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3 years ago

A sector has an area of 1/2 π and the central angles of 1/9 π radians. What is the area of the circle?

Mathematics

1 answer:

zhenek [66]3 years ago

6 0

Answer:

Area of circle is 9π

Step-by-step explanation:

The area of sector of a circle is given by $A=\frac{1}{2}r^2\theta$

Plugging the given values in the formula, we get

$\frac{1}{2}\pi=\frac{1}{2}r^2\cdot\frac{1}{9}\pi$

Cancel out 1/2 and π from both sides, we are left with

$1=r^2\cdot\frac{1}{9}$

Cross multiplying, we get

$r^2=9\\\\r=3$

Therefore, area of circle is given by

$A=\pi r^2\\\\A=\pi(3)^2\\\\A=9\pi$

Area of circle is 9π

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Find the volume of the rectangular prism. 19 cm 9 cm 2 cm

Makovka662 [10]

Answer: 342 cm³

Step-by-step explanation: To find the volume of the rectangular prism, start with the formula for the volume or a prism.

Volume = length × width × height

Since we are not sure what the length, width, or height is in this problem, we can plug any of these numbers in for the length, width, or height. The commutative property of multiplication states that changing the order of the factors does not change the product.

Volume = (19 cm) (9 cm) (2 cm)

Volume = 342 cm³

Therefore, the volume of the rectangular prism is 342 cm³.

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3 years ago

Find the derivative of cscx/3sinx

Neporo4naja [7]

$\frac{csc x}{3sinx} = \frac{1}{3sin ^{2}x }$

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3 years ago

What is (4c)^2d ? c = 5 and d = 8

Arte-miy333 [17]

Answer:

3200

Step-by-step explanation:

Replace the variables with their values and do the arithmetic.

(4·5)²·8 = 20²·8 = 400·8 = 3200

6 0

3 years ago

Assume that the paired data came from a population that is normally distributed. using a 0.05 significance level and dequalsxmin

Artemon [7]

"Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find $\bar{d}$ , $s_{d}$ , the t-test statistic, and the critical values to test the claim that $\mu_{d} = 0$ "

You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.

For the example, please refer to the attached picture.

A) Find $\bar{d}$
You are asked to find the mean difference between the two variables, which is given by the formula:
$\bar{d} = \frac{\sum (x - y)}{n}$

These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)

In our example:
 $\bar{d} = \frac{6}{8} = 0.75$ 

B) Find $s_{d}$
You are asked to find the standard deviation, which is given by the formula:
 $s_{d} = \sqrt{ \frac{\sum(d - \bar{d}) }{n-1} }$

These are the steps to follow:
1) Subtract the mean difference from each pair's difference
2) square the differences found
3) sum the squares
4) divide by the degree of freedom DF = n - 1

In our example:
$s_{d} = \sqrt{ \frac{101.5}{8-1} }$
= √14.5
= 3.81

C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
$t = \frac{(\bar{x} - \bar{y}) - \mu_{d} }{SE}$

where SE = standard error is given by the formula:
$SE = \frac{ s_{d} }{ \sqrt{n} }$

These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
2) calculate the mean value of x (sum all the values of x and then divide by the number of pairs)
3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
4) subtract the mean y value from the mean x value
5) from this difference, subtract $\mu_{d}$
6) divide by the standard error

In our example:
SE = 3.81 / √8
= 1.346

The problem gives us $\mu_{d} = 0$ , therefore:
t = [(9.75 - 9) - 0] / 1.346
= 0.56

D) Find $t_{\alpha / 2}$
You are asked to find what is the t-value for a 0.05 significance level.

In order to do so, you need to look at a t-table distribution for DF = 7 and A = 0.05 (see second picture attached).

We find $t_{\alpha / 2} = 1.895$ 

Since our t-value is less than $t_{\alpha / 2}$ we can reject our null hypothesis!!

7 0

3 years ago

Please be kind enough to help me with this question in my geometry test thank you i’m very grateful

WARRIOR [948]

Answer:

yes

Step-by-step explanation:

5 0

3 years ago