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3 years ago

8

Elizabeth has two identical number cubes. Both cubes have faces numbered 1 thourgh 6. if Elizabeth rolls each cube once, what is

the probability that the sum of the two numbers on the top faces will be 10.

1 answer:

n200080 [17]3 years ago

7 0

I believe the answer is 4 out of 12.

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A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation

Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an $m\times n$ matrix. Let $T :U\to V$ be the corresponding linear transformationover the field F and $\theta$ be identity vector in V. Now if $x\in Ker( T)\implies T(x)=\theta$ .

(1) The kernel of a linear transformation is a vector space : True.

Let $x,y\in Ker( T)$ , then,

$T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)$

hence the kernel is closed under addition.

Let $\lambda\in F, x\in Ker( T)$ , then

$T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta$

$\lambda x\in Ker(T)$ and thus Ket(T) is closed under multiplication

Finally, fore all vectors $u\in U$ ,

$T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta$

$\implies \theta\in Ker(T)$

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is $\mathbb R^m$ : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in $\mathbb R^m$

: False

The null space that is dimension of solution space of an m x n matrix is always in $\mathbb R^n$ .

(4) The column space of A is the range of the mapping $x\to Ax$

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0

3 years ago

Malkia is thinking of a mystery number. She cuts it in half then adds 5. The result is 24. Determine the mystery number. I need

White raven [17]

Answer:38

Step-by-step explanation:if you take 24 and subtract the five she added, it gives you 19 and since she divided it by two you would multiply it by two to get the original number she was thinking of

Hope this helps :)

6 0

3 years ago

Read 2 more answers

This the questions that have me stuck

IRINA_888 [86]

First a and then b.

4 0

3 years ago

A right-angled triangle has shorter side lengths exactly c^2-b^2 and 2bc units respectively, where b and c are positive real num

yKpoI14uk [10]

Answer: hypotenuse = $c^{2} + b^{2}$

Step-by-step explanation: Pythagorean theorem states that square of hypotenuse (h) equals the sum of squares of each side ( $s_{1},s_{2}$ ) of the right triangle, .i.e.:

$h^{2} = s_{1}^{2} + s_{2}^{2}$

In this question:

$s_{1}$ = $c^{2}-b^{2}$

$s_{2} =$ 2bc

Substituing and taking square root to find hypotenuse:

$h=\sqrt{(c^{2}-b^{2})^{2}+(2bc)^{2}}$

Calculating:

$h=\sqrt{c^{4}+b^{4}-2b^{2}c^{2}+(4b^{2}c^{2})}$

$h=\sqrt{c^{4}+b^{4}+2b^{2}c^{2}}$

$c^{4}+b^{4}+2b^{2}c^{2}$ = $(c^{2}+b^{2})^{2}$ , then:

$h=\sqrt{(c^{2}+b^{2})^{2}}$

$h=(c^{2}+b^{2})$

Hypotenuse for the right-angled triangle is $h=(c^{2}+b^{2})$ units

3 0

3 years ago

Simplify (79)<br> O A. 353<br> O B. 78<br> O c. 715<br> OD. ()<br> SUBMIT

SOVA2 [1]

Answer:
C. You have to multiply both powers to simplify.

8 0

3 years ago