Given:
The system of inequalities is
To find:
The values of a for which the system has no solution.
Solution:
We have,
...(1)
It means the value of x is less than or equal to 5.
...(2)
It means the value of x is greater than or equal to a
Using (1) and (2), we get
But if a is great than 5, then there is no value of which satisfies this inequality.
Therefore, the system has no solution for a>5.
Answer:
600 books
Step-by-step explanation:
The bin's dimensions are
5 by 2 by 3
THe volume of the bin is the multiplication of the 3 dimensions given.
Volume of Bin = 5 * 2 * 3 = 30 cubic feet
Now, volume of each book would be gotten the same way. The dimensions of one book is:
1 by 0.5 by 0.1
Volume of 1 book = 1 * 0.5 * 0.1 = 0.05 cubic feet
The number of books that will fit in the bin would be:
30/0.05 = 600 books
Answer:
the expected value of Xn , E(Xn) = 0 and the variance σ²(Xn) = n*(1-2n)
Step-by-step explanation:
If X1= number of tails when n fair coins are flipped , then X1 follows a binomial distribution with E(X1) = n*p , p=0,5 and the number of heads obtained is X2=n-X1
therefore
Xn =X1-X2 = X1- (n-X1) = 2X1-n
thus
E(Xn) =∑ (2*X1-n) p(X1) = 2*∑[X1 p(X1)] -n∑p(X1) = 2*E(X1)-n = 2*n*p--n= 2*n*1/2 -n = n-n =0
the variance will be
σ²(Xn) = ∑ [Xn - E(Xn)]² p(Xn) = ∑ [(2X1-n) - 0 ]² p(X1) = ∑ (4*X1²-4*X1*n+n²) p(X1) = = 4*∑ X1²p(X1) - 4n ∑X1 p(X1) - n²∑p(X1) = 2*E(X1²) -4n*E(X1)- n²
since
σ²(X1) = n*p*(1-p) = n*0,5*0,5=n/4
and
σ²(X1) = E(X1²) - [E(X1)]²
n/4 = E(X1²) - (n/2)²
E(X1²) = n(n+1)/4
therefore
σ²(Xn) = 4*E(X1²) -4n*E(X1)- n² = 4*n(n+1)/4 - 4*n*n/2 - n² = n(n+1) - 2n² - n²
= n - 2n² = n(1-2n)
σ²(Xn) = n(1-2n)
Answer:
The answer is 103
Step-by-step explanation:
The given expression is:
300-7[4(3+5)]+3 to the 3rd power
3 to the 3rd power means 3^3
Therefore,
300-7[4(3+5)]+3^3
First we will solve the round bracket and find the cube
300-7[4(8)]+27
Now we will solve square bracket
300-7[32]+ 27
300-224+27
76+27
103
Thus the answer we get is 103....
