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Sliva [168]
3 years ago
12

A fair 6-sided die is rolled 4 times and the resulting sequence of 4 numbers is recorded. How many different sequences consist e

ntirely of even numbers
Mathematics
1 answer:
Charra [1.4K]3 years ago
7 0

Answer:

81

Step-by-step explanation:

Rolling 6-sided fair die you can throw out three even numbers: 2, 4, 6.

If a fair 6-sided die is rolled 4 times, then each of 4 times each of three even numbers can be thrown out. Then the number of different sequences that consist entirely of even numbers is

3\cdot 3\cdot 3\cdot 3=3^4=81.

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All vectors are in Rn. Check the true statements below:
Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that ||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then ||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||.

C) Consider S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2. This set is orthogonal because (0,2)\cdot(2,0)=0(2)+2(0)=0, but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in \mathbb{R}^n. Then the columns of A form an orthonormal set. We have that A^{-1}=A^t. To see this, note than the component b_{ij} of the product A^t A is the dot product of the i-th row of A^t and the jth row of A. But the i-th row of A^t is equal to the i-th column of A. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then A^t A=I    

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set \{u_1,u_2\cdots u_p\} and suppose that there are coefficients a_i such that a_1u_1+a_2u_2\cdots a_nu_n=0. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then a_i||u_i||=0 then a_i=0.  

5 0
3 years ago
The question is the picture , if you know it please answer I’m having trouble with this particular question
baherus [9]

Answer:

d

Step-by-step explanation:

the slopes (2/3x and -5/4x) are not equal but the y-intercepts (3) are and d is the only one that states that

5 0
2 years ago
Math help me))))))))please
olasank [31]
X^2/(x- 9 = 81/(x - 9)
This is the equation for which you want the solution.
Multiplying both sides of the equation by (x - 9) we get
x^2(x - 9)/(x - 9) = 81(x - 9)/(x - 9)
So the (x - 9) goes out from both the denominator and the numerator and then the simplified equation becomes
x^2 = 81
x ^2 = (9)^2
x = 9
So the value of the unknown variable x comes out to be 9.
6 0
3 years ago
Read 2 more answers
Ted's company has recieved an order to print 10^6 pages. ted's company has 100 machines , each of which can print 10^4 pages a d
Ludmilka [50]

Answer:

10^0=1 day

Step-by-step explanation:

10^4 x 100=10^4 x 10²

     =10^(4+2)

     =10^6

Then:

10^6/10^6=10^(6-6)=10^0=1 day

7 0
3 years ago
Read 2 more answers
Shade a model that shows 0.674
Ratling [72]
0.674 means that it 674/1000

which mean that if the model consists of 1000 squares, you have to shade 674 of the squares.

If the model consists of 500 squares, you have to shade 337 of the squares  ( you get the number after dividing both 674 and 1000 with 2)


5 0
3 years ago
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