Answer:
Step-by-step explanation:
Find the GCF of the numbers 48, 6 and 26.
The largest number each can be divided by is 2, which is the GCF.
Find the GCF of 
The GCF is always the smallest exponent, so 
is the GCF
Combine the two GCF for the answer
Answer:
There are 108 inches in 9 feet
Step-by-step explanation:
Well, two unit multipliers mean we have to convert through two units before we arrive at our final answer so we can convert from feet to yards to inches!
We know that 3 feet equal a yard, right?
So we can divide 9 by 3 to get the amount that 9 feet translates to in yards.
So we are now done with our first conversion! Our second is going to be from yards to inches!
There are 36 inches in 1 yard so we should multiply 3 by 36 to get the amount in inches!
Answer:
The probability of choosing a professor or an instructor is 47.22%.
Step-by-step explanation:
Given that the mathematics faculty at a college consists of 11 professors, 12 associate professors, 7 assistant professors, and 6 instructors, if a faculty member is selected, to find the probability of choosing a professor or an instructor the following calculation must be performed:
11 + 12 + 7 + 6 = 100
11 + 6 = X
36 = 100
17 = X
17 x 100/36 = X
1700/36 = X
47.22 = X
The probability of choosing a professor or an instructor is 47.22%.
It would be 8.5 because all you have to do is add 3 to 2.5 then you’ll get 5.5 then do that one more time.
Let x be the distance traveled on the highway and y the distance traveled in the city, so:
Now, the system of equations in matrix form will be:
![\left[\begin{array}{ccc}1&1&\\ \frac{1}{65} & \frac{1}{25} &\end{array}\right] \left[\begin{array}{ccc}x&\\y&\end{array}\right] = \left[\begin{array}{ccc}375&\\7&\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26%5C%5C%20%5Cfrac%7B1%7D%7B65%7D%20%26%20%5Cfrac%7B1%7D%7B25%7D%20%26%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%26%5C%5Cy%26%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D375%26%5C%5C7%26%5Cend%7Barray%7D%5Cright%5D%20)
Next, we are going to find the determinant:
![D= \left[\begin{array}{ccc}1&1\\ \frac{1}{65} & \frac{1}{25} \end{array}\right] =(1)( \frac{1}{25}) - (1)( \frac{1}{65} )= \frac{8}{325}](https://tex.z-dn.net/?f=D%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C%20%5Cfrac%7B1%7D%7B65%7D%20%26%20%5Cfrac%7B1%7D%7B25%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%281%29%28%20%5Cfrac%7B1%7D%7B25%7D%29%20-%20%281%29%28%20%5Cfrac%7B1%7D%7B65%7D%20%29%3D%20%5Cfrac%7B8%7D%7B325%7D%20)
Next, we are going to find the determinant of x:
![D_{x} = \left[\begin{array}{ccc}375&1\\7& \frac{1}{25} \end{array}\right] = (375)( \frac{1}{25} )-(1)(7)=8](https://tex.z-dn.net/?f=%20D_%7Bx%7D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D375%261%5C%5C7%26%20%5Cfrac%7B1%7D%7B25%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%28375%29%28%20%5Cfrac%7B1%7D%7B25%7D%20%29-%281%29%287%29%3D8)
Now, we can find x:
Now that we know the value of x, we can find y:
Remember that time equals distance over velocity; therefore, the time on the highway will be:
An the time on the city will be:
We can conclude that the bus was five hours on the highway and two hours in the city.
