All categories

2 years ago

Write the simplified expression: 2x + 3(x - 2) - 3(x -6)

Mathematics

2 answers:

frozen [14]2 years ago

6 0

Answer:

2x + 12

Step-by-step explanation:

distribute numbers inside parentheses

2x + 3x -6 -3x + 18

add x values together and integers together

2x + 3x -3x = 2x

-6 + 18 = 10

simplified to 2x + 12

Bas_tet [7]2 years ago

4 0

Answer:

2x+12

Step-by-step explanation:

2x+3(x−2)−3(x−6)

Distribute:

=2x+(3)(x)+(3)(−2)+(−3)(x)+(−3)(−6)

=2x+3x+−6+−3x+18

Combine Like Terms:

=2x+3x+−6+−3x+18

=(2x+3x+−3x)+(−6+18)

=2x+12

Answer:

=2x+12

You might be interested in

Using coal, steam, and _____, the fischer-tropsch procedure converts coal into a liquid fuel.

ANTONII [103]

Answer:

Using coal, steam, and <u>OXYGEN,</u> the fischer-tropsch procedure converts coal into a liquid fuel.

Step-by-step explanation:

A series of chemical reactions in which hydrogen and carbon monoxide converges into liquid hydrocarbons by using a metal catalyst. This process is called The Fischer-Tropsch process.

Converting Coal into Liquid Fuel is know as Coal liquification.

IN Liquification process Oxygen, heat is used.

Therefore steam is for heat and oxygen to covert coal into liquid fuel.

7 0

2 years ago

Suppose that W1, W2, and W3 are independent uniform random variables with the following distributions: Wi ~ Uni(0,10*i). What is

nadya68 [22]

I'll leave the computation via R to you. The $W_i$ are distributed uniformly on the intervals $[0,10i]$ , so that

$f_{W_i}(w)=\begin{cases}\dfrac1{10i}&\text{for }0\le w\le10i\\\\0&\text{otherwise}\end{cases}$

each with mean/expectation

$E[W_i]=\displaystyle\int_{-\infty}^\infty wf_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac w{10i}\,\mathrm dw=5i$

and variance

$\mathrm{Var}[W_i]=E[(W_i-E[W_i])^2]=E[{W_i}^2]-E[W_i]^2$

We have

$E[{W_i}^2]=\displaystyle\int_{-\infty}^\infty w^2f_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac{w^2}{10i}\,\mathrm dw=\frac{100i^2}3$

so that

$\mathrm{Var}[W_i]=\dfrac{25i^2}3$

Now,

$E[W_1+W_2+W_3]=E[W_1]+E[W_2]+E[W_3]=5+10+15=30$

and

$\mathrm{Var}[W_1+W_2+W_3]=E\left[\big((W_1+W_2+W_3)-E[W_1+W_2+W_3]\big)^2\right]$

$\mathrm{Var}[W_1+W_2+W_3]=E[(W_1+W_2+W_3)^2]-E[W_1+W_2+W_3]^2$

We have

$(W_1+W_2+W_3)^2={W_1}^2+{W_2}^2+{W_3}^2+2(W_1W_2+W_1W_3+W_2W_3)$

$E[(W_1+W_2+W_3)^2]$

$=E[{W_1}^2]+E[{W_2}^2]+E[{W_3}^2]+2(E[W_1]E[W_2]+E[W_1]E[W_3]+E[W_2]E[W_3])$

because $W_i$ and $W_j$ are independent when $i\neq j$ , and so

$E[(W_1+W_2+W_3)^2]=\dfrac{100}3+\dfrac{400}3+300+2(50+75+150)=\dfrac{3050}3$

giving a variance of

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{3050}3-30^2=\dfrac{350}3$

and so the standard deviation is $\sqrt{\dfrac{350}3}\approx\boxed{116.67}$

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

$\mathrm{Var}[W_1+W_2+W_3]$

$=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])$

and since the $W_i$ are independent, each covariance is 0. Then

$\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]$

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3$

and take the square root to get the standard deviation.

8 0

2 years ago

Please help me with my questions!! It’s in my profile. Please help me, and I’ll help you with your questions!!!

nataly862011 [7]

Answer:

help me

Step-by-step explanation:

I am having trouble in math please help it's a quiz and I need to pass it

5 0

2 years ago

(b-2)x= 8

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

(2-2)x = 8

(0)x = 8

x = 8/0

no solution

6 0

2 years ago

On a coordinate plane, an absolute value graph has a vertex at (10, 6).

lorasvet [3.4K]

Answer: (10, ∞)

Step-by-step explanation:

See the graph in the attached image.

4 0

11 months ago