For positive integer n, the factorial notation n! represents the product of the integers from n to 1. (For example, 6! = 6*5*4*3
1 answer:
Answer:
The value of N that satisfies the equation is
Step-by-step explanation:
First we open the factorial of 12, to simplify the expression:
12! = 12*11*10*9!
So
5!*9! = 12!*N
5!*9! = 12*11*10*9!N
12*11*10N = 5!
Now we open the factorial of 5. So
12*11*10*N = 5*4*3*2*1
Since 5*2 = 10, 4*3 = 12, we have that:
12*11*10*N = 10*12*1
Now, simplifying by 10*12
11N = 1
This is the value of N that satisfies the equation
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Answer and Step-by-step explanation:
a.)x^2 and y^2 are always greater than zero.(assuming real x and y).
=>x^2<=x^2+y^2
=>|x|(x^2)<=|x|(x^2+y^2)
=>|x^3|<=|x|(x^2+y^2)
b. similarly, |y^3|<=|y|(x^2+y^2)
=>|f(x,y)|=|x^3+y^3|/(x^2+y^2)=|x|+|y|
c. let h is very small number (close to zero but positive)
lim (x,y)-> (0,0) f(x,y)=(x^3+y^3)/(x^2+y^2)
putting x=h and y=h and approaching h->0
lim h->0 f(h)=2h=0
There is another explanation attached below
Answer:
The probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.
Step-by-step explanation:
Denote the events as follows:
<em>X</em> = a fisher at Clearwater Park had a fishing license
<em>Y</em> = a fisher at Mountain View Park had a fishing license
The two events are independent.
The information provided is:
n (X) = 48
n (X') = 32
n (Y) = 72
n (Y') = 18
Then,
N (X) = n (X) + n (X')
= 48 + 32
= 80
N (Y) = n (Y) + n (Y')
= 72 + 18
= 90
Compute the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license as follows:
Thus, the probability that the fisher chosen from Clearwater did not have a license and the fisher chosen from Mountain View had a license is 0.32.