Answer:
0 ≤ x ≤ 2
Step-by-step explanation:
A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.
In this question, the volume of the water is the dependent variable and the time taken is the independent variable. Let y represent the volume of the water and x represent the time taken. Therefore:
y = 0.75x
The domain of the function is the set of independent variable, it can be gotten by determining x when y is minimum and maximum. Hence:
For y = 0
0 = 0.75x
x = 0/ 0.75 = 0
For y = 1.5 gallon
1.5 = 0.75x
x = 1.5/0.75 = 2
Hence, the domain = 0 ≤ x ≤ 2
The given matrix equation is,
![1.5\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y\left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]](https://tex.z-dn.net/?f=%201.5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%266%5C%5C8%264%5Cend%7Barray%7D%5Cright%5D%20%2By%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%264%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20)
.
Multiplying the matrices with the scalars, the given equation becomes,
![\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%269%5C%5C12%266%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%264y%5C%5C3y%262y%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20)
Adding the matrices,
![\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%2By%269%2B4y%5C%5C12%2B3y%266%2B2y%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20)
Matrix equality gives,
Solving the equations together,
We can see that the equations are not consistent.
There is no solution.
36j + j = 37j
Explanation.
You could translate this sum into a normal sebtence: I have 36 apples and add 1 apple more.
The sum will then be 36 apples + apple = 37 apples.
Replacing the word (in this explanation 'apple') by a letter learns us 36a + a = 37a
Hence 36j + j = 37j
Answer:
-2
Step-by-step explanation:
24 - 4x =32
-4x =32 - 24
-4x=8
x=-8 :4
x=-2
Answer:
The correlation between exam score and amount of time spent on the exam is an example of a <u>negative correlation</u>.
Step-by-step explanation:
Consider the provided statement.
College professor reports that students who finish exams early tend to get better grades than students who hold on to exams until the last possible moment.
That means the student who finish the exam early will get the highest marks. One who finish after the first student will get second highest mark and the one who finish in the end will get the least marks.
Now consider time as first variable and marks as second variable.
That means as the first variable increase the second variable decreases.
According to the definition of Negative correlation: It is a relationship between two variables in which one variable increases as the other decreases, and vice versa.
Hence, the correct answer is negative correlation.
