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Artist 52 [7]
4 years ago
9

-x=-y+2 and 3y+4=2x solve using matrices

Mathematics
1 answer:
MissTica4 years ago
8 0

\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}

In matrix form, this is

\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}

The coefficient matrix has determinant

\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0

so it has an inverse, which is

\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}

Multiply both sides by the inverse matrix:

\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}

\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}

so that x=-10 and y=-8.

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TV advertising agencies face increasing challenges in reaching audience members because viewing TV programs via digital streamin
oksian1 [2.3K]

Answer:

The 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.514, 0.566). This means that we are 99% sure that the true proportion of all American adults surveyed said they have watched digitally streamed TV programming on some type of device is between 0.514 and 0.566.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

A poll reported that 54% of 2342 American adults surveyed said they have watched digitally streamed TV programming on some type of device.

This means that \pi = 0.54, n = 2342

99% confidence level

So \alpha = 0.01, z is the value of Z that has a p-value of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.54 - 2.575\sqrt{\frac{0.54*0.46}{2342}} = 0.514

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.54 + 2.575\sqrt{\frac{0.54*0.46}{2342}} = 0.566

The 99% confidence level for the proportion of all adult Americans who watched streamed programming up to that point in time is (0.514, 0.566). This means that we are 99% sure that the true proportion of all American adults surveyed said they have watched digitally streamed TV programming on some type of device is between 0.514 and 0.566.

6 0
3 years ago
On a six-day vacation, the forecast is a 30% chance of rain every day. What’s the probability that it rains every day? Enter a f
Anestetic [448]

The probability that it rains everyday is 0.000729

Forecast for rain = 30%

Since it's a 6 days vacation, the probability that it rains every day will be:

= 30% × 30% × 30% × 30% × 30% × 30%

= 0.3 × 0.3 × 0.3 × 0.3 × 0.3 × 0.3

= 0.000729

Therefore, the probability is 0.000729

Read related link on:

brainly.com/question/24676154

7 0
3 years ago
Brian divided 64 ounces of fruit punch into 6 1/3 ounce servings.He has 2/3 ounce of punch left over.How many 6 1/3 ounce servin
ziro4ka [17]
Brian made 10 servings
7 0
4 years ago
Suppose the sound wave has the form y=7cos(3x-pi/6) for x in the interval [pi/6 , 7pi/18]. Express x as a function of y, and sta
Vesnalui [34]

Answer:

x = ⅓ acos(y/7) + π/18, [-7, 7/2]

Step-by-step explanation:

y = 7 cos(3x − π/6)

Solving for x:

y/7 = cos(3x − π/6)

acos(y/7) = 3x − π/6

acos(y/7) + π/6 = 3x

x = ⅓ acos(y/7) + π/18

The domain of x is the same as the range of y.

When x = π/6:

y = 7 cos(3π/6 − π/6)

y = 7 cos(π/3)

y = 7/2

When x = 7π/18:

y = 7 cos(21π/18 − π/6)

y = 7 cos(π)

y = -7

So the domain of x as a function of y is [-7, 7/2].

5 0
4 years ago
15 POINTS PLEASE ANSWER
Tema [17]

Answer:

91

Step-by-step explanation:

Just do 130-30% and you get 91.

6 0
3 years ago
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