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Zepler [3.9K]
3 years ago
15

The figure shows a circle with center P and inscribed isosceles Triangle ABC. If AC has the same length as the radius of the cir

cle, what is the measure of angle ABC

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
7 0

Answer:

<ABC = 30^{0} (The central angle of a circle is twice any inscribed angle subtended by the same arc).

Step-by-step explanation:

From the diagram, ABC is an inscribed isosceles triangle. But the radius of the circle equals the length AC.

Join P to A and C to form an equilateral triangle. An equilateral triangle has equal sides and angles. So, the value of each interior angle of the equilateral triangle is;

Sum of angle in a triangle = 180^{0}

So that each interior angle = \frac{180^{0} }{3}

                                            = 60^{0}

The value of each interior angle of the triangle is 60^{0}. Thus, <APC = 60^{0}.

⇒ <ABC = 30^{0} (The central angle of a circle is twice any inscribed angle subtended by the same arc.)

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Step-by-step explanation:

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Step-by-step explanation:

https://www.khanacademy.org/math/cc-fourth-grade-math/plane-figures/imp-classifying-triangles/v/scalene-isosceles-equilateral-acute-right-obtuse#:~:text=Learn%20to%20categorize%20triangles%20as,acute%2C%20right%2C%20or%20obtuse.

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3 years ago
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Answer:

Modification has not reduced the number of accidents.

Step-by-step explanation:

H_0: \mu\geq0\\H_a:\mu

                                 A  B  C   D   E   F  G   H

Before modification 5  7  6   4    8   9   8   10

After modification    3  7  7   0    4   6   8    2

Difference                -2 0  1   -4   -4   -3  0   -8

Mean of differences M_d = \frac{sum}{8}=\frac{2+0-1+4+4+3-0+8}{8}=2.5

Standard deviation of differences = \sqrt{\frac{\sum(x-\bar{x})^2}{n}}=2.9277

Formula of paired t test :

t=\frac{M_d}{\frac{s}{\sqrt{n}}}\\t=\frac{2.5}{\frac{2.9277}{\sqrt{8}}}\\t = 2.4152

Df = n-1 = 8-1 =7

t critical = t_{(df, \alpha)}=t_{7,0.01}=2.998

t critical> t calculated

So, We failed to reject null hypothesis

Hence modification has not reduced the number of accidents.

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