BRAINLIEST, THANKS AND 5 STARS IF ANSWERED CORRECTLY.
2 answers:
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Answer:
BD = <u>1</u> unit
AD = <u>1</u> unit
AB = <u>1.6</u> units
AC = <u>1.6</u> units
Step-by-step explanation:
In the picture attached, the triangle ABC is shown.
Given that triangle ABC is isosceles, then ∠B = ∠C
∠A + ∠B + ∠C = 180°
36° + 2∠B = 180°
∠B = (180° - 36°)/2
∠B = ∠C = 72°
From Law of Sines:
sin(∠A)/BC = sin(∠B)/AC = sin(∠C)/AB
(Remember that BC is 1 unit long)
AB = AC = sin(72°)/sin(36°) = 1.6
In triangle ABD, ∠B = 72°/2 = 36°, then:
∠A + ∠B + ∠D = 180°
36° + 36° + ∠D = 180°
∠D = 180° - 36° - 36° = 108°
From Law of Sines:
sin(∠A)/BD = sin(∠B)/AD = sin(∠D)/AB
(now ∠A = ∠B)
BD = AD = sin(∠A)*AB/sin(∠D)
BD = AD = sin(36°)*1.6/sin(108°) = 1
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:
At the alternative hypothesis, it is tested if they are different, hence:
For each sample, they are given as follows:
Hence, for the distribution of differences, they are given by:
.
The test statistic is given by:
In which is the value tested at the null hypothesis.
Hence:
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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