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NeX [460]
3 years ago
11

Are the following angle relationships possible? Explain.

Mathematics
1 answer:
mel-nik [20]3 years ago
7 0

Answer:

no

Step-by-step explanation:

The 5x+30 is the supplementary angle of the interior one:

180 - 5x - 30 = -5x + 150

Then they have to add up to 180:

4x-9 + 2x+3 -5x + 150 = 180

which simplifies to x = 36

So the angles would be 135, 75 and -30, which is impossible!

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Please help me IDK how to do this!!!!!!
tatiyna
A parallelogram should have 2 sets of parallel lines. Let's find the slope of line PQ and RS to test.

PQ:
(4-2)/(1-(-3))
2/4
1/2

RS:
(2-0)/(3-1)
2/2
1

Because 1 does not equal 1/2 (the slopes are different) the lines are not parallel. Thus, the figure is not a parallelogram.
5 0
3 years ago
What is 2 ÷ <br> 1<br> 6<br> ?<br><br> StartFraction 1 Over 12 EndFraction<br> 2<br> 6<br> 12
nexus9112 [7]

Answer:

0.125

Step-by-step explanation:

I calculated 2 divided by 16, and got 0.125.

5 0
2 years ago
Which equation or function is linear?
zepelin [54]

9514 1404 393

Answer:

  C.  2y = (2x-1)/4

Step-by-step explanation:

An equation is linear when the exponents of the variables are 1 and the sum of the exponents of the variables in any term is 1.

a) 3xy = 4 . . . . sum of exponents is 1+1=2

b) f(x) = 2/3(1 -x^2) . . . . exponent is 2

c) 2y = (2x -1)/4 . . . . all exponents are 1 (linear)

d) y = 3/(x+1)  ⇒  xy +y = 3 . . . . sum of exponents is 1+1 = 2

8 0
3 years ago
The cost of a type of educational toy is expressed as y = 3x + 2. Find the rate of change.
NNADVOKAT [17]

Answer:

3

Step-by-step explanation:

<em>Rate of Change </em>is the same as <em>Slope</em><em>.</em><em> </em>According to the Slope-Intercept Formula, <em>y</em><em> </em><em>=</em><em> </em><em>mx</em><em> </em><em>+</em><em> </em><em>b</em><em>,</em><em> </em><em>m</em><em> </em>is the <em>Rate</em><em> </em><em>of</em><em> </em><em> </em><em>Change</em><em> </em>[<em>Slope</em>].

I am joyous to assist you anytime.

6 0
3 years ago
Let X1,X2......X7 denote a random sample from a population having mean μ and variance σ. Consider the following estimators of μ:
Viefleur [7K]

Answer:

a) In order to check if an estimator is unbiased we need to check this condition:

E(\theta) = \mu

And we can find the expected value of each estimator like this:

E(\theta_1 ) = \frac{1}{7} E(X_1 +X_2 +... +X_7) = \frac{1}{7} [E(X_1) +E(X_2) +....+E(X_7)]= \frac{1}{7} 7\mu= \mu

So then we conclude that \theta_1 is unbiased.

For the second estimator we have this:

E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu

And then we conclude that \theta_2 is unbiaed too.

b) For this case first we need to find the variance of each estimator:

Var(\theta_1) = \frac{1}{49} (Var(X_1) +...+Var(X_7))= \frac{1}{49} (7\sigma^2) = \frac{\sigma^2}{7}

And for the second estimator we have this:

Var(\theta_2) = \frac{1}{4} (4\sigma^2 -\sigma^2 +\sigma^2)= \frac{1}{4} (4\sigma^2)= \sigma^2

And the relative efficiency is given by:

RE= \frac{Var(\theta_1)}{Var(\theta_2)}=\frac{\frac{\sigma^2}{7}}{\sigma^2}= \frac{1}{7}

Step-by-step explanation:

For this case we assume that we have a random sample given by: X_1, X_2,....,X_7 and each X_i \sim N (\mu, \sigma)

Part a

In order to check if an estimator is unbiased we need to check this condition:

E(\theta) = \mu

And we can find the expected value of each estimator like this:

E(\theta_1 ) = \frac{1}{7} E(X_1 +X_2 +... +X_7) = \frac{1}{7} [E(X_1) +E(X_2) +....+E(X_7)]= \frac{1}{7} 7\mu= \mu

So then we conclude that \theta_1 is unbiased.

For the second estimator we have this:

E(\theta_2) = \frac{1}{2} [2E(X_1) -E(X_3) +E(X_5)]=\frac{1}{2} [2\mu -\mu +\mu] = \frac{1}{2} [2\mu]= \mu

And then we conclude that \theta_2 is unbiaed too.

Part b

For this case first we need to find the variance of each estimator:

Var(\theta_1) = \frac{1}{49} (Var(X_1) +...+Var(X_7))= \frac{1}{49} (7\sigma^2) = \frac{\sigma^2}{7}

And for the second estimator we have this:

Var(\theta_2) = \frac{1}{4} (4\sigma^2 -\sigma^2 +\sigma^2)= \frac{1}{4} (4\sigma^2)= \sigma^2

And the relative efficiency is given by:

RE= \frac{Var(\theta_1)}{Var(\theta_2)}=\frac{\frac{\sigma^2}{7}}{\sigma^2}= \frac{1}{7}

5 0
3 years ago
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