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:
a(n) = 20*2.5^(n - 1)
Step-by-step explanation:
Note that 50 is 2.5 times 20, and that 125 is 2.5 times 50. Thus the common factor is 2.5. The formula for the nth term is
a(n) = a(1)*r^(n - 1) => a(n) = 20*2.5^(n - 1)
Cds 3 dvds 5
Sue will use 6 shelves with 3 cds on each and 5 dvds on each.
$22x5% = $1.10 or 22x.05= 1.1
$22.00 + $1.10 = $23.10
Answer:
The highest score is 94.
Step-by-step explanation:
Let the highest score be denoted by, <em>A</em>, the lowest score be, <em>B</em> and the middle score be <em>X</em>.
Then,
A + X + B = 87 × 3 = 261 ...(i)
X + B = 83.5 × 2 = 167 ...(ii)
⇒ B = 167 - X ...(iii)
A + X = 89 × 2 = 178 ...(iv)
⇒ A = 178 - X ...(v)
Substitute (iii) and (v) in (i) and solve for <em>X</em> as follows:
A + X + B = 261
178 - X + X + 167 - X = 261
345 - X = 261
X = 84
Substitute the value of <em>X</em> in (iii) and solve for B as follows:
B = 167 - X
= 167 - 84
= 83
Substitute the value of <em>X</em> in (v) and solve for A as follows:
A = 178 - X
= 178 - 84
= 94
Thus, the highest score is 94.
