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3 years ago

If you answer yo get 20 points

Mathematics

2 answers:

Elodia [21]3 years ago

6 0

Answer:

n = 2 + 2√3 and n = 2 - 2√3

Step-by-step explanation:

Let the number be n.

Then n² + 1 = 4n.

Rearranging this in proper quadratic format:

n² - 4n + 1

Here the coefficients are a = 1, b = -4 and c = 1.

Then the discriminant is b²-4ac, or (-4)²-4(1)(1) ), or 16 - 4, or 12.

By applying the quadratic formula, we find that the roots are:

- (-4) ± √12

n = ------------------

or n = 2 + 2√3 and n = 2 - 2√3

Ierofanga [76]3 years ago

5 0

Answer:

3.732 or 0.268 to the nearest thousandth.

Exact values are 2 + √12/2 or 2 - √12/2.

Step-by-step explanation:

Let the original number be x, then:

x^2 + 1 = 4x

x^2 - 4x + 1 = 0

x = [-(-4) +/- sqrt(16 - 4*1*1]) / 2

x = (4 + sqrt12)/ 2 , (4 - sqrt12) / 2

= 3.732, 0.268.

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3 years ago

Read 2 more answers

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard

Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81$

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

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

By the Central Limit Theorem

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

$Z = \frac{30732 - 30393}{472.81}$

$Z = 0.72$

$Z = 0.72$ has a pvalue of 0.7642.

X = 30054

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

$Z = \frac{30054 - 30393}{472.81}$

$Z = -0.72$

$Z = -0.72$ has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

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3 years ago

The linear equation y = 32x + 240 models the relationship between the value of an investment stock, y, and the number of years i

goldfiish [28.3K]

I think answer should be d. Please give me brainlest let me know if it’s correct or not okay thanks bye

8 0

3 years ago

Combine the following fractions. a. 3/5 + 4/15 b. 5/6 - 1/4

Ne4ueva [31]

Hello there! :)

Answer:

1. $\boxed{\frac{13}{15} }$