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iragen [17]
3 years ago
15

∆ABC is rotated 100° counterclockwise about point P to create ∆A'B'C'. what is angle m C'A'B'?

Mathematics
2 answers:
dolphi86 [110]3 years ago
7 0
The answer would be c, 70

Kobotan [32]3 years ago
4 0

Answer:

Option C.

Step-by-step explanation:

A triangle ABC is rotated counterclockwise (about a point P) by an angle = 100° to create a new triangle A'B'C'.

After rotation points A,B and C will overlap A', B' and C' respectively but angles A, B and C of triangle ABC will remain unchanged.

Therefore, ∠C'A'B' ≅ ∠CAB ≅ 70°

Option C will be the answer.

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3 years ago
P(B)=1320,P(A∩B)=1325,P(A|B)=?
Dafna1 [17]
Formula for the Conditional Probability is:
P ( A \ B ) = P ( A ∩ B ) / P ( B )
But it is not possible to have the probability greater than 1.
0 ≤ P ( n ) ≤ 1 
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3 0
3 years ago
Please answer the image below
nikklg [1K]

Answer:

<h2>301.593</h2><h2 />

Step-by-step explanation:

surface area = 2πrh + 2πr²

where r = 4 km radius

           h = 8 km

<u>plugin values into the formula</u>

surface area = 2πrh + 2πr²

                     = 2π (4) 8  +  2π (4)²

                     = 201.062  +  100.531

                     = 301.593 km²

7 0
2 years ago
A business school has a goal that the average number of years of work experience of its MBA applicants is more than three years.
gizmo_the_mogwai [7]

Answer:

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

p_v =P(z>0.280)=0.390  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=3.1 represent the sample mean

\sigma=\sqrt{6} represent the sample standard deviation for the sample

n=47 sample size  

\mu_o =3 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3  

Alternative hypothesis:\mu > 3  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

P-value

Since is a one side test the p value would be:  

p_v =P(z>0.280)=0.390  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

3 0
3 years ago
*In ∆ABC, on the extension of the side BC , draw a line segment CD ≅ CA . Draw the segment AD . The line segment CE is the angle
Leya [2.2K]

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Step-by-step explanation:

In ∆ABC

  • On the extension of the side BC , draw a line segment CD ≅ CA
  • Draw the segment AD
  • The line segment CE is the angle bisector of ∠ACB
  • The line segment CF is the median towards AD in ∆ ACD

We want to prove that CF ⊥ CE

Look to the attached figure

In Δ ABC

∵ CE is the bisector of angle ACB

∴ ∠ACE ≅ ∠BCE

In Δ ACD

∵ CA = CD

∴ Δ ACD is an isosceles triangle

∵ AD is the median towards AD

- In any isosceles triangle the median from a vertex to its opposite

  side bisects this vertex

∴ AD bisects ∠ACD

∴ ∠ACF ≅ ∠DCF

∵ BCD is a straight segment

∵ CE , CA , CF are drawn from point C

∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°

∵ m∠ACE ≅ m∠BCE

∵ m∠ACF ≅ m∠DCF

- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF

∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°

∴ 2 m∠ACE + 2 m∠ACF = 180°

- Divide all terms by 2

∴ m∠ACE + m∠ACF = 90°

∴ EC ⊥ CF

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Learn more:

You can learn more about perpendicular lines in brainly.com/question/11223427

#LearnwithBrainly

7 0
3 years ago
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