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2 years ago

Find the radius of the sphere with a volume of 32/81π cubic yards. Write your answer as a fraction in simplest form. PLEASE HELP

1 answer:

8 0

Area of a sphere = 4(pi)(r)^2
Reverse the equation to find the radius (r)
The answer will be in pi form

32/81(pi)

8/20.25(pi)

Square root of 8/20.25(pi) = radius

r = 2.8(rounded)/4.5(pi)

:)

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Se the distributive property to remove the parentheses. -(-3v-4w+1)

KIM [24]

Hii!

$\leadsto\parallel\boldsymbol{Answer.}\parallel\gets$

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3v+4w-1

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$\leadsto\parallel\boldsymbol{Explanation.}\parallel\gets$

We use the distributive property to "distribute" the minus sign.

$\sf -(-3v-4w+1)=-1\cdot(-3v)+(-1)\cdot(-4w)+(-1)\cdot1}$ .

Simplify!

$\sf 3v+4w-1}$ . Which is our final answer.

Hope that this helped! Best wishes.

$\textsl{Reach far. Aim high. Dream big.}$

$\boldsymbol{-Greetings!-}$

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4 0

1 year ago

Outline the steps for taking cross sections of a rectangular prism.

fgiga [73]

Answer:

find a suitable cutting tool
cut the prism on the plane of interest

Step-by-step explanation:

A cross section is the intersection of a cut plane with the object of interest. In a classroom setting, we often try to do the cross sectioning mentally or with diagrams, rather than physically cutting anything. Sometimes, there is no substitute for actually performing the cut to see what the cross section looks like.

For certain samples that don't take kindly to cutting, we sometimes encase them in a block of material that helps them hold their shape during the process. Sometimes the "cutting" is performed by grinding away the portion of the material on one side of the cut plane.

7 0

2 years ago

Name the polygon. State whether it is convex or concave.

valina [46]

Answer:

Pentagon, convex

Step-by-step explanation:

All of the interior angles are less than 180. Hope this helps.

7 0

2 years ago

Read 2 more answers

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.6 ppm and standard de

Setler79 [48]

We assume that question b is asking for the distribution of $\\ \overline{x}$ , that is, the distribution for the average amount of pollutants.

Answer:

a. The distribution of X is a normal distribution $\\ X \sim N(8.6, 1.3)$ .

b. The distribution for the average amount of pollutants is $\\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})$ .

c. $\\ P(z>-0.08) = 0.5319$ .

d. $\\ P(z>-0.47) = 0.6808$ .

e. We do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for $\\ \overline{X}$ is also normal because the sample was taken from a normal distribution.

f. $\\ IQR = 0.2868$ ppm. $\\ Q1 = 8.4566$ ppm and $\\ Q3 = 8.7434$ ppm.

Step-by-step explanation:

First, we have all this information from the question:

The random variable here, X, is the number of pollutants that are found in waterways near large cities.
This variable is normally distributed, with parameters:
$\\ \mu = 8.6$ ppm.
$\\ \sigma = 1.3$ ppm.
There is a sample of size, $\\ n = 38$ taken from this normal distribution.

a. What is the distribution of X?

The distribution of X is the normal (or Gaussian) distribution. X (uppercase) is the random variable, and follows a normal distribution with $\\ \mu = 8.6$ ppm and $\\ \sigma =1.3$ ppm or $\\ X \sim N(8.6, 1.3)$ .

b. What is the distribution of $\\ \overline{x}$ ?

The distribution for $\\ \overline{x}$ is $\\ N(\mu, \frac{\sigma}{\sqrt{n}})$ , i.e., the distribution for the sampling distribution of the means follows a normal distribution:

$\\ \overline{X} \sim N(8.6, \frac{1.3}{\sqrt{38}})$ .

c. What is the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants?

Notice that the question is asking for the random variable X (and not $\\ \overline{x}$ ). Then, we can use a standardized value or z-score so that we can consult the standard normal table.

$\\ z = \frac{x - \mu}{\sigma}$ [1]

x = 8.5 ppm and the question is about $\\ P(x>8.5)$ =?

Using [1]

$\\ z = \frac{8.5 - 8.6}{1.3}$

$\\ z = \frac{-0.1}{1.3}$

$\\ z = -0.07692 \approx -0.08$ (standard normal table has entries for two decimals places for z).

For $\\ z = -0.08$ , is $\\ P(z$ .

But, we are asked for $\\ P(z>-0.08) \approx P(x>8.5)$ .

$\\ P(z-0.08) = 1$

$\\ P(z>-0.08) = 1 - P(z$

$\\ P(z>-0.08) = 0.5319$

Thus, "the probability that one randomly selected city's waterway will have more than 8.5 ppm pollutants" is $\\ P(z>-0.08) = 0.5319$ .

d. For the 38 cities, find the probability that the average amount of pollutants is more than 8.5 ppm.

Or $\\ P(\overline{x} > 8.5)$ ppm?

This random variable follows a standardized random variable normally distributed, i.e. $\\ Z \sim N(0, 1)$ :

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

$\\ z = \frac{\overline{8.5} - 8.6}{\frac{1.3}{\sqrt{38}}}$

$\\ z = \frac{-0.1}{0.21088}$

$\\ z = \frac{-0.1}{0.21088} \approx -0.47420 \approx -0.47$

$\\ P(z$

Again, we are asked for $\\ P(z>-0.47)$ , then

$\\ P(z>-0.47) = 1 - P(z$

$\\ P(z>-0.47) = 1 - 0.3192$

$\\ P(z>-0.47) = 0.6808$

Then, the probability that the average amount of pollutants is more than 8.5 ppm for the 38 cities is $\\ P(z>-0.47) = 0.6808$ .

e. For part d), is the assumption that the distribution is normal necessary?

For this question, we do not need to assume that the distribution from we take the sample is normal. We already know that the distribution for X is normally distributed. Moreover, the distribution for $\\ \overline{X}$ is also normal because the sample was taken from a normal distribution. Additionally, the sample size is large enough to show a bell-shaped distribution.

f. Find the IQR for the average of 38 cities.

We must find the first quartile (25th percentile), and the third quartile (75th percentile). For $\\ P(z$ , $\\ z \approx -0.68$ , then, using [2]: