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3 years ago

What is 1/4 times exponent 4

Mathematics

1 answer:

lilavasa [31]3 years ago

5 0

Change 1/4 to a decimal is an exponent by 4 and the answer would be 0.0039

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A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a random

Zielflug [23.3K]

Answer: The 95% confidence interval for the mean of x is (94.08, 101.92) .

Step-by-step explanation:

We are given that ,

A random variable x has a Normal distribution with an unknown mean and a standard deviation of 12.

i.e. $\sigma= 12$

Also, it is given that , Sample mean $\overline{x}=98$ having sample size : n= 36

For 95% confidence ,

Significance level : $\alpha=1-0.95=0.05$

By using the z-value table , the two-tailed critical value for 95% Confidence interval :

$z_{\alpha/2}=z_{0.025}=1.96$

We know that the confidence interval for unknown population mean $(\mu)$ is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

, where $\overline{x}$ = Sample mean

$\sigma$ = Population standard deviation

$z_{\alpha/2}$ = Critical z-value.

Substitute all the given values, then the required confidence interval will be :

$98\pm (1.96)\dfrac{12}{\sqrt{36}}$

$=98\pm (1.96)\dfrac{12}{6}$

$=98\pm (1.96)(2)$

$=98\pm 3.92=(98-3.92,\ 98+3.92)\\\\=( 94.08,\ 101.92)$

Therefore, the 95% confidence interval for the mean of x is (94.08, 101.92) .

6 0

3 years ago

Simplify.

NikAS [45]

Answer:

Step-by-step explanation:

5 0

3 years ago

4) If x-1/x=5, fand the value of x²+ 1/x²

tangare [24]

Given:

$\sf x\ -\ \dfrac{1}{x}\ =\ 5$

To find:

$\sf The\ value\ of\ x^2\ +\ \dfrac{1}{x^2}.$

Answer:

$\sf x\ -\ \dfrac{1}{x}\ =\ 5$

Let's square the above expression.

$\sf \bigg(x\ -\ \dfrac{1}{x}\bigg)^2\ =\ 5^2$

According to the identities, (a - b)² = a² - 2ab + b². Using the same logic for the expression above,

$\sf x^2\ -\ 2\ \times\ x\ \times\ \dfrac{1}{x}\ +\ \dfrac{1}{x^2}\ =\ 25\\\\\\x^2\ -\ 2\ +\ \dfrac{1}{x^2}\ =\ 25\\\\\\x^2\ +\ \dfrac{1}{x^2}\ =\ 25 + 2\\\\\\x^2\ +\ \dfrac{1}{x^2}\ =\ 27$

Therefore, the value of x² + 1/x² is 27.

8 0

3 years ago

OMGGG PLS HELP PLS I WILL GIVE YOU POINTS AND STUFF PLS HELP MEH Figure A is a scale image of Figure B. B: side length x A: side

Digiron [165]

try this answer good luck

Answer:

Answer:<u> 1/2 </u>

Step-by-step explanation:

Given : Figure B is a scaled copy of Figure A.

We know that the scale factor is the ratio of the corresponding sides of two similar figures.

From , the graph we assume that that one point = one unit of length.

Then, the dimension of one side of figure A = 4 units and the dimension of corresponding side of Figure B = 2.

Then, the scale factor is given by:

k = 2/4 = 1/2

Hence, the scale factor is <u>1/2</u>

7 0

4 years ago

Write the equation of the line perpendicular to 2x-3y=12 which passes through the point (16,-7).

Elanso [62]

Y= mx+b

(16, -7) = (x,y)

2(16) - 3y = 12
32 - 3y = 12
32 - 12 = 3y
20/3 = y
6.6 = y

2x-3(-7) = 12
2x+21 = 12
2x = 12 - 21
x = -9/2

Insert the values into y = mx + b
solve for m and then solve for b

3 0

3 years ago