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Paul [167]
1 year ago
13

Use the Factor Theorem to determine whether x + 1 is a factor of P(x) = 2x³+4x²–2x−8.

Mathematics
1 answer:
Harman [31]1 year ago
5 0

Answer: 2x^2+2x-4-\frac{4}{x+1}

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1  ║ 2 | 4 | -2 | -8

   ║    | -2| -2 |  4

   ║ 2 | 2|  -4 |  -4

2x^2+2x-4-\frac{4}{x+1}

PS: if anyone knows a better way to do a synthetic division chart please let me know.

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a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

Step-by-step explanation:

1) 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".  

2) Solution to the problem

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

X \sim N(30,8)  

Where \mu=30 and \sigma=8

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

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

P(X>a)=0.15   (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 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

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=1.04

And if we solve for a we got

a=30 +1.04*8=38.32

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.  

C) 38.32

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