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4 years ago

Which of the following is an equation of a circle in

Mathematics

1 answer:

DaniilM [7]4 years ago

7 0

Answer:

$x^2 + (y - 4)^2 = \dfrac{25}{9}$

Step-by-step explanation:

The equation of a circle with center at (h, k) and radius r is

$(x - h)^2 + (y - k)^2 = r^2$

You have center (0, 4).

We get:

$(x - 0)^2 + (y - 4)^2 = r^2$

$x^2 + (y - 4)^2 = r^2$

To find the radius, we use the distance formula to find the distance from the center of the circle to the given point on the circle.

$r = d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$r = \sqrt{(\dfrac{4}{3} - 0)^2 + (5 - 4)^2}$

$r = \sqrt{(\dfrac{4}{3})^2 + 1^2}$

$r = \sqrt{\dfrac{16}{9} + \dfrac{9}{9}}$

$r = \sqrt{\dfrac{25}{9}}$

We need r^2 in the equation of the circle, so

$r^2 = \dfrac{25}{9}$

The equation of the circle is

$x^2 + (y - 4)^2 = \dfrac{25}{9}$

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You wonder if one's age is independent of whether or not one's willingness to wear masks in public. You ask 100 people whether t

antiseptic1488 [7]

Answer:

The statistical conclusion is:

a) Your results are significant; one's willingness to wear masks is not independent of one's age.

Step-by-step explanation:

From this experiment,

The null hypothesis is established as:

H 0 = one's willingness to wear masks is independent of one's age.

The alternate hypothesis is established as:

H 1 = one's willingness to wear masks is not independent of one's age.

In statistics, if the absolute value of the test statistic is greater than the critical value, we declare statistical significance and reject the null hypothesis.

Since the test statistic = 16.5, which is higher than the critical value of 7.82, this establishes statistical significance. Thus, the null hypothesis is rejected.

Therefore, the statistical conclusion is that one's willingness to wear masks is not independent of one's age.

7 0

3 years ago

If a man drives 600km from Johannesburg to Durban. He starts his journey with a full tank of petrol. If the man drives at an ave

arlik [135]

Answer:

I think it's 5

Step-by-step explanation:

im not sure

but correct me if I'm wrong

7 0

2 years ago

Please help and i will brainliestttt

Nutka1998 [239]

Answer:

All you need to do is substitute.

$-3+(-6)^2/ 9$

-3 + 36/9

-3 + 4

= 1

3 0

3 years ago

What is 6x - 9 = 15?

11111nata11111 [884]

Add 9 to both sides and you get 6x=24 then you divide 6 from both sides to get x by its self and the final answer will be 4

6 0

3 years ago

100 POINTS! College Statistics

kirza4 [7]

(a) Collision claims tend to be skewed right because there are a few very large collision claims relative to the majority of claims.

These large collision claims skew the data to the right because they are outliers that draw the mean higher than it should be.

The answer cannot be "no large collision claims" or "many large collision claims" because then the data would not be skewed.

(b) Since there are two random samples comparing two means, we will be using a 2-Samp-T-Test. We will use Welch's approximate t-test, where we test the hypothesis that these two populations have the same mean.

We want to determine if 20-24 year old drivers have the same mean collision cost as 30-59 year old drivers.

(c) The null hypothesis is that the mean claim of collision costs for 20-24 year old drivers is the same as the mean claim of collision costs for 30-59 year old drivers.

We can also rewrite this as:

H₀: μ₁ = μ₂
where μ₁ is the mean collision claims for 20-24 year old drivers
and μ₂ is the mean collision claims for 30-59 year old drivers

The alternative hypothesis is that the mean claim of collision costs for 20-24 year old drivers is higher than the mean claim of collision costs for 30-59 year old drivers.

We can rewrite this as:

H₁: μ₁ > μ₂
Our variables have already been defined

(d) In order to calculate the p-value, we must find the test statistic first.

We can do so by using this formula:

$\displaystyle t=\frac{x_1-x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }}$

We are given these variables in the problem:

$x_1=4590$
$s_1=2302$
$x_2=3670$
$s_2=2029$
$n_1=40$
$n_2=40$

Substitute these variables into the formula for the test statistic.

$\displaystyle t=\frac{4590-3670}{\sqrt{\frac{2302^2}{40} +\frac{2029^2}{40} } }$

You can use the calculator to solve this expression, or plug the numbers into your calculator using: STAT - TESTS - 4:2-SAMPTTEST.

Your test statistic should be: t = 1.8962.

The calculator should also tell you the p-value; p = .0308.

(e) Since p = .0308 < α = .1, reject the null. We have convincing statistical evidence that the mean claim of collision costs for 20-24 year old drivers is higher than the mean claim of collision costs for 30-59 year old drivers.

4 0

2 years ago