Answer:
p=0.25
Step-by-step explanation:
Given that a club can select one member to attend a conference. All of the club officers want to attend. There are a total of four officers, and their designated positions within the club are President (P), Vice dash President (Upper V )comma Secretary (Upper S )comma nbspand Treasurer (Upper T ).
Sample space would be
a){ {P}, {V}, {S} {T}} is the sample space with notations standing for as given in the question
b) Each sample is equally likely. Hence we have equal chances for selecting any one out of the four.
If probability of selecting a particular sample of size I is p, the by total probability axiom we have
\begin{gathered}4p =1\\p =0.25\end{gathered}
4p=1
Answer:
![\left[\begin{array}{ccc}3&-5 &|12\\4&-2 &|15\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-5%20%20%26%7C12%5C%5C4%26-2%20%20%26%7C15%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:
- a column for the values of x in each equation
- a column for the values of y in each equation
- a column for the independent values of each equation
since our system of equations is:

we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:
![\left[\begin{array}{ccc}3&&\\4&&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26%26%5C%5C4%26%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now for the values of y we hvae -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:
![\left[\begin{array}{ccc}3&-5&\\4&-2&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-5%26%5C%5C4%26-2%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:
![\left[\begin{array}{ccc}3&-5&12\\4&-2&15\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-5%2612%5C%5C4%26-2%2615%5C%5C%5Cend%7Barray%7D%5Cright%5D)
usually there is a line separating the columns for the values of x and y, and the independent values:
![\left[\begin{array}{ccc}3&-5 &|12\\4&-2 &|15\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-5%20%20%26%7C12%5C%5C4%26-2%20%20%26%7C15%5C%5C%5Cend%7Barray%7D%5Cright%5D)
this is the matrix of the system of equations
Answer: 35
Step-by-step explanation:
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 35-x. ( hope this helps have a good day/night :) )
Answer:
the average rate of change is 4.
Step-by-step explanation:
Find the average rate of change of f(x)=x^2 on the interval [1,3].
The average rate of change of f(x) on the interval [a,b] is f(b)−f(a)/b−a.
We have that a=1, b=3, f(x)=x^2.
Thus, f(b)−f(a)/b−a=((3))^2−(((1))^2)/3−(1) = 4.