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VladimirAG [237]
3 years ago
9

What is the product of x and y values 2x+8y=24 -7x-6y=26

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
3 0

Answer:

x= -8

y=5

Step-by-step explanation:

2x + 8y =24

2(x+4y)=24

x+4y=24/2

x+4y=12

x=12-4y

-7x-6y=26

-7(12-4y)-6y=26

22y-84=26

22y=26+84

22y=110

y=110/22

y=5

x=12-4y

x=12-4×5

x= -8

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A random variable X with a probability density function () = {^-x > 0
Sliva [168]

The solutions to the questions are

  • The probability that X is between 2 and 4 is 0.314
  • The probability that X exceeds 3 is 0.199
  • The expected value of X is 2
  • The variance of X is 2

<h3>Find the probability that X is between 2 and 4</h3>

The probability density function is given as:

f(x)= xe^ -x for x>0

The probability is represented as:

P(x) = \int\limits^a_b {f(x) \, dx

So, we have:

P(2 < x < 4) = \int\limits^4_2 {xe^{-x} \, dx

Using an integral calculator, we have:

P(2 < x < 4) =-(x + 1)e^{-x} |\limits^4_2

Expand the expression

P(2 < x < 4) =-(4 + 1)e^{-4} +(2 + 1)e^{-2}

Evaluate the expressions

P(2 < x < 4) =-0.092 +0.406

Evaluate the sum

P(2 < x < 4) = 0.314

Hence, the probability that X is between 2 and 4 is 0.314

<h3>Find the probability that the value of X exceeds 3</h3>

This is represented as:

P(x > 3) = \int\limits^{\infty}_3 {xe^{-x} \, dx

Using an integral calculator, we have:

P(x > 3) =-(x + 1)e^{-x} |\limits^{\infty}_3

Expand the expression

P(x > 3) =-(\infty + 1)e^{-\infty}+(3+ 1)e^{-3}

Evaluate the expressions

P(x > 3) =0 + 0.199

Evaluate the sum

P(x > 3) = 0.199

Hence, the probability that X exceeds 3 is 0.199

<h3>Find the expected value of X</h3>

This is calculated as:

E(x) = \int\limits^a_b {x * f(x) \, dx

So, we have:

E(x) = \int\limits^{\infty}_0 {x * xe^{-x} \, dx

This gives

E(x) = \int\limits^{\infty}_0 {x^2e^{-x} \, dx

Using an integral calculator, we have:

E(x) = -(x^2+2x+2)e^{-x}|\limits^{\infty}_0

Expand the expression

E(x) = -(\infty^2+2(\infty)+2)e^{-\infty} +(0^2+2(0)+2)e^{0}

Evaluate the expressions

E(x) = 0 + 2

Evaluate

E(x) = 2

Hence, the expected value of X is 2

<h3>Find the Variance of X</h3>

This is calculated as:

V(x) = E(x^2) - (E(x))^2

Where:

E(x^2) = \int\limits^{\infty}_0 {x^2 * xe^{-x} \, dx

This gives

E(x^2) = \int\limits^{\infty}_0 {x^3e^{-x} \, dx

Using an integral calculator, we have:

E(x^2) = -(x^3+3x^2 +6x+6)e^{-x}|\limits^{\infty}_0

Expand the expression

E(x^2) = -((\infty)^3+3(\infty)^2 +6(\infty)+6)e^{-\infty} +((0)^3+3(0)^2 +6(0)+6)e^{0}

Evaluate the expressions

E(x^2) = -0 + 6

This gives

E(x^2) = 6

Recall that:

V(x) = E(x^2) - (E(x))^2

So, we have:

V(x) = 6 - 2^2

Evaluate

V(x) = 2

Hence, the variance of X is 2

Read more about probability density function at:

brainly.com/question/15318348

#SPJ1

<u>Complete question</u>

A random variable X with a probability density function f(x)= xe^ -x for x>0\\ 0& else

a. Find the probability that X is between 2 and 4

b. Find the probability that the value of X exceeds 3

c. Find the expected value of X

d. Find the Variance of X

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Hayden Grace and Gaytar went to the store. They did not go anymore.
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Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to origin
seropon [69]

Answer:

Part a) The ratio of the perimeters is 3

Part b) The ratio of the areas is 9

Step-by-step explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

z=\frac{x}{y}

we have

z=3

substitute

\frac{x}{y}=3

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

z^{2}=\frac{x}{y}

we have

z=3

substitute

\frac{x}{y}=3^{2}

\frac{x}{y}=9}

3 0
3 years ago
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m_a_m_a [10]
Horizontal- y=-1/2
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A typical song downloaded from the internet is 4 megabytes in size. Lindy has satellite internet, and her computer downloads mus
nasty-shy [4]
So the first thing you do is you divide 1024 by 256. you will come out with the answer of 4. it takes 4 seconds to download 1 megabyte. but, it takes 4 megabytes, so you need to multiply 4 by 4. you will get 16. it takes 16 seconds to download 1 song. 

to figure out how many songs Lindy can download in 2 hours, you multiply 60 by 60. you will get an answer of 3600. there are 3,600 seconds in an hour. now to find out how many are in 2 hours you multiply 3,600 by 2. you will get a sum of 7,200

now to figure out how many songs Lindy can download in 2 hours, you divide 7,200 by 16. you will come out with a quotient of 450.

Lindy can download a total of 450 songs in the space of 2 hours.
6 0
3 years ago
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