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RUDIKE [14]
3 years ago
9

Solve for x in the equation 3 x squared minus 18 x + 5 = 47.

Mathematics
1 answer:
Rudik [331]3 years ago
5 0

Answer:

x = -1.796, 7.796

Step-by-step explanation:

3x² - 18x + 5 = 47

3x² - 18x - 42 = 0

use quadratic equation

x = -1.796, 7.796

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There are 6! = 720 ways of arranging the lamps.

If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.

Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.

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P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4

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A very large data set (N > 10,000) has a mean value of 1.65 units and a standard deviation of 72.26 units. Determine the rang
Romashka [77]

Answer:

z=-0.674

And if we solve for a we got

a=1.65 -0.674*72.26=-47.05

z=0.674

And if we solve for a we got

a=1.65 +0.674*72.26=50.35

So then the limits where 50% of the data lies are -47.05 and 50.35

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 variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(1.65,72.26)  

Where \mu=1.65 and \sigma=72.26

For this case we want the limits for the 50% of the values.

So on the tails of the distribution we need the other 50% of the data, and on ach tail we need to have 25% since the distribution is symmetric.

Lower tail

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.75   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.674

And if we solve for a we got

a=1.65 -0.674*72.26=-47.05

So the value of height that separates the bottom 25% of data from the top 75% is -47.05.  

Upper tail

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=1.65 +0.674*72.26=50.35

So the value of height that separates the bottom 75% of data from the top 25% is 50.35.  

So then the limits where 50% of the data lies are -47.05 and 50.35

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3 years ago
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