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3 years ago

Factored 8x2y3-5= I need the answer

Mathematics

1 answer:

ANTONII [103]3 years ago

5 0

Answer: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y3" was replaced by "y^3". 1 more similar replacement(s).

STEP

Equation at the end of step 1

(23x2 • y3) - 5

STEP

Trying to factor as a Difference of Cubes

2.1 Factoring: 8x2y3-5

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 8 is the cube of 2

Check : 5 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

8x2y3 - 5

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What is the product of 0 and 8?

Lostsunrise [7]

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3 years ago

Scotland has been a member of the United Kingdom since the 1707 Act of Union. In a recent poll, 38% of Scots would vote in favor

Pani-rosa [81]

Answer:

57.39% probability that between 50 and 60 of them were in favor of leaving the U.K.

Step-by-step explanation:

I am going to use the normal approximmation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 135, p = 0.38$

$\mu = E(X) = np = 135*0.38 = 51.3$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{135*0.38*0.62} = 5.6397$

What is the probability that between 50 and 60 of them were in favor of leaving the U.K.?

Using continuity correction, this is $P(50-0.5 \leq X \leq 60 + 0.5) = P(49.5 \leq X \leq 60.5)$ . So this is the pvalue of Z when X = 60.5 subtracted by the pvalue of Z when X = 49.5. So