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2 years ago

10

Solve the system using a matrix. (8x + 5y = 38 (3x + 2y = 14 ([ ? ],[_])

1 answer:

kogti [31]2 years ago

6 0

Answer:

(x, y) = (6, -2)

Step-by-step explanation:

A suitable calculator or spreadsheet can do the row-reduction or matrix inversion required to solve this system.

(x, y) = (6, -2)

_____

For matrices ...

$A=\left[\begin{array}{cc}8&5\\3&2\end{array}\right],\ B=\left[\begin{array}{c}38\\14\end{array}\right] ,\ X=\left[\begin{array}{c}x\\y\end{array}\right]$

The solution can be found as ...

$AX=B\ \longrightarrow\ X=A^{-1}B$

or by row-reducing the augmented matrix ...

$[A|B]\ \longrightarrow\ [I|X]$

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Read 2 more answers

Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college i

vladimir1956 [14]

Answer:

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable <em>X</em> be defined as the number of students at a particular college who are smokers

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But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

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Thus, a Normal approximation to binomial can be applied.

So,

$X\sim N(\mu=600, \sigma=\sqrt{120})$

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

= P (X > 280.50)

$=P(\frac{X-\mu}{\sigma}>\frac{280-300}{\sqrt{120}}\\=P(Z>-1.83)\\=P(Z$

*Use a <em>z</em>-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

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3 years ago