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3 years ago

Factor 4x^3-16x^2+12-3x

2 answers:

5 0

4x^3-16x^2+12-3x
Rearrange: (4x^3-16x^2)-(3x+12)
Factor out GCF : 4x^2(x-4)-3(x-4)
Answer: (4x^2-3)(x-4)
I hope this helped! :)

sveticcg [70]3 years ago

5 0

4x^3-16x^2-3x+12
first you would have to find the GFC but there is none.
since there are 4 terms in this equation you have to group the numbers.
In 4x^3-16x^2 the GCf is 4x^2 and in -3x+12 the GCF is -3
4x^3-16x^2-3x+12
=4x^2(x-4)-3(x-4)
when your finding the GCF you are practically dividing you GCF with the 2 terms that were in common. that is how i got (x-4). you would keep your GCF in the front of you equation like so, 4x^2(x-4)-3(x-4).

later you would take the numbers outside of the bracket and combine them, leading you to (4x^2-3) with (x-4)
therefore your answer would be (4x^2-3)(x-4)
4x^3-16x^2-3x+12
=4x^2(x-4)-3(x-4)
=(4x^2-3)(x-4)
because both (x-4)'s are the same and so are the signs, you do not need to square it or put two of the terms together like this, (4x^2-3)(x-4)(x-4). since they are both the same you leave one out.

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4 years ago

It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally dis

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b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 7.5, \sigma = 1.2$

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?

This is the pvalue of Z when X = 4. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4 - 7.5}{1.2}$

$Z = -2.92$

$Z = -2.92$ has a pvalue of 0.0018.

So 0.18% of cold sufferers experience fewer than 4 days of symptoms.

b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So

X = 10

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 7.5}{1.2}$

$Z = 2.08$

$Z = 2.08$ has a pvalue of 0.9812.

X = 7

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{7 - 7.5}{1.2}$

$Z = -0.42$

$Z = -0.42$ has a pvalue of 0.3372.

So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

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