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3 years ago

Solve 5x(x-4) using distributive property

Mathematics

2 answers:

JulsSmile [24]3 years ago

8 0

Answer:

5x^2 - 20x.

Step-by-step explanation:

a(b +c ) = ab + ac is the distributive property, so we have:

5x(x - 4)

= 5x*x + 5x * -4

= 5x^2 - 20x.

vodomira [7]3 years ago

4 0

Answer:

5x² - 20x

Step-by-step explanation:

multiply each term in the parenthesis by the 5x outside

5x(x - 4)

= (5x × x ) + (5x × - 4 )

= 5x² + (- 20x) = 5x² - 20x

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The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

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 distributions 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.

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This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

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$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

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

$Z = \frac{27.5 - 22.88}{4.2245}$