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2 years ago

Which represents the solution to the absolute value equation? 3|2x+4|-1=11

1 answer:

5 0

The first step for absolute value equations is to isolate the expression contained within the absolute value bars:

3|2x+4|-1 = 11
3|2x+4| = 12
|2x+4| = 4

so |2x+4| is 4 units away from 0 on a number line, but we don't know in which direction -- negative or positive? you'll have two answers.

2x+4 = 4

AND

2x+4 = -4

solve both of those two step equations and you'll get

x = 0

AND

x = -4

so 0 and -4 are your solutions.

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What is 0.11 as a fraction in simplest form

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0.31 repeating as a fraction

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I believe its 31/100! To write 0.3111 as a fraction you have to write 0.3111 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

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Solve for x X 170 X=

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Step-by-step explanation:

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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:

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

So let's find the expected values for each estimator:

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

Using properties of expected value we have this:

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

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

For the second estimator we have:

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

Using properties of expected value we have this:

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

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

Part b

For the variance we need to remember this property: If a is a constant and X a random variable then:

$Var(aX) = a^2 Var(X)$

For the first estimator we have:

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

$Var(\hat \theta_1) =\frac{1}{4} Var(X_1 +X_2)=\frac{1}{4} [Var(X_1) + Var(X_2) + 2 Cov (X_1 , X_2)]$

Since both random variables are independent we know that $Cov(X_1, X_2 ) = 0$ so then we have:

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

For the second estimator we have:

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

$Var(\hat \theta_2) =\frac{1}{16} Var(X_1 +3X_2)=\frac{1}{4} [Var(X_1) + Var(3X_2) + 2 Cov (X_1 , 3X_2)]$

Since both random variables are independent we know that $Cov(X_1, X_2 ) = 0$ so then we have:

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

7 0

2 years ago

Please help, will give extra points

adelina 88 [10]

Answer:x=31

angle AOC = 124

angle BOC = 56

Step-by-step explanation:

We first need to solve for x to solve the rest. We would normally solve for x by setting 2 equations equal to each other, in this case however, we know that the two angles are adjacent and in total add up to 180. Therefore we combine like terms of both angles, and set them equal to 180.

So, we do

3x+31+2x-6=180 We will combine like terms

5x+25=180 Now we will do inverse operations

5x=155

x=31

We plug x into angle AOC to solve for it

3(31)+31= 124

180-124=56 or angle BOC because the whole angle is 180, and if we subtract 124 from 180 we get the remainder which is angle BOC

Or if you want,

2(31)-6=56

5 0

2 years ago

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