Answer:
0.189
Step-by-step explanation:
We are using combination to solve for this.
C(n,r) = nCr = n!/r! (n - r)!
We have 10 total students and 11 total faculty = 21 people
Step 1
Selecting 3 students out of 10 total students
= 10× 9× 8×7×6×5×4×3×2×1/ 3×2×1 × 7×6×5×4×3×2×1/
= 120
Step 2
Select 6 faculty out of 11 faculty
11C6 = 11!/6!(11 - 6)!
= 11!/6! × 5!
= 11×10× 9× 8×7×6×5×4×3×2×1/6×5×4×3×2×1 × 5×4×3×2×1/
= 462
Step 3
Selecting 9 people out of 21 people to form a committee
21C9 = 21!/9!(21 - 9)!
= 21!/9! × 12!
= 293,930
Step 4
The fourth and final step of having a committee of 9 people =
(120 × 462)/293,930
= 55440/293,930
= 0.1886163372
Rounded to 3 decimal places = 0.189
Therefore, the probability that you select 3 students and 6 faculty = 0.189
Into an improper fraction. An improper fraction is a fraction where the denominator is smaller than the numerator.
Example: Mixed number: 1 2/3
Improper fraction: 5/3
Answer:
x = 3
y = 3/2
Step-by-step explanation:
look at the hangers to form an equation:
x + x + x + 3 + 3 + 3 = x + x + y + y + y + y
simplify
3x + 3 = 2x + 4y
x + 3 = 4y
x = 4y - 3
you also know that
x + x = y + y + y + y
2x = 4y
substitute x = 4y - 3 into this equation ^
2x = 4y
2(4y - 3) = 4y
8y - 6 = 4y
4y = 6
y = 6/4
y = 3/2
2x = 4y
2x = 12/2
2x = 6
x = 3

So each bag will contain 1/6 kilogram of popcorn