We have been given that a colleague has been tutoring six students in 11th grade to prepare for the ACT. Student scores were as follows: 20, 18, 16, 15, 23, 20. We are asked to find the mean of the ACT scores.
We will use mean formula to solve our given problem.
Upon rounding to nearest whole number, we will get:
Therefore, the mean of the ACT scores is 19 and option 'c' is the correct choice.
The initial statement is: QS = SU (1)
QR = TU (2)
We have to probe that: RS = ST
Take the expression (1): QS = SU
We multiply both sides by R (QS)R = (SU)R
But (QS)R = S(QR) Then: S(QR) = (SU)R (3)
From the expression (2): QR = TU. Then, substituting it in to expression (3):
S(TU) = (SU)R (4)
But S(TU) = (ST)U and (SU)R = (RS)U
Then, the expression (4) can be re-written as:
(ST)U = (RS)U
Eliminating U from both sides you have: (ST) = (RS) The proof is done.
Universe exploded into existence
To find the GCF of the two terms, continuous division must be done.
What can be used to divide both terms such that there is not a remainder?
Start small, let's take 2. It could be a GCF.
Move up higher, say 3. Yes, it can be a GCF.
To see if there might be a greater common factor, divide the constants by 3.
48/3 = 16
81/3 = 27
Upon inspection and contemplation, there is no more common factor between 16 and 27. So, 3 is the GCF.
Moving on, when it comes to variables. The variable with the least exponents is easily the GCF. For the variable m, the GCF is m2 and for n, the GCF is n.
Combining the three, we have the overall GCF = 3m2n
