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3 years ago

How do i divide and multiply rational expressions?

Mathematics

1 answer:

notka56 [123]3 years ago

4 0

Answer:

To multiply rational expressions, first factor all numerators and denominators and cancel any factors you can. Then multiply what you have left.

Step-by-step explanation:

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The pizza shop sells artwork by local artists. For each piece it sells, the shop receives a 15 percent commission. The most expe

Margarita [4]

Answer:

The 15 percent commission is what the shop received.

Step-by-step explanation:

It said that the most expensive piece it ever sold was 225

not that the most money they made is 225

5 0

3 years ago

Write an inequality that represents the graph.

Dimas [21]

Answer:

y=2x+1

Step-by-step explanation:

Y intercept is 1 and slope is 2/1

5 0

3 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

3 years ago

<img src="https://tex.z-dn.net/?f=3.18%20%5Cdiv%2010" id="TexFormula1" title="3.18 \div 10" alt="3.18 \div 10" align="absmiddle"

Maslowich

Answer:

0.318

Step-by-step explanation:

on division with 10, the value reduces.... decimal moves forward

on multiplication, the value increases decimal moves backward....

eg: 3.18 x 10 = 31.8

5 0

3 years ago

PLEASE HELP it should be easy for someone but I can’t do it

-Dominant- [34]

Answer:

Total crackers on the plate are 12

Step-by-step explanation:

Manuel ate crackers = $\frac{1}{3}$

His brother ate crackers = $\frac{1}{4}$

Crackers left on the plate = 5

We need to find how many crackers were there on the plate.

Let x be the total crackers on the plate

So, we can write the equation

$x-\frac{1}{3}x-\frac{1}{4}x=5$

Because 1/3 and 1/4 crackers are eaten and 5 are left so, we subtract 1/3x and 1/4x from x and equal it to 5

$\frac{12x-4x-3x}{12}=5\\\frac{12x-7x}{12}=5\\\frac{5x}{12}=5\\x=\frac{5*12}{5}\\x=12$

So, we get x = 12

Therefore, total crackers on the plate are 12

8 0

3 years ago