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2 years ago

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(x + 7) + (y + 4)2 = 16 Center: Radius:

2 answers:

tigry1 [53]2 years ago

6 0

Answer:

Center: (-7, -4)

radius = 4

Explanation:

Equation: (x + 7)² + (y + 4)² = 16

Circle formula:

(x - h)² + (y - k)² = r²

(h, k) denotes the center of the circle, "r is radius"

Rewrite the following equation in standard form:

(x - (-7))² + (y - (-4))² = 4²

From this identify:

h = -7, k = -4, radius = 4

gladu [14]2 years ago

5 0

General equation

(x-h)²+(y-k)²=r²

So

(x+7)²+(y+4)²=16
(x+7)²+(y+4)²=4²

Center=(-7,-4)

Radius=4

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Please solve the problem with steps

Debora [2.8K]

Answer:

Infinite series equals 4/5

Step-by-step explanation:

Notice that the series can be written as a combination of two geometric series, that can be found independently:

$\frac{3^{n-1}-1}{6^{n-1}} =\frac{3^{n-1}}{6^{n-1}} -\frac{1}{6^{n-1}} =(\frac{1}{2})^{n-1} -\frac{1}{6^{n-1}}$

The first one: $(\frac{1}{2})^{n-1}$ is a geometric sequence of first term ( $a_1$ ) "1" and common ratio (r) " $\frac{1}{2}$ ", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: $Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{2} } =\frac{1}{\frac{1}{2} } =2$

The second one: $\frac{1}{6^{n-1}}$ is a geometric sequence of first term "1", and common ratio (r) " $\frac{1}{6}$ ". Again, since the common ratio is smaller than one, we can find its infinite sum:

$Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{6} } =\frac{1}{\frac{5}{6} } =\frac{6}{5}$

now we simply combine the results making sure we do the indicated difference: Infinite total sum= $2-\frac{6}{5} =\frac{10-6}{5} =\frac{4}{5}$

8 0

3 years ago

Read 2 more answers

Please Help! Multiple Choice!

Katyanochek1 [597]

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis we test if the means are equal, hence:

$H_0: \mu_D - \mu_C = 0$

At the alternative hypothesis, it is tested if they are different, hence:

$H_1: \mu_D - \mu_C \neq 0$

<h3>What are the mean and the standard error for the distribution of differences?</h3>

For each sample, they are given as follows:

$\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086$

$\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556$

Hence, for the distribution of differences, they are given by:

$\overline{x} = 12 - 14 = -2$ .

$s = \sqrt{0.6086^2 + 0.4556^2} = 0.76$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$z = \frac{\overline{x} - \mu}{s}$

$z = \frac{-2 - 0}{0.76}$

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

Hence option B is correct.

More can be learned about the z-distribution at brainly.com/question/13873630

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Step-by-step explanation:

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