Answer:
The image of ![\left[\begin{array}{c}4&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D)
through T is ![\left[\begin{array}{c}24&-8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D24%26-8%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We know that 
→ is a linear transformation that maps 
into 
⇒
And also maps 
into 
⇒
We need to find the image of the vector
We know that exists a matrix A from 
(because of how T was defined) such that :
for all x ∈
We can find the matrix A by applying T to a base of the domain ().
Notice that we have that data :
{
}
Being 
the cannonic base of
The following step is to put the images from the vectors of the base into the columns of the new matrix A :
![T(\left[\begin{array}{c}1&0\end{array}\right])=\left[\begin{array}{c}4&5\end{array}\right]](https://tex.z-dn.net/?f=T%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%260%5Cend%7Barray%7D%5Cright%5D%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%265%5Cend%7Barray%7D%5Cright%5D)
(Data of the problem)
![T(\left[\begin{array}{c}0&1\end{array}\right])=\left[\begin{array}{c}-2&7\end{array}\right]](https://tex.z-dn.net/?f=T%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%261%5Cend%7Barray%7D%5Cright%5D%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-2%267%5Cend%7Barray%7D%5Cright%5D)
(Data of the problem)
Writing the matrix A :
![A=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C5%267%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now with the matrix A we can find the image of ![\left[\begin{array}{c}4&-4\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D)
such as :
⇒
![T(\left[\begin{array}{c}4&-4\end{array}\right])=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]\left[\begin{array}{c}4&-4\end{array}\right]=\left[\begin{array}{c}24&-8\end{array}\right]](https://tex.z-dn.net/?f=T%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D%29%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C5%267%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%26-4%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D24%26-8%5Cend%7Barray%7D%5Cright%5D)
We found out that the image of through T is the vector
Answer:
For the sampling distribution,
a) Mean = μₓ = 55.0 students.
b) Standard Deviation = 1.8 students.
Step-by-step explanation:
The complete Question is attached to this solution.
The Central limit theorem explains that for the sampling distribution, the mean is approximately equal to the population mean and the standard deviation of the sampling distribution is related to the population standard deviation through
σₓ = (σ/√n)
where σ = population standard deviation = 4
n = sample size = 5
Mean = population mean
μₓ = μ = 55 students.
Standard deviation
σₓ = (σ/√n) = (4/√5) = 1.789 students = 1.8 students to 1 d.p
Hope this Helps!!!
Answer: Its B
Step-by-step explanation: trust me i had this test
Answer :E) Not enough information is given to determine the probability.
Step-by-step explanation:
Le A denotes the event that households in the United States own dogs .
and B denotes the event that households in the United States own cats.
As per given , we have
P(A)=36.5%= 0.365
P(B)=30.4% = 0.304
To find the probability that the selected household will own a dog or a cat, we apply the following formula :
P(A or B)=P(A)+P(B)+P(A and B)
But P(A and B) is not given to us.
i..e the probability that a house hold own both a cat and adg is not given to us.
Therefore, The correct option is (E) Not enough information is given to determine the probability.
The inverse of the the function above is y = 
In order to find the inverse of any function, you need to switch the x and y values. Once you've done that, you need to solve for the new y value. The resulting equation will be your inverse. The work for this one is below.
y = 2x^2 - 8 ----> Switch the terms
x = 2y^2 - 8 ----> Add 8 to both sides.
x + 8 = 2y^2 ----> Divide both sides by 2.
= y^2 ----> Now take the square root of both sides.
= y
What's left is your inverse. You can change the order so that it is in a more acceptable form.
y =
