What is the radius of a circle whose equation is x2 + (y – 8)2 = 25?

1 answer:

6 0

The formula for a circle is (x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center and r is the radius.
x^2 + (y - 8)^2 = 25
25 = r^2
So the radius is sqrt 25 or 5.
Radius = 5

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Need help asap pleas and thank you .

Arisa [49]

Answer:

The answer that is <em>not </em>true when x = -4 is <u>B</u>.

Step-by-step explanation:

Since x = -4, that means all we have to do to eliminate answers is plug -4 in place of x.

A is incorrect because 2 × -4 = -8, which means that answer IS true and we're looking for the one that isn't true.

Same with C, -4 + -4 + -4 added together gives you -12 = -12, therefore isn't the right choice.

Finally D. -4/4 divided equals -1, so that would make it -1 = -1.

B is the only one that doesn't make sense, therefore you have your answer.

4 0

3 years ago

Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle

nirvana33 [79]

Answer:

i) $ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And replacing we got:

$ME= 1.96*\sqrt{\frac{0.8 (1-0.8)}{400}} =0.0392$

ii) $Lower = 0.8-0.0392= 0.7608$

$Upper = 0.8 +0.0392= 0.8392$

Step-by-step explanation:

Notation and definitions

$X=320$ number of people that claimed always buckle up.

$n=400$ random sample taken

$\hat p=\frac{320}{400}=0.8$ estimated proportion of people that claimed always buckle up

$p$ true population proportion of people that claimed always buckle up

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

Part i

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: