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charle [14.2K]
3 years ago
12

Extra points and top BRAINIEST!!Lorie correctly determines that for the triangles below, the statement and the statement both de

scribe the relationship between the two triangles.
Which best describes why both similarity statements are correct?
Each triangle has two congruent angle and .
Each triangle has two similar angles and
The triangles each have two given angle measures and one unknown angle measure.
All statements, regardless of the order of the vertices, define the same triangles.

Mathematics
1 answer:
Allushta [10]3 years ago
3 0

The rest of the question is the attached figure

========================================

solution:

========

As show in the attached figure


∠M = ∠R = 54.4°


∠N = ∠T = 71.2°


∠O = 180° - (∠M + ∠N) = 180° - (54.4°+71.2°) = 54.4°


∠S = 180° - (∠R + ∠T) = 180° - (54.4°+71.2°) = 54.4°


∠O = ∠S = 36°


∴ Δ MNO is similar to Δ RTS


So, the correct statement:


The triangles each have two given angle measures and one unknown angle measure.



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A probability experiment is conducted in which the sample space of the experiment is upper s equals startset 4 comma 5 comma 6 c
olchik [2.2K]
The correct question statement is:

A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in E^{c}. Find P(E^{c}).

Solution:

Part 1:

E^{c} means compliment of the set E. A compliment of a set can be obtained by finding the difference of the set from the universal set. The universal set is the set which contains all the possible outcomes of the events which is S in this case.

So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:

E^{c}=S-E \\  \\ 
E^{c}=(4,5,6,7,8,9,10,11,12,13,14,15)-(7,8,9,10,11,12,13,14,15) \\  \\ 
E^{c}=(4,5,6)

Thus the set compliment of E will contain the elements {4,5,6}.So

E^{c} = {4,5,6}

Part 2)

P(E^{c}) means probability that if we select any number from the Sample Space S, it will belong the set E compliment.

P(E^{c}) = (Number of Elements in E^{c})/Number of elements in S

Number of elements in set S = n(S) = 12
Number of elements in set E^{c} = n(E^{c})=3

So, 

P(E^{c})= \frac{n(E^{c}) }{n(S)} \\  \\ 
P(E^{c})= \frac{3}{12} \\  \\ 
P(E^{c})= \frac{1}{4}
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