Answer:
a) 66
b) 45
Step-by-step explanation:
We have 12 horses and after the first race 2 of them have to be eliminated
that condition is equal to consider that 10 horses will be available for the second race.
The number of possiblities we have for the first race is the combination of 12 horses in group of 10
C¹²₁₀ = 12!/ (2!)* (12-2)! = 12*11/2 = 66
For the second race
C¹⁰₈ = 10! / 8! * (10-8)! = 10*9/ 2 = 45
The answer for your problem is shown on the picture.
1. You must use the formula for calculate the volume of a rectangular prism, which is:
V=(h)(l)(w)
V: It is the volumen of the rectangular prism (V=1152 inches³).
h: It is the height of the rectangular prism (h=18-w).
l:It is the lenght of the rectangular prism (l=2w+4).
2. When you substitute these calues into the formula, you obtain:
V=(h)(l)(w)
1152=(18-w)(2w+4)(w)
(18-w)(2w+4)(w)-1152=0
3. Then, you should mutiply them:
36w²-2w³+72w-4w²-1152=0
32w²-2w³+72w-1152=0
4. When you factor, you obtain:
2(w-16)(w-6)(w+6)
w1=16
w2=6
w3=-6
5. The problem says that the height is greater than the width, therefore, the widht is:
w=6 inches
6. The length is:
l=2w+4
l=2(6)+4
l=16 inches
7. And the height is:
h=18-w
h=18-6
h=12 inches
What are the dimensions of the bag?
The dimensions of the bag are:
l=16 inches
h=12 inches
w=6 inches
