List the angles of triangle ABC in order from smallest to largest measure if AB = 9, AC = 11, and BC = 10.

1 answer:

4 0

Across smallest side- smallest angle.
across largest side- largest angle
largest side is AC, so largest angle is B
smallest side is AB, so smallest angle is C
angles from smallest to largest : C, A, B

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Find the measure of the numbered angle.

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The angle adjacent to angle 6 is the one we need to find first. To do this, add the measures of the intercepted arcs and divide by 2. 60 + 50 = 110, and half of that is 55. That means that both adjacent angles to the angle 6 are 55 (vertical angles are congruent). The measure of all the angles added together is 360 and angle 6 is vertical to the other "sideways" angle, so they are congruent as well. 360 - 55 - 55 = 250. Split that up between angle 6 and its vertical angle to get that each of those measure 125. Angle 6 measures 125, choice b from above.

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Answer

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Otrada [13]

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given: Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: $\hat{p}=\dfrac{440}{525}\approx0.838$

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)$

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

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