All categories

2 years ago

Write the standard equation for the circle

Mathematics

1 answer:

saw5 [17]2 years ago

3 0

Answer:

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

Step-by-step explanation:

You might be interested in

1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several ti

uysha [10]

Answer:

1) $0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

b) $ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

Step-by-step explanation:

Information given

0.082601, 0.082621, 0.082589, 0.082617, 0.082598

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=0.0826052$ represent the sample mean

$\mu$ population mean

s=0.000013424 represent the sample standard deviation

n=5 represent the sample size

Part 1

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom, given by:

$df=n-1=5-1=4$

The Confidence level is 0.95 or 95%, and the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ , the critical value would be using the t distribution with 4 degrees of freedom: $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

Part 2

The original margin of error is given by:

$ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

3 0

3 years ago

The perimeter of a rectangle is 54 meters. One side is three meters less than four times the length of the other side. Find the

Elenna [48]

Answer:

6 and 21 meters long

Step-by-step explanation:

You make an equation from what you got (there are 2 widths and 2 lengths)

2(4w-3)+2w=54---->10w-6=54---> 10w=60 ----> w=6 ---> plug in the rest and you get 21 as the length.

or... make W+L=28 and guess and check!!! takes longer but works!

7 0

3 years ago

which of the following group of numbers are all prime numbers a.2,5,15,19 b.7,17,29,49 c.3,11,23,31 d.2,3,5,9,

antoniya [11.8K]

Prime numbers are those that cannot be divided by another number (other than themselves and 1). In other words, prime numbers have factors of themselves and 1.

For example, 3 is a prime number because its only factors are 3 and 1.

6 is not a prime number because it can be factored to 3*2.

Therefore, the correct answer is c. 3,11,23,31

6 0

3 years ago

Read 2 more answers

In how many ways can the letters in the word MATHEMATICS be reshuffled so that all consonants appear together?

steposvetlana [31]

Answer:

75600

Step-by-step explanation:

We are given that a word MATHEMATICS

Total letters =11

M repeated 2 times

T repeated 2 times

A repeated 2 times

Total vowels=4

Let MTHMTCS=P

Total number of ways in which MTHMTCS can be arranged= $\frac{7!}{2!2!}$

PAEAI

Total number of ways in which PAEAI can arranged= $\frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!}{2!2!}\times \frac{5!}{2!}$

Total number of arrangements when all consonant appear together= $\frac{7!5!}{2\times 2\times 2}=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1}{8}=75600$

By using formula ; $n!=n(n-1)(n-2)...2\times 1$

4 0

3 years ago

What’s the whole number preceding a whole number 2x?

Phantasy [73]

Answer:

2x -1

Step-by-step explanation:

the whole number preceding a whole number 2x = 2x-1

5 0

3 years ago