Answer: 15120
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Work Shown:
There are 4 appetizers total. We want to select 3 of them. Order doesn't matter.
Use the nCr formula with n = 4 and r = 3
n C r = (n!)/(r!*(n-r)!)
4 C 3 = (4!)/(3!*(4-3)!)
4 C 3 = (4!)/(3!*1!)
4 C 3 = (4*3!)/(3!*1!)
4 C 3 = (4)/(1!)
4 C 3 = (4)/(1)
4 C 3 = 4/1
4 C 3 = 4
There are 4 ways to select just the appetizers
Call this value M = 4 (we'll use it later)
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There are 10 main courses total. We want to select 8 of them. Order doesn't matter.
Use the nCr formula with n = 10 and r = 8
n C r = (n!)/(r!*(n-r)!)
10 C 8 = (10!)/(8!*(10-8)!)
10 C 8 = (10!)/(8!*2!)
10 C 8 = (10*9*8!)/(8!*2!)
10 C 8 = (10*9)/(2!)
10 C 8 = (10*9)/(2*1)
10 C 8 = 90/2
10 C 8 = 45
There are 45 ways to select just the main courses
Call this value N = 45 (we'll use it later)
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There are 9 desserts total. We want to select 3 of them. Order doesn't matter.
Use the nCr formula with n =9 and r = 3
n C r = (n!)/(r!*(n-r)!)
9 C 3 = (9!)/(3!*(9-3)!)
9 C 3 = (9!)/(3!*6!)
9 C 3 = (9*8*7*6!)/(3!*6!)
9 C 3 = (9*8*7)/(3!)
9 C 3 = (9*8*7)/(3*2*1)
9 C 3 = 504/6
9 C 3 = 84
There are 84 ways to select just the desserts
Call this value P = 84 (we'll use it later)
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Multiply the results from earlier:
M*N*P = 4*45*84 = 15120 which is the final result.
C. $30.00 is the answer !!!!!!
Answer:
foot
Step-by-step explanation:
9514 1404 393
Answer:
156 cm³
Step-by-step explanation:
The volume of any prism is the product of the base area and the height of the prism. Here, we can take the "base" to be the front face of the assembly, and its "height" to be the 3 cm distance between the front and back faces.
The front face area is the sum of the triangle area and the rectangle area.
A = 1/2bh + LW
A = (1/2)(10 cm)(4 cm) + (16 cm)(2 cm) = 52 cm²
Then the volume is ...
V = Bh = (52 cm²)(3 cm) = 156 cm³ . . . . total volume of the two blocks
Answer:
C) $10,000 invested at 6.7% compounded quarterly over 7 years yields the greater return.
Step-by-step explanation:
-We determine the effective interest rate in both scenarios and use it to calculate the investment's value after 7 years.
#Given n=7yrs, P=$10,000 and i=6.6% compounded monthly:
#Given n=7rs, P=10000, i=6.7%
Hence, the investment has the largest value($15,921.75) when the interest rate is compounded quarterly.
