Ranking is very critical in this problem. Therefore, the most applicable mathematical theory is permutations.
Ranking possible for the cellists:
Needed cellists = 5
Total available cellists = 10
Possible number of rankings = 10P5 = 10!/(10-5)! = 30240
Ranking possible for the violinists:
Needed violinists = 5
Total available = 16
Possible number of rankings = 16P5 = 16!/(16-5)! = 524160
Therefore,
Ratio of rankings (cellists to violinists) = 30240/524160 = 3/52
Answer:

Step-by-step explanation:
We have been given that line m is parallel to line p,
and
.
Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.
We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.
We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

Upon substituting our given values we will get,


Therefore, measure of angle EFG is 52 degrees.
Answer:
3/4
Step-by-step explanation:
1/3 + 1/4 + 1/6
notice that the denominators consists of the numbers 3, 4 and 6 and that the lowest common multiple for all 3 numbers is 12, hence all these fractions can be expressed with a denominator of 12
i.e
1/3 = 4/12
1/4 = 3/12
1/6 = 2/12
hence,
1/3 + 1/4 + 1/6
= 4/12 + 3/12 + 2/12
= (4+3+2) / 12
= 9/12 (simply)
= 3/4