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2 years ago

Find the roots of x^4-1=0

Mathematics

1 answer:

serg [7]2 years ago

7 0

Answer:

x = +1

x = -1

Step-by-step explanation:

x^4-1=0

x^4=+1

fourth root of x^4= fourth root of +1

x = +1

x = -1

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Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know 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:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

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

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0

3 years ago

Find the product of (3.7 × 104) and 2.<br> (Can you please put the answer in scientific notation)

OverLord2011 [107]

(3.7 x 104)2 = 769.6
In Scientific notation:
7.696 x 10^2

8 0

3 years ago

In how many ways can a class of 10 students be assigned 1 a, 2 b;s

nalin [4]

2.b..........................

6 0

4 years ago

Read 2 more answers

What is the mean of this data set? If necessy, round your answer to the nearest tenth. 12,16,22,23,34,44,46,47,48,64,67,73,83,88

Dmitry_Shevchenko [17]

The mean for the data set is 50.4

Rounded to the nearest 10th is 50

8 0

3 years ago

Use the figure shown. Find the slope of the line.

lilavasa [31]

Answer:

The slope is $-\frac{1}{2}$

Step-by-step explanation:

With points A(-2, 1), and B(-4, 2), slope (m) of the line can be calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ ,

Where,

$y_2 = 2$

$y_1 = 1$

$x_2 = -4$

$x_1 = -2$

Plug in the values into the slope formula:

$m = \frac{2 - 1}{-4 -(-2)}$

$m = \frac{2 - 1}{-4 + 2}$

$m = \frac{1}{-2}$

$m = -\frac{1}{2}$

8 0

3 years ago

Find the roots of x^4-1=0​

Find the roots of x^4-1=0