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marishachu [46]
3 years ago
13

The length of a rectangle is seven times its width. The area of the rectangle is 175 square centimeters. Find the dimensions of

the rectangle.
Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

<h3>The length is 35cm</h3><h3>The width is 5cm</h3><h3 />

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

The length is seven times the width is written as

l = 7w

Area of the rectangle = 175 cm²

7w × w = 175

7w² = 175

Divide both sides by 7

w² = 25

Find the square root of both sides

w = √25

w = 5cm

But l = 7w

l = 7(5)

l = 35cm

The length is 35cm

The width is 5cm

Hope this helps you.

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RSB [31]

Answer:

The value of E(Y/X) is 2.

Step-by-step explanation:

As the complete question is not given, thus the complete question is found online and is attached herewith.

So the joint density function is given as

f(x,y)=\left \{ {{\dfrac{x}{8}e^{-\dfrac{x+y}{2}}    \,\,\,\,0 \leq x,0\leq y \atop {0}} \right.

So the marginal function for X is given as

f_x=\int\limits^{\infty}_0 {f(x,y)} \, dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x+y}{2} }dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x}{2}}e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{8}e^{-\frac{x}{2}}\int\limits^{\infty}_0e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{4}e^{-\frac{x}{2}}

Now

f(Y/X)=\dfrac{f(X,Y)}{f(X)}\\f(Y/X)=\dfrac{\dfrac{x}{8}e^{-\frac{x+y}{2} }}{\dfrac{x}{4}e^{-\frac{x}{2}}}\\f(Y/X)=\dfrac{1}{2}e^{-\frac{y}{2} }

Now the value of E(Y/X) is given as

E(Y/X)=\int\limits^{\infty}_0 {yf_{Y/X}} \, dy \\E(Y/X)=\int\limits^{\infty}_0 {y\dfrac{1}{2}e^{-\frac{y}{2} } }\, dy\\E(Y/X)=\dfrac{1}{2}\dfrac{\sqrt{2}}{(\dfrac{1}{2})^2}=2

So the value of E(Y/X) is 2.

3 0
3 years ago
The experimental probability of rain in a certain town is 20 percent. In the next 45 days, how many days can one expect it to ra
Hatshy [7]

9.

hope this helps :)

8 0
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SIZIF [17.4K]
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3 years ago
Please help very urgent
Arturiano [62]

Answer:

<em>Marika's calculation is correct</em>

Step-by-step explanation:

<em>Lori has erroneously identified a common ratio of the geometion sequence</em>

<em>one has to divide subsequent term by the preceding term as was correctly by Marika. so Marika's calculation is correct.</em>

<em>hope it helps...</em>

<em>have a great day !!!</em>

8 0
3 years ago
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Step-by-step explanation:

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3 0
3 years ago
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