The number of 10 chips stacks that Dave can make if two stacks are not considered distinct is 110.
The solution
To get the symmetric stacks, one has to subtract the symmetric stacks to know the ones that are asymmetric.
The symmetric are flipped. Given that they are double counted what we have to do is to divide through by 2.
6/2 = 3
10/2 = 5
4/2 = 2
1/2(10C6) - (5C3) + (5C3)
0.5(210-10+10)
= 110
One way:
3x + 4x + 5 x = 30
12 x = 30
Divide by 12
x = 2.5
3x = 7.5 (2.5x3)
4x = 10 (2.5x4)
5x = 12.5 (2.5x5)
7.5cm + 10cm +12.5cm = 30cm There are your three sides.
let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:
2p + 3d = 18.25
4p + 2d = 27.50
From this, we can use substitution or elimination to solve:
For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.
For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.
I'll be using elimination in this case:
-2(2p + 3d = 18.25) --> -4p - 6d = -36.50
-4p - 6d = -36.50
4p + 2d = 27.50
-4d = -9.00
d = 2.25
4p + 2 * 2.25 = 27.50
4p + 4.50 = 27.50
4p = 23.00
p = 5.75
Now let's check our answer:
2 * 5.75 + 3 * 2.25 = 18.25
11.50 + 6.75 = 18.25
18.25 = 18.25
So drinks cost $2.25 and popcorn $5.75
Answer:
The prime factors that 27 and 36 share is 3x3.
Step-by-step explanation:
The prime factorization of 27 is: 3 x 3 x 3. The prime factorization of 36 is: 2 x 2 x 3 x 3. The prime factors and multiplicities 27 and 36 have in common are: 3 x 3. 3 x 3 is the gcf of 27 and 36.
Answer:
x10000000 • (103x990000000 - 470)
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100
