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2 years ago

How do I simplify this exponent problem???

Mathematics

1 answer:

Nikolay [14]2 years ago

8 0

Hello from MrBillDoesMath!

Answer:

(3/4) a^(-5)b^(-3)c^2

Discussion:

(18 a^-3b^2c^6)/ (24 a^2b^5c^4) =

(18/24) a^ (-3-2) b^(2-5) c^(6-4) =

as a^-3/a^-2 = a ^ (-3-2) = a^(-5), for examples

(3/4) a^(-5)b^(-3)c^2

Thank you,

MrB

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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) .

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2 years ago

A rope from the top of a pole is anchored to the ground which is 55 ft away from the base of the pole. The pole is 48 ft tall. W

Irina-Kira [14]

Answer:

73 feet.

Step-by-step explanation:

Given:

A rope from the top of a pole is anchored to the ground which is 55 ft away from the base of the pole.

The pole is 48 ft tall.

Question asked:

What is the length of the rope?

Solution:

Here we found that a right angle triangle is formed in which base and height is given <u>as shown in the figure, </u>we have to find the longest side of the triangle,

Base = 55 feet

Height = 48 feet

Length of the rope = ?

By Pythagoras theorem:

Square of longest side = Square of base + Square of height

$(Longest\ side)^{2} =$ $55^{2} +48^{2}$