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3 years ago

A circle has a diameter of 10 cm. What is the best approximation of its area? Use 3.14 to approximate for π .

Mathematics

2 answers:

Tasya [4]3 years ago

6 0

Diameter = 10cm
radius =10/2 = 5 cm

Area = πr² = 3.14 * 5² = 78.5cm²

stich3 [128]3 years ago

6 0

Answer: 78.5 is your answer have a good one

Can I get brainliest pls

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Y=x²-6x+8 what is y when x is 0?

jarptica [38.1K]

Answer:

The value of y is 8.

Step-by-step explanation:

In order to find the value of y, you have to put in x = 0 into the equation :

$y = {x}^{2} - 6x + 8$

Let x = 0,

$y = {0}^{2} - 6(0) + 8$

$y = 8$

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3 years ago

What is the difference between a ray and line segment line segment is a part of a line bound by multiple points along the line;

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A line segment is a part of a line bound by two points; a ray is a line with one endpoint that extends to infinity in one direction. is the difference between a ray and line segment.

Option: C.

Step-by-step explanation:

A line is a set of multiple points that extends from one point to its opposite direction without any end. Ray and Line segments are the two parts that can occur in a line.

A ray is a line with an endpoint in which the line can be extended from that point to infinity in a direction. A line segment also another part line and it consists of two points. Moreover, The line is bounded between those points.

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3 years ago

Ethan was feeling adventurous at lunch. Rather than choosing a single drink, he decided to mix together all the drink choices. H

jarptica [38.1K]

Answer:

1.7

Step-by-step explanation:

I divided 7 by 12 to get 1.7. Each soda gets at least 1 ounce.

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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]:

$\\ -0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}$

$\\ (-0.68 *0.21088) + 8.6 = \overline{X}$

$\\ \overline{x} =8.4566$

$\\ Q1 = 8.4566$ ppm.

For Q3

$\\ 0.68 = \frac{\overline{X} - 8.6}{\frac{1.3}{\sqrt{38}}}$

$\\ (0.68 *0.21088) + 8.6 = \overline{X}$

$\\ \overline{x} =8.7434$

$\\ Q3 = 8.7434$ ppm.

$\\ IQR = Q3-Q1 = 8.7434 - 8.4566 = 0.2868$ ppm

Therefore, the IQR for the average of 38 cities is $\\ IQR = 0.2868$ ppm. $\\ Q1 = 8.4566$ ppm and $\\ Q3 = 8.7434$ ppm.

4 0

2 years ago

Find the area of the triangle with A =42 degrees, b = 8 feet, and c = 5 feet. Round to the nearest tenth.

emmasim [6.3K]

We will use the formula:
Area = 1/2*a*c*sinB

where a and c are the length of the sides and B is the angle between those 2 sides

Area = 1/2*5*8*sin42
Area = 20*sin42
sin 42 = 0.669130606359
Area = 13.38261212718

Rounded to the nearest tenth Area is equal to 13.4

5 0

2 years ago

Read 2 more answers