Answer:
11,880 different ways.
Step-by-step explanation:
We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.
We will use permutations for solve our given problem.
, where,
n = Number of total items,
r = Items being chosen at a time.
For our given scenario 
and 
.
Therefore, offices can be filled in 11,880 different ways.
Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= - 
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
= - 
= - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
Answer:
the length of CD is 4
the length of DE is 2
the ratio of CD to DE is 2:1
Step-by-step explanation:
Answer:
54minutes
Step-by-step explanation:
Let the time taken to clean up be t
Let the number of people cleaning be n
If the time it takes to clean up after an anniversary party varies inversely as the number of people cleaning then;
t = k/n
k is the constant of proportionality
If 3 people work together to clean, and took them 90 minutes, this means
at t = 90, n=3
Substitute
90 = k/3
k = 3×90
k = 270
To et the time it will take 5people to clean, the will say;
t =k/n
t =270/5
t = 54 minutes
Hence it will take 5 people 54minues to clean
The answer is the third one
