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4 years ago

7+ 2x divided by 5= 13

Mathematics

2 answers:

Troyanec [42]4 years ago

4 0

Answer:

$x=29$

Step-by-step explanation:

Given equation :

$\frac{(7+2x)}{5} =13$

Making the terms of 'x' to one side and constants to the other.

$(7+2x)=13*5$

$7+2x=65$

$2x=65-7$

$2x=58$

$x=\frac{58}{2}$

$x=29$

So, the value of 'x' is 29.

Masja [62]4 years ago

3 0

Answer:

x = 29

Explanation:

7 + 2x / 5 = 13

Multiply both sides by 5

7 + 2x / 5 = 13 · (5) = (13) · (5)

7 + 2x = 65

Simplify both sides of the equation

2x + 7 = 65

Subtract 7 from both sides

2x + 7 − 7 = 65 − 7

2x = 58

Divide both sides by 2

2x / 2 = 58 / 2

x = 29

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Answer:

Step-by-step explanation:

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3 years ago

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3 years ago

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3 years ago

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rosijanka [135]

Answer:

Characteristic equation:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda$

Eigen values:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

Step-by-step explanation:

We are given the matrix:

$\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]$

The characteristic equation can be calculated as:

$det(A-\lambda I) = 0\\|A-\lambda I| = 0$

We follow the following steps to calculate characteristic equation:

$=det\Bigg(\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]-\lambda\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\Bigg)\\\\= det\Bigg(\displaystyle\left[\begin{array}{ccc}-14-\lambda&-6&6\\28&12-\lambda&-4\\0&0&4-\lambda\end{array}\right]\Bigg)\\\\=(-14-\lambda)[(12-\lambda)(4-\lambda)]+6[28(4-\lambda)]-6[(28)(0)-(12-\lambda)(0)]\\\\= -\lambda^3 + 2\lambda^2 + 8\lambda$

$p(\lambda)= -\lambda^3 + 2\lambda^2 + 8\lambda$

To obtain the eigen values, we equate the characteristic equation to 0:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda = 0\\-\lambda(\lambda^2-2\lambda-8) = 0\\-\lambda(\lambda^2-4\lambda+2\lambda-8) = 0\\-\lambda[(\lambda(\lambda-4)+2(\lambda-4)] = 0\\-\lambda(\lambda+2)(\lambda-4) = 0 \\\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

We can arrange the eigen values as:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4\\-2 < 0 < 4\\\lambda_2 < \lambda_1 < \lambda_3$

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3 years ago

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lakkis [162]

Answer:

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Step-by-step explanation:

The probability that an intern uses drugs, given that the test is negative, is determined by the probability of false negative divided by the probability of a negative (true or false).

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$P(FN) = 0.10*(1-0.80)=0.02$

A true negative occurs when an intern who does not use drugs (90%) takes the test and gets a negative. Since the test gets it wrong 3% of the time, the probability of this happening is:

$P(TN) = 0.90*(1-0.03)=0.873$

Therefore, the probability that an intern uses drugs, given that the test is negative is:

$P(D|N) = \frac{P(FN)}{P(FN)+P(TN)} \\P(D|N) = \frac{0.02}{0.02+0.873} \\P(D|N) = 0.0224 = 2.24\%$

The probability is 0.0224 or 2.24%.

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3 years ago

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