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3 years ago

The dimensions of a rectangle are 3x - 4 and 5x - 11. Which formula can be used to find the perimeter p of the rectangle?

Mathematics

2 answers:

Elenna [48]3 years ago

4 0

Answer:

P = 16x - 30 units

Step-by-step explanation:

Let the length and width of the rectangle be (3x - 4) & (5x - 11)

$perimeter \: of \: rectangle \\ = 2(l + w) \\ = 2(3x - 4 + 5x - 11) \\ = 2(8x - 15) \\ = (16x - 30) \: units$

Lorico [155]3 years ago

3 0

Answer:

P = 16x - 30

Step-by-step explanation:

P = 2L + 2W

P = 2(3x - 4) + 2(5x - 11)

P = 6x - 8 + 10x - 22

P = 16x - 30

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Step-by-step explanation:

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P(Y₁ > Y₂ | Y₁ < 2 Y₂) = P((Y₁ > Y₂) and (Y₁ < 2 Y₂)) / P(Y₁ < 2 Y₂)

Use the joint density to compute the component probabilities:

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$=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1$

$=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty$

$=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16$

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$P(Y_1$

(I leave the details of the second integral to you)

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