All categories

2 years ago

How did the π invented?

Mathematics

1 answer:

Sloan [31]2 years ago

3 0

Answer:

The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.

You might be interested in

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }$ , $5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }$ ]

= [5.10 , 5.20]

Therefore, 95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0

3 years ago

Find the median. 90, 88, 100, 82, 80. PLEASE

Ludmilka [50]

Answer:

Step-by-step explanation:

80, 82, 88, 90, 100

Now cross out the numbers starting with 80 and 100 and keep going till you get the middle number which would be 88

5 0

3 years ago

Read 2 more answers

What is the equation for the line of reflection that maps the trapezoid onto itself?

kvv77 [185]

The line that maps a figure onto itself is a line of symmetry of the figure.

From the given trapezoid, the line of symmetry of the trapezoid is x = -2.

Therefore, the equation for the line of reflection that maps the trapezoid onto itself is x = -2.

6 0

3 years ago

Read 2 more answers

A set of numbers is shown below: {0, 0.4, 1, 2, 3} Which of the following shows all the numbers from the set that make the inequ

klemol [59]

Answer:

{1,2,3}

Step-by-step explanation:

The others will not show all the numbers from the set to make the inequality true

8 0

3 years ago

Isla was researching kiwi birds. She categorized each bird she observed by species and gender. The two-way frequency table below