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nataly862011 [7]
3 years ago
6

Find the vertex for the equation: y = 3x^2 + 18x + 30 (-3, 3) (-3, -51) (3, 111)

Mathematics
2 answers:
Papessa [141]3 years ago
8 0
I think (-3, 3 ) !!!!!!!!!!!
Tems11 [23]3 years ago
4 0
Y = 3x^2 + 18x + 30
a = 3, b = 18, c = 30

h = -b/2a = -18 / 6 = -3
<span>k = (4ac – b^</span>2<span>) / 4<span>a = (360 - 324)/12 = 36/12 = 3
</span></span>
vertex (h, k) = (-3,3)


answer
(-3, 3)
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.895 g and a standard deviation
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3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.

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Normal probability distribution

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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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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 0.895, \sigma = 0.292, n = 37, s = \frac{0.292}{\sqrt{37}} = 0.048

Find the probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.

This is the pvalue of Z when X = 0.809.

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

By the Central Limit Theorem

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

Z = \frac{0.809 - 0.895}{0.048}

Z = -1.79

Z = -1.79 has a pvalue of 0.0367

3.67% probability of randomly seleting 37 cigarettes with a mean of 0.809 g or less.

5 0
2 years ago
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