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3 years ago

What is the solution to the equation 1/6x=2?

Mathematics

1 answer:

iris [78.8K]3 years ago

7 0

Answer:

x = 12

Step-by-step explanation:

Multiplying (1/6) by 6 will isolate the variable x. That's what we want.

6(1/6)x = 6(2) leads to x = 12

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A certain industrial process yields a large number of steel cylinder whose lengths are distributed normally with mean 3.25 inche

Taya2010 [7]

Answer:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.25,0.05)$

Where $\mu=3.25$ and $\sigma=0.05$

We slect two observations $X_1, X_2$

And let denote the combined lenght as:

$Y = X_1 + X_2$

If we find the expected value of Y we got:

$E(Y) = E(X_1) + E(X_2) = 3.25 + 3.25 =6.5$

And for the variance we assume that we have independent random variables for X1 and X2 so then we have:

$Var(Y) = Var(X_1) + Var(X_2) = \sigma^2 + \sigma^2 = 2 \sigma^2 = 2*(0.05^2) = 0.005$

And the deviation $Sd(Y) = \sqrt{0.005}=0.0707$

So then our random variable Y have the following distribution:

$Y \sim N (\mu =6,5 , \sigma = 0.0707)$

And we want to find this probability:

$P(Y$

And we can use the z score formula given by:

$z=\frac{y -\mu_y}{\sigma_y}$

And if we use the z score formula we got:

$P(Y$

3 0

3 years ago

CosA + cosB + cosC = 1 + 4sinA/2 sinB/2 sinC/2

bulgar [2K]

$\cos(A) + \cos( B ) + \cos(C) \\ = 2 \cos( \frac{A + B}{2} ) \cos( \frac{ A- B}{2} ) + 1 - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2\cos( \frac{\pi - C}{2} ) \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}] \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A + B}{2} )] \\ = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2} +\frac{A - B}{2} }{2} ) \sin( \frac{ \frac{A + B}{2} - \frac{A - B}{2} }{2} ) \\ = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$

6 0

3 years ago

What is 3x+8 if x=8

Mazyrski [523]

Answer:

y=32

Step-by-step explanation:

y=3(8)+8

y=24+8

24+8=32

y=32

4 0

3 years ago

Read 2 more answers

The diameter of each circular hole in a paint palette is 42 millimeters.

Andrews [41]

Answer:

Step-by-step explanation:

The circumference is just diameter x π (3.14 in this case) so 42 x 3.14 = 131.88

8 0

3 years ago

Why is x=6 a solution to the proportion 192/36=32/x

Norma-Jean [14]

Answer:

They're both equal each other!

Step-by-step explanation:

Because 32/6 is 5.33... on the calculator and when you divide 192/36 is 5.33 and so on. X = 6 is the solution because both of these divisors equal each other!!! Hope this helps!

7 0

4 years ago