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OleMash [197]
3 years ago
9

the set M contains 4positive integers - if the average is 7 what is the highest possible integer in the set M

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
4 0
4 positive integers : x, x + 2, x + 4, x + 6

((x) + (x + 2) + (x + 4) + (x + 6)) / 4 = 7...combine like terms
(4x + 12) / 4 = 7...multiply both sides by 4
4x + 12 = 7 * 4
4x + 12 = 28
4x = 28 - 12
4x = 16
x = 16/4
x = 4

x + 2 = 4 + 2 = 6
x + 4 = 4 + 4 = 8
x + 6 = 4 + 6 = 10

lets check...
(4 + 6 + 8 + 10) / 4 = 7
28/4 = 7
7 = 7 (correct)

the highest possible integer is 10
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Answer:

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

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 = 1164, p = 0.038

So

\mu = E(X) = np = 1164*0.038 = 44.232

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = 6.5231

Estimate the probability that at least 47 people experience flu symptoms.

Using continuity correction, this is P(X \geq 47 - 0.5) = P(X \geq 46.5), which is 1 subtracted by the pvalue of Z when X = 46.5.

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

Z = \frac{46.5 - 44.232}{6.5231}

Z = 0.35

Z = 0.35 has a 0.6368

1 - 0.6368 = 0.3632

36.32% probability that at least 47 people experience flu symptoms. This is not an unlikely event, so this suggests that flu symptoms are not an adverse reaction to the drug.

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Answer:

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Derek is training for a half-marathon. His training plan sets his goal for this week at 18 miles with three short runs and one l
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Answer:

8.65 miles

Step-by-step explanation:

The total of his short runs are 9.35 so you need to find out how many miles he has left till he reaches 18 miles.

The equation you can use is 9.35 + x = 18 x will equal the number of miles for the long run.

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you will get:

x = 8.65

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3 years ago
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