Ask question

Ask question

All categories

3 years ago

6

Use the terms 4,12a,6,2a,and 24 to make equivalent expressions. Use each term only once. Use substitution to prove that the expr

essions are equivalent

1 answer:

kvasek [131]3 years ago

7 0

In this problem, our best option is to just guess-and-check.

6(2a + 4) = 12a + 24

Now let’s check this!

Distribute the 6:: 12a + 24 = 12a + 24

Both sides look the same so that’s our answer.

And there you have it! 6(2a + 4) = 12a + 24 is your final equation. You can split up both sides into individual expressions (writing them separately without = ).

For using substitution, choose a random number for a and put it into both separate expressions, and they should result in the same number.

Ex. a = 1
6(2+4) = 6(6) = 36. 12+24=36

And that should be it for this question!

You might be interested in

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

7 0

2 years ago

Due in 10 min help! <br> Find t.

lys-0071 [83]

Given:

A right angle triangle with angles 45, 45, 90 degrees.

Hypotenuse of the triangle = $7\sqrt{2}$ mm

Base of the triangle = t

To find:

The value of t.

Solution:

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

Using this trigonometric ratio in the given triangle, we get

$\cos (45^\circ)=\dfrac{t}{7\sqrt{2}}$

$\dfrac{1}{\sqrt{2}}=\dfrac{t}{7\sqrt{2}}$

$\dfrac{7\sqrt{2}}{\sqrt{2}}=t$

$7=t$

Therefore, the value of t is 7 millimetres.

8 0

3 years ago

The perimeter of a rectangle is 54 feet. The area of the rectangle is 176 square feet. Find the dimensions of the rectangle.

Murrr4er [49]

11 by 16

Explanation:

Set up two equations

2

x

+

2

y

=

54

x

×

y

=

176

Solving the first equation for x

2

x

+

2

y

−

2

y

=

54

−

2

y

this gives

2

x

=

54

−

2

y

Divide both sides by 2

(

2

x

2

)

=

54

−

2

y

2

This gives.

x

=

27

−

y

putting this value into the second equation gives.

(

27

−

y

)

×

y

=

176

multiplying across the parenthesis gives

27

y

−

y

2

=

176

subtracting 176 from both sides gives

is

27

y

−

y

2

−

176

=

0

multiplying by negative one gives

−

27

y

+

y

2

+

176

=

0

factoring this into y gives

(

y

−

11

)

×

(

y

−

16

)

=

0

Solving for both y's gives

y

=

11

,

y

=

16

6 0

2 years ago

In 2010, a city population was 55,210 and it was declining at a rate of 1.09 each year. What is the best prediction for when the

PSYCHO15rus [73]

48000=55210(1-0.0109)^t
Solve for t
t=12.77 =13 years
2010+13=2023

So the answer is c

5 0

4 years ago

Read 2 more answers

Andrew had $46 he got for his birthday. He split the money into 1/4 to give to the 4 people he owed money too. How much money di

Ivanshal [37]

Answer:

2.75

Step-by-step explanation:

46 divided by 4 is 11r2 then convert the 2 into a decimal which is 11.02 then divide it by 4 which is 2.75 i didn't double check so its its wrong im sorry

3 0

3 years ago