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3 years ago

PLEASE HELP

Mathematics

1 answer:

Anna007 [38]3 years ago

7 0

Answer:

Step-by-step explanation:

The triangle is an isosceles triangle (2 sides same).

The sides BC and AC are radius of the circles, so these 2 sides are congruent. So, the opposite angles are equal as well. Since one angle is given as 20, the other angle is also 20.

So, we have the three angles of the triangle as:

20, x, and 20

We know, sum of 3 angles of a triangle is 180, thus we can write:

20 + x + 20 = 180

Now, we solve for x:

20 + x + 20 = 180

40 + x = 180

x = 180 - 40

x = 140

Correct answer is D

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3 years ago

Convert from rectangular to polar coordinates: note: choose rr and θθ such that rr is nonnegative and 0≤θ<2π0≤θ<2π (a)(9,0

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Answer:

Step-by-step explanation:

Convert rectangle (x , y) to polar coordinates ( r , θ)

$x=r \cos \theta, y= r \sin \theta$

$r=\sqrt{x^2+y^2} , \theta =tan^-^1 (\frac{y}{x} )$

a) converts (9, 0) to polar coordinates ( r , θ)

$r=\sqrt{x^2+y^2} \\\\=\sqrt{9^2+0} \\\\=9$

$\theta= \tan^-^1 (\frac{0}{9} )\\\\=0$

b) Convert $(18,\frac{18}{\sqrt{3} } )$ to polar coordinates ( r, θ)

$r = \sqrt{18^2+(\frac{18}{\sqrt{3} })^2 } \\\\=\sqrt{324+108} \\\\=\sqrt{432}$

$\frac{x}{y} \theta = \tan^-^1(\frac{\frac{18}{\sqrt{3} } }{18} )\\\\= \tan ^-^1(\frac{1}{\sqrt{3} } )\\\\= \frac{\pi}{6}$

c) converts (-5, 5) to polar coordinates ( r , θ)

$r =\sqrt{(-5)^2+(5)^2} \\\\=\sqrt{50} \\\\=5\sqrt{2}$

$\theta=\tan^-^1(\frac{5}{-5} )\\\\= \tan^-^1(-1)\\\\=\frac{3\pi}{4}$

d) converts (-1, √3) to polar coordinates ( r , θ)

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

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3 years ago

Evaluate how organizations can use one-sample hypothesis testing to determine if there are performance issues in the organizatio

Margarita [4]

Answer:

Organizations can use one-sample hypothesis test to determine if there are performance issues in many ways.

It can be applied to the performance of a sector, a machine, a product, an advertising campaing, etc.

For example, we can take the example of a machine. It may be claimed that a specific machine performs significantly worse than the average.

This average would be the population mean: the average performance of the machines of the same type or process.

Then, a sample of the performance of the machine in study is taken and the hypothesis test can be performed to test the claim that this machine performs significantly worse.

Step-by-step explanation:

For example, we have an historic performance for this type of machine of 100 units a day. The machine A in study is sampled 14 days and have a performance of 92 units a day, with a sample standard deviation of 12 units/day. We have to test the claim that the machine A makes less units per day than the average.

Then, the null and alternative hypothesis are:

$H_0: \mu=100\\\\H_a:\mu< 100$

The significance level is 0.05.

The sample has a size n=14.

The sample mean is M=92.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{14}}=3.2071$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{92-100}{3.2071}=\dfrac{-8}{3.2071}=-2.4944$

The degrees of freedom for this sample size are:

$df=n-1=14-1=13$

This test is a left-tailed test, with 13 degrees of freedom and t=-2.4944, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.0134) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that machine A produces significantly less units per day than the average.

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3 years ago

Consider the statement : Congruent triangles are always similar. Which of the following statements is an example of the statemen

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Answer:

Yes, the congruent triangles are always similar. The following statements are applicable

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2) Sides are the same size.

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Step-by-step explanation:

Yes, they are similar.

For two triangles to be similar, it is sufficient if two angles of one triangle are equal to two angles of the other triangle. Note that if two angles of one are equal to two angles of the other triangle, the third angles of the two triangles too will be equal.

If two triangles are congruent then all corresponding sides as well as corresponding angles of one triangle are equal to those of other triangles. This can happen in four cases

1)- when all sides of triangles are equal,

2) - if one side and two angles of one are equal to one side and two angles of other triangle.

3) - if two sides and included angle of one triangle are equal to two sides and included angle of other triangle

4)- if in two right angled triangles, one side and hypotenuse of one triangle are equal to one side and hypotenuse of other triangle.

Observe that for triangles to be similar, we just need all angles to be equal. But for triangles to be congruent, angles as well as sides should be equal.

Hence, while congruent triangles are similar, similar triangles may not be congruent ( but the converse is not true) .

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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