2x373 because 2 and 373 are both prime meaning they can only be divided by one and themselves
compare the triangles ΔABC and ΔBCD
∡ABC = ∡BCD (given)
AB = CD (given)
BC = BC (common) } = > (SAS) ΔABC ≡ ΔBCD = > AC = BD
First, 5 students and 2 teachers is 7 different people. That means there are 7! Ways they can stand in a line. (7! Means 7x6x5x4x3x2x1)
That is 5040 ways.
Having the teachers on either side with the five students in the middle splits the question. There are 2 ways the teachers could stand (TA on left, TB on right or vice versa). There are 5! Ways to arrange the students in the middle. That is, 120. So combined, there are 2x120 ways to have them lined up with the teachers on either side. 240 ways.
Out of the 5040 ways for all of them to line up, one teacher will be in the middle 3 spaces 3/7 of the time. The second teacher will be on one of the remaining 2 central spaces 2/6 (1/3) of the time. 3/7x1/3 = 1/7. That means 1/7 or 14.29% of the time, the two teachers will occupy two of the three middle slots.
The correct answer is Choice B.
The first step in this problem is to divide both sides by 64.
On the left side, you will have b squared.
On the right side, you will have 1/4.
Now, take the square root of both sides.
The square root of 1/4 is positive or negative 1/2.
