Answer:
1. 19C8 = 75582
2. 19P8= 3047466240
Step-by-step explanation:
First, find the number of ways to get 8 sticks from 19. At first, you have 19 choices, then 18, then 17, all the way to 12. Giving you 19*18*17*...*13*12, or 19!/11!.
Combination:
When order doesn't matter, you have to divide 19!/11! by the number of ways to order 8 sides, or 19!/11!/8!=19C8=75582
Permutation:
When order doesn't matter, you don't have to divide 19!/11! by the number of ways to order 8 sides, since you count each of these, and 19!/11!=19P8=3047466240.
Answer:
A
Step-by-step explanation:
Answer:
x = 60°
y = 72°
z = 48°
Step-by-step explanation:
x = 180 - p = 180 - 120 = 60
Since y;z = 3:2 , 2y = 3z or z = 2y/3
Now, x + y + z = 180
60 + y + 2y/3 = 180 Multiply thru by 3 to remove the fraction
180 + 3y + 2y = 540
180 + 5y = 540
5y = 360
y = 72
z = 2(72)/3 = 48
Check: 60 + 72 + 48 = 180
Answer:
Problem 9: -1/2
Problem 10: 1/5
Step-by-step explanation:
Problem 10: Label the given ln e^(1/5) as y = ln e^(1/5).
Write the identity e = e. Raise the first e to the power y and the second e to the power 1/5 (note that ln e^(1/5) = 1/5). Thus, we have:
e^y = e^(1/5), so that y = 1/5 (answer).
Problem 9: Let y = (log to the base 4 of) ∛1 / ∛8, or
y = (log to the base 4 of) ∛1 / ∛8, or
y = (log to the base 4 of) 1 /2
Write out the obvious:
4 = 4
Raise the first 4 to the power y and raise the second 4 to the power (log to the base 4 of) 1 /2. This results in:
4^y = 1/2. Solve this for y.
Note that 4^(1/2) = 2, so that 4^(-1/2) = 1/2
Thus, y = -1/2
