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nika2105 [10]
2 years ago
15

What is the 5th term of the geometric sequence with a1=4 and ratio (multiplier) =8?

Mathematics
2 answers:
enot [183]2 years ago
6 0
Hello,

a_{1}=4
a_{2}=4*8^1
a_{3}=4*8^2

a_{n}=4*8^{n-1}

a_{5}=4*8^4=16384




sergij07 [2.7K]2 years ago
5 0
A(5) = 4 * 8^ (5 - 1)
a(5) = 4 * 8^4
a(5) = 4 * 4096
a(5) = 16384
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Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question, we have that:

\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when X = 260. So

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

By the Central Limit Theorem

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

Z = \frac{260 - 270}{21.2}

Z = -0.47

Z = -0.47 has a pvalue of 0.3192.

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2 years ago
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guapka [62]

Answer:

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Step-by-step explanation:

The given equation is 4 + 2/3 x = -5

Taking variable on one side and constants on other side, we get

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x = (\frac{3}{2})(-9) = \frac{-27}{2} = (-13)(\frac{1}{2}) = -13.5

The number in decimal form is given by -13.5

The number in fraction form is given as \frac{-27}{2} = (-13)(\frac{1}{2})

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