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3 years ago

What is proving triangles congruent by ASA and AAS

1 answer:

6 0

So ASA is angle side angle, and that means that if you prove that the side, and the side adjacent to that side and the angle between those two sides are all congruent to another triangle's sides and angle, the triangles are both congruent.
The AAS is angle angle side, or something, so say you have a triangle and you prove that two of its angles are congruent along with a side to another triangle's, then it's AAS. I understand where the confusion might be. I guess it's just a matter of what you state first in your proof?

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A sample of 47 observations is selected from a normal population. The sample mean is 30, and the population standard deviation i

erma4kov [3.2K]

Answer:

We accept the null hypothesis and reject the alternate hypothesis. There is no evidence to conclude that the population mean is greater than 29. The population mean is less than or equal to 29.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 29

Sample mean, $\bar{x}$ = 30

Sample size, n = 47

Alpha, α = 0.05

Population standard deviation, σ = 5

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 29\\H_A: \mu > 29$

a) This is a one-tailed test because the alternate hypothesis is in greater than direction.

We use One-tailed z test to perform this hypothesis.

b) $z_{stat} > z_{critical}$ , we reject the null hypothesis and accept the alternate hypothesis and if $z_{stat} < z_{critical}$ , we accept the null hypothesis and reject the alternate hypothesis.

c) Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{30 - 29}{\frac{5}{\sqrt{47}} } = 1.37$

d) Now, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

Since,

$z_{stat} < z_{critical}$

We accept the null hypothesis and reject the alternate hypothesis. There is no evidence to conclude that the population mean is greater than 29. The population mean is less than or equal to 29.

e) P-value is 0.0853

On the basis of p value we again accept the null hypothesis.

5 0

3 years ago

A:Write (⅔)² in expanded form,<br> B. And then evaluate.

KatRina [158]

Answer:

4/9

Step-by-step explanation:

(2/3)^2

(2/3) x (2/3)

2 x 2 is 4

3 x 3 is 9

4/9

4 0

2 years ago

Find the missing side and round to the nearest tenth

xxMikexx [17]

In this problem you use cosine because you know the hypotenuse and you want to know the adjacent side of the triangle. So in your calculator you would input cos(52). Then you would multiply that answer with the hypotenuse side. So your equation would be this: cos(52) x 13

5 0

3 years ago

Simplify fractions 25 z to 2nd power over 150 z to 3rd power

Darina [25.2K]

Answer:

1/6z.

Step-by-step explanation:

25z^2 / 150z^3

25 divides 6 times into 150 and z^3 / z^2 = z

so the answer is 1/6z.

6 0

2 years ago

Un<br> How many solutions does this system have?<br> 12x-4y=-8<br> y=3x+2

Talja [164]

Answer:

Infinite

Step-by-step explanation:

Get both in the form y = first.

12x - 4y = -8

-4y = -8 - 12x

y = 2 + 3x

y = 3x + 2

These are the same line so all points are the same so that means there are infinite answers.

If ONLY the number in front of the x was the same there would be 0 answers, they would be parallel lines, and if the number in front of the xs were different there would only be one answer.

3 0

2 years ago