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2 years ago

Assume the radius of a circle is

Mathematics

1 answer:

Lisa [10]2 years ago

7 0

Answer:

Step-by-step explanation:

They want you to see how radius is important. Just remember that one radian is one radius, that should help you see why radius is important.

They ask for the unit circle , that is a circle of one unit for the radius, which makes it super easy to calculate things for it, they ask what is the area, which is that famous formula, π $r^{2}$ , then they ask what's its circumference. which is that other famous formula 2πr

so to go all the way around a circle of one unit radius, it's 2π exactly or about 6.28..... units, call it meters, or feet or inches, it doesn't mater here.

the size of the circle doesn't matter here either, b/c we are using the radius , that relaationship doesn't change , all circles, what ever size , have this same relationship between the radius and radians. :P this is handy.

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Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.a. If the distri

zalisa [80]

Answer:

$P(\= X \ge 51 ) =0.0062$

$P(\= X \ge 51 ) = 0$

Step-by-step explanation:

From the question we are told that

The mean value is $\mu = 50$

The standard deviation is $\sigma = 1.2$

Considering question a

The sample size is n = 9

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{9} }$

=> $\sigma_x = 0.4$

Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_{x}} \ge \frac{51 - 50 }{0.4 } )$

$\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )$

$P(\= X \ge 51 ) = P( Z \ge 2.5 )$

=> $P(\= X \ge 51 ) =1- P( Z < 2.5 )$

From the z table the area under the normal curve to the left corresponding to 2.5 is

$P( Z < 2.5 ) = 0.99379$

=> $P(\= X \ge 51 ) =1-0.99379$

=> $P(\= X \ge 51 ) =0.0062$

Considering question b

The sample size is n = 40

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{40} }$

=> $\sigma_x = 0.1897$

Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_x} \ge \frac{51 - 50 }{0.1897 } )$

=> $P(\= X \ge 51 ) = P(Z \ge 5.2715 )$

=> $P(\= X \ge 51 ) = 1- P(Z < 5.2715 )$

From the z table the area under the normal curve to the left corresponding to 5.2715 and

=> $P(Z < 5.2715 ) = 1$

$P(\= X \ge 51 ) = 1- 1$

=> $P(\= X \ge 51 ) = 0$

5 0

3 years ago

0.2x + (-0.9) + 1.7 = 9.6<br> 0.2x + 0.8 = 9.6

user100 [1]

Answer:44

Step-by-step explanation:

0.2x+(-0.9)+1.7==9.6

0.2x+0.8=9.6

Subtract 0.8 from both sides

0.2x+0.8-0.8=9.6-0.8

0.2x=8.8

Divide both sides by 0.2

0.2x ➗ 0.2=8.8 ➗ 0.2

x=44

6 0

3 years ago

Lorico [155]

Answer:

I just found it out, 200 Student tickets were sold.

8 0

3 years ago

What is the value of x?

vredina [299]

Add all the angle and =to 180 because all the angle in a triangle add up to 180 then put all numbers on one side and all x terms on the other side then you find x

8 0

3 years ago

What is the greatest common factor of 96 and 72

Marianna [84]

First, do the prime factorization.

96 = 2 x 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

The GCF is the product of their shared factors.

They share 2, 2, 2, and 3.

2 x 2 x 2 x 3 = 24.

Their GCF is 24.

8 0

3 years ago