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3 years ago

(4x + 17) What is the measure of AC ? Enter your answer in the box. (4x – 3.5)

Mathematics

1 answer:

Natasha2012 [34]3 years ago

3 0

Answer: $AC=41\°$

Step-by-step explanation:

<h3> The complete exercise is attached.</h3>

For this exercise it is important to remember that, by definition, if an angle formed by two intersecting chords has its vertex on a circle, this is called an "Inscribed angle".

The following formula is used to calculate the measure of an Inscribed angle:

$Inscribed\ angle = \frac{1}{2}\ Intercepted\ Arc$

You can identify in the figure that:

$Inscribed\ angle=ABC=(4x -3.5)\\\\Intercepted\ Arc=AC=(4x + 17)$

Then you can substitute values into the formula and solve for "x":

$(4x -3.5)= \frac{1}{2}(4x + 17)\\\\8x-7=4x+17\\\\4x=24\\\\x=6$

Then, AC is:

$AC=(4(6)+ 17)\\\\AC=24+17\\\\AC=41\°$

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Size of u.s. states the total surface area (in square miles) for each of six selected eastern states is listed here. 28,995 pa 3

KonstantinChe [14]

<span>Standard deviation of first data set = 5879.1 Standard deviation of second data set = 14768.78 The second data set is more variable. The basic definition of standard deviation is the square root of the mean of the squares of the difference from the mean. It's a bit of a mouthful, but easy enough to do. For the first data set, first calculate the mean. (28995 + 37534 + 31361 + 27087 + 20966 + 37741) / 6 = 30614 Now calculate the square of the differences from the mean (28995 - 30614)^2 = 2621161 (37534 - 30614)^2 = 47886400 (31361 - 30614)^2 = 558009 (27087 - 30614)^2 = 12439729 (20966 - 30614)^2 = 93083904 (37741 - 30614)^2 = 50794129 And now the average of the squares (2621161 + 47886400 + 558009 + 12439729 + 93083904 +50794129) / 6 = 34563888.67 And finally, take the square root to get the standard deviation. sqrt(34563888.67) = 5879.1 Now for the second data set of western states. First, the mean (72964 + 70763 + 101510 + 62161 + 66625 + 54339) / 6 = 71393.67 Now the squares of the differences (72964 - 71393.67)^2 = 2465946.778 (70763 - 71393.67)^2 = 397740.4444 (101510 - 71393.67)^2 = 906993533.4 (62161 - 71393.67)^2 = 85242133.78 (66625 - 71393.67)^2 = 22740181.78 (54339 - 71393.67)^2 = 290861655.1 And the average of the squares is 218116865.2 Finally, the square root of the average is 14768.78 So the standard deviation of the 2nd data set is 14768.78 And since the standard deviation of the 2nd data set is larger than the standard deviation of the 1st data set, that means that the 2nd data set is more variable.</span>

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3 years ago

Plz Help I will give Brainliest Answer.

Anni [7]

the answer is C, because you solve 2.815-749, and after you divide the result per 4, so it is 1/4

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3 years ago

A company wants to find out if the average response time to a request differs across its two servers. Say µ1 is the true mean/ex

lorasvet [3.4K]

Answer:

a) The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

Test statistic t=0.88

The P-value is obtained from a t-table, taking into acount the degrees of freedom (419) and the type of test (two-tailed).

b) A P-value close to 1 means that a sample result have a high probability to be obtained due to chance, given that the null hypothesis is true. It means that there is little evidence in favor of the alternative hypothesis.

c) The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

d) The consequences of the confidence interval containing 0 means that the hypothesis that there is no difference between the response time (d=0) is not a unprobable value for the true difference.

This relate to the previous conclusion as there is not enough evidence to support that there is significant difference between the response time, as the hypothesis that there is no difference is not an unusual value for the true difference.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is significant difference in the time response for the two servers.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

$M_d=M_1-M_2=12.5-12.2=0.3$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{196}+\dfrac{4^2}{225}}\\\\\\s_{M_d}=\sqrt{0.046+0.071}=\sqrt{0.117}=0.342$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.3-0}{0.342}=\dfrac{0.3}{0.342}=0.88$

The degrees of freedom for this test are:

$df=n_1+n_2-1=196+225-2=419$

This test is a two-tailed test, with 419 degrees of freedom and t=0.88, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>0.88)=0.381$

As the P-value (0.381) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.

<u>Confidence interval </u>

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

The estimated standard error of the difference is s_Md=0.342.

The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_{M_d}=1.966 \cdot 0.342=0.672$

Then, the lower and upper bounds of the confidence interval are:

$LL=M_d-t \cdot s_{M_d} = 0.3-0.672=-0.372\\\\UL=M_d+t \cdot s_{M_d} = 0.3+0.672=0.972$

The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

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3 years ago

the value of c guaranteed to exist by the Mean Value Theorem for V(x) = x² in the interval [0, 3] is...? a) 1 b) 2 c) 3/2 d) 1/2

lilavasa [31]

Answer: c) $\dfrac{3}{2}$ .

Step-by-step explanation:

Mean value theorem : If f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

$\begin{displaymath}f'(c) = \frac{f(b) - f(a)}{b-a} \cdot\end{displaymath}$

Given function : $f(x) = x^2$

Interval : [0,3]

Then, by the mean value theorem, there is at least one number c in the interval (0,3) such that

$f'(c)=\dfrac{f(3)-f(0)}{3-0}\\\\=\dfrac{3^2-0^2}{3}=\dfrac{9}{3}\\\\=3$

$\Rightarrow\ f'(c)=3\ \ \ ...(i)$

Since $f'(x)=2x$

then, at x=c, $f'(c)=2c\ \ \ ...(ii)$

From (i) and (ii), we have

$2c=3\\\\\Rightarrow\ c=\dfrac{3}{2}$

Hence, the correct option is c) $\dfrac{3}{2}$ .

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3 years ago

What is y = -3x in standard form?

worty [1.4K]

For Ax+By=C, we have y=-3x. We want both the y and x variable on the same side, and that leads us to either subtract y from both sides or add 3x to both sides. You can do either, but I personally prefer the latter, so we have 3x+y=0. We have A=3 (since that is the coefficient for x) and B=1 (since 1*y=y). Lastly, C=0

Feel free to ask further questions!

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3 years ago