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2 years ago

Write an expression that represents the width of a rectangle with length x+5 and area x^3+12x^2+47x+60

Mathematics

1 answer:

xeze [42]2 years ago

6 0

Area divided by length= width
x^3+12x^2+47x+60 ÷ x+5=w

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Computer purchases: Out of 809 large purchases made at a computer retailer, 347 were personal computers, 398 were laptop compute

Luda [366]

Step-by-step explanation:

personal- 347 ÷ 809 = 0.43%

lap top- 398 ÷ 809 = 0.49%

printer- 64 ÷ 809 = 0.08%

6 0

3 years ago

X-y+z=-4 3x+2y-z=5 -2x+3y-z=15 How do I solve this?

Lera25 [3.4K]

$1)\ \ \ x-y+z=-4\ \ \ \Rightarrow\ \ \ z=-4-x+y\\\\2)\ \ \ 3x+2y-z=5 \\.\ \ \ \ \Rightarrow\ \ 3x+2y-(-4-x+y)=5 \\.\ \ \ \ \Rightarrow\ \ 3x+2y+4+x-y=5 \\.\ \ \ \ \Rightarrow\ \ 4x+y=1\\\\3)\ \ \ -2x+3y-z=15\\.\ \ \ \ \Rightarrow\ \ -2x+3y-(-4-x+y)=15\\.\ \ \ \ \Rightarrow\ \ -2x+3y+4+x-y=15\\.\ \ \ \ \Rightarrow\ \ -x+2y=11\\--------------------\\$

$z=-4-x+y\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ and\\ \left \{ {{4x+y=1\ \ \ \ } \atop {-x+2y=11\ /\cdot4}} \right. \\\\\left \{ {{4x+y=1\ \ \ \ } \atop {-4x+8y=44}} \right. \\-------\\y+8y=1+44\\9y=45\ /:9\\y=5\\\\-x+2y=11\ \ \ \Rightarrow\ \ \ x=2y-11\ \ \ \Rightarrow\ \ \ x=2\cdot5-11=-1\\\\z=-4-x+y=-4-(-1)+5=-4+1+5=2\\\\Ans.\ x=-1\ \ \ and\ \ \ y=5\ \ \ and\ \ \ z=2$

5 0

3 years ago

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Elenna [48]

Answer:

the answer is B. 150

6 0

2 years ago

Can someone help me with this

Phantasy [73]

These are the the letters that look the same when reflected across the line B,C,D,E,H,I,K,O,X

8 0

2 years ago

Read 2 more answers

Let X1 and X2 be independent random variables with mean μand variance σ².

My name is Ann [436]

Answer:

a) $E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu$

So then we conclude that $\hat \theta_1$ is an unbiased estimator of $\mu$

$E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu$

So then we conclude that $\hat \theta_2$ is an unbiased estimator of $\mu$

b) $Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}$

$Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}$

Step-by-step explanation:

For this case we know that we have two random variables:

$X_1 , X_2$ both with mean $\mu = \mu$ and variance $\sigma^2$

And we define the following estimators:

$\hat \theta_1 = \frac{X_1 + X_2}{2}$

$\hat \theta_2 = \frac{X_1 + 3X_2}{4}$

Part a

In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:

$E(\hat \theta_i) = \mu , i = 1,2$