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3 years ago

Help me what’s the answer .

Mathematics

1 answer:

Mandarinka [93]3 years ago

8 0

Answer:

x=3

Step-by-step explanation:

i helped my friend on this before but it was a word problem

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Of the last 24 balloons sold at a party store 6 were white. Find the experimental probability that the next balloon sold will be

Alekssandra [29.7K]

Answer: 1 out of 4

Step-by-step explanation:

If you divided the total amount of balloons that were sold by the amount of white balloons, it would be 4. The 1 comes from 1 in 4 being the probability of them being white. You can check this by multiplying the 1 and 4 by 6 and it would be 6 out of 24, which shows our answer is correct.

8 0

3 years ago

A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

Solve the system 2x+4y=16 5x +3y=19 then find the value of y/x

AURORKA [14]

Answer:

I would change 2x+4y=24 into x=12–2y

To do that, divide both sides by 2 and then subtract 2y on each side.

After that, substitute for x. 3x+2y=19 would become 3(12–2y)+2y=19.

Then solve.

3(12–2y)+2y=19

36–6y+2y=19

-4y+36=19

-4y=-17

y=4.25

Then, substitute y in either equation.

Either this:

3x+2y=19

3x+2(4.25)=19

3x+8.5=19

3x=10.5

x=3.5

Or:

2x+4y=24

2x+4(4.25)=24

2x+17=24

2x=7

x=3.5

Or you could solve it in the equation you created in the beginning:

x=12–2y

x=12–2(4.25)

x=12–8.5

x=3.5

The coordinates where the lines intercept are (3.5, 4.25).

Sorry for the long answer!

4 0

3 years ago

which of the following graphs shows a negative linear relationship with a correlation coefficient, r, close to -0.5.

Harrizon [31]

Answer:

In the graph attached there is a sample generated with a correlation coefficient r=-0.5.

Step-by-step explanation:

A value of r that is -0.5 shows that there is a certain correlation and that this correlation is negative.

As there are no examples in this question, I searched for a generator of random samples with a user-input correlation coefficient between the two variables.

In the graph attached there is a sample generated with a correlation coefficient r=-0.5.

3 0

3 years ago

The expression once The left side of an equation is shown below. 3(x+1)+9 if the equation has no solution which expression can b

lys-0071 [83]

<h3>Answer:</h3>

C. 4(x-3)-x

<h3>Step-by-step explanation:</h3>

All of the given expressions are equivalent to 3x+12 except selection C. Using that in your equation makes it be ...

... 3(x +1) +9 = 4(x -3) -x

... 3x +12 = 3x -12

... 12 = -12 . . . . . <em>false</em>

There is no value of x that will make this true, hence NO SOLUTION.

_____

<em>Comment on the other choices</em>

3x+12 = 3x+12 has an <em>infinite number of solutions</em>, as <u><em>any</em></u> value of x will make this true.

7 0

3 years ago

Read 2 more answers