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3 years ago

Find the 11th term of the geometric sequence 10, 20, 40, ...10,20,40,

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

8 0

11th term is 10240

Step-by-step explanation:

Step 1: Given the sequence 10,20,40. So a(1) = 10, common ration, r = 20/10 = 2 Find the 11th term using the nth term formula, a(n) = ar^n-1

⇒ a(11) = 10 × 2^10 = 10 × 1024 = 10240

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Step-by-step explanation:

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3 years ago

A sample of 5 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the pop

Helen [10]

Answer:

$s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

But we need to calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_I}{n}$

And replacing we got:

$\bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072$

And for the sample variance we have:

$s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003$

And thi is the best estimator for the population variance since is an unbiased estimator od the population variance $\sigma^2$

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Step-by-step explanation:

For this case we have the following data:

1.04,1.00,1.13,1.08,1.11

And in order to estimate the population variance we can use the sample variance formula:

$s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

But we need to calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_I}{n}$

And replacing we got:

$\bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072$

And for the sample variance we have:

$s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003$

And thi is the best estimator for the population variance since is an unbiased estimator od the population variance $\sigma^2$

$E(s^2) = \sigma^2$

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Next, find the slope. For every 1/2 moving to the right, it also vertically increased by 1/2.

(1/2)/(1/2)

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Step-by-step explanation:

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

Also, important to remember that the standard deviation is the square root of the variance.

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Problems of normally distributed samples are solved using the z-score formula.

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