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3 years ago

What is the standard form of the equation of the circle in the graph?

Mathematics

2 answers:

Dahasolnce [82]3 years ago

8 0

Answer:

$(x-1)^2+(y-2)^2=16$

Step-by-step explanation:

The standard form of a circle is given by

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

Here, (h,k) is the center and r is the radius.

From the given graph,

center = (1,2)

thus, h = 1, k = 2

The distance from the center to any point on the circle is the radius.

Hence, radius is 4 units. r = 4

Substituting the values of h, k and r in the equation of circle

$(x-1)^2+(y-2)^2=4^2\\\\(x-1)^2+(y-2)^2=16$

dezoksy [38]3 years ago

7 0

Example 3: 2x2 + 2y2 = 8. (a) Find the center and radius of the circle. (b) Graph the circle.First divide the equation by 2. The new equation is :x2 + y2 = 4 .The standard form:(x - h)2 + (y - k)2 = r2(x - 0)2 + (y - 0)2 = (2)2. Now, you can identify the center correctly.

You might be interested in

Q(x)=12x−3; q(x)=−4 What is the value of x.

Contact [7]

Answer:

12x=-1

Step-by-step explanation:

if q(x)=4, plug -4 because that equals -4.

-4=12x-3

add -3 to each side

-1=12x

7 0

3 years ago

In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from

Maksim231197 [3]

Answer:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

Step-by-step explanation:

1) Data given and notation

n=420095 represent the random sample taken

X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$\hat p=\frac{135}{420095}=0.0003214$ estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$p_o=0.00034$ is the value that we want to test

$\alpha=0.005$ represent the significance level

Confidence=99.5% or 0.995

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :

Null hypothesis: $p=0.00034$

Alternative hypothesis: $p \neq 0.00034$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.005$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

4 0

3 years ago

Find sum 3.24 +.07 =

BartSMP [9]

Answer:

3.94

Step-by-step explanation:

5 0

3 years ago