Which expression is equivalent to 1/2(2n + 6)?

Mathematics

1 answer:

larisa [96]3 years ago

3 0

Answer:

n+3

Step-by-step explanation:

hello :

1/2(2n + 6) = (1/2)(2n) +(1/2)(6)

the expression is equivalent to 1/2(2n + 6) is n+3

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A Circular pie with a diameter of 10” Is cut into six equal pieces. What is the surface area of two slices of pie?

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To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.

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The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning at

tamaranim1 [39]

Answer:

Between 0.01 and 0.20

Step-by-step explanation:

I am going to use the normal approximation 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:

$n = 500, p = 0.05$

$\mu = E(X) = np = 500*0.05 = 25$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]
Find the probability of winning at least 30 times.Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)$ . So this is 1 subtracted by the pvalue of Z when X = 29.5. Then