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Olenka [21]
3 years ago
7

SEQUENCES AND SERIES

Mathematics
1 answer:
Romashka [77]3 years ago
5 0

Answer:

Step-by-step explanation:

As we Know that formula for arithmetic sequence is

a_n=a_1+(d-1)

and for geometric sequence is

a_n=a1*r^(n-1)

So,

According to given conditions

     a+7d=a*r^5                              (i)\\ a+19d=a*r^7                           (ii)

By dividing equation (i) and (ii)

Hence proved that

r^2=a+19d/a+7d

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What is 948 divided by 1,000
lana [24]

948 divided by 1,000 is 0.948

4 0
3 years ago
What is the answer to <br> -3-7x - 41 - 7&gt;68
Makovka662 [10]

Answer:

x < -17

Step-by-step explanation:

-3-7x - 41 - 7>68

Combine like terms

-7x-51>68

Add 51 to each side

-7x-51+51>68+51

-7x > 119

Divide each side by -7, remembering to flip the inequality

-7x/-7 < 119/-7

x < -17

7 0
3 years ago
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3639 3639 miles, with a var
Andrei [34K]

Answer:

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

Step-by-step explanation:

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

A reminder is that the standard deviation is the square root of the variance.

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.

In this question:

\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5

Probability that the mean of the sample would differ from the population mean by less than 126 miles

This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So

X = 3765

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

By the Central Limit Theorem

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

Z = \frac{3765 - 3639}{59.5}

Z = 2.12

Z = 2.12 has a pvalue of 0.983

X = 3513

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

Z = \frac{3513 - 3639}{59.5}

Z = -2.12

Z = -2.12 has a pvalue of 0.017

0.983 - 0.017 = 0.966

96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles

3 0
3 years ago
Mr. Rogers recorded the height of 15 students from two of his classes. Based on these samples, what generalization can be made?
Sati [7]
You are not giving enough information but in one of the calsses the average of student's height might be greater than the other class beacause one of the two classes needs to have 1 extra person than the other calss
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What is the velocity of it?
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I don't know the answet
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