%5C-0.5%26-0.5%260.5%260.5%5Cend%7Barray%7D%5Cright%5D)
Multiplied by four:
![\left[\begin{array}{cccc}-4&4&4&-4\\-2&-2&2&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-4%264%264%26-4%5C%5C-2%26-2%262%262%5Cend%7Barray%7D%5Cright%5D)
This gives us the points of
<em>Q'</em> = (-4, -2)
<em>R' </em>= (4, -2)
<em>S'</em> = (4, 2)
<em>T'</em> = (-4, 2)
which are our answers.
C. 1/2x-10 _>0
can be ued to find the domin of f(x)