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Vilka [71]
3 years ago
8

Which of the following theorems verifies that ABC~WXY?

Mathematics
1 answer:
Bumek [7]3 years ago
7 0

Answer:

The correct answer is option <em>B. AA</em>

<em></em>

Step-by-step explanation:

Given two triangle:

\triangle ABC  and \triangle WXY.

The dimensions given in \triangle ABC are:

\angle A = 27^\circ\\\angle B = 90^\circ

We know that the sum of three angles in a triangle is equal to 180^\circ.

\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow 27+90+\angle C=180^\circ\\\Rightarrow \angle C = 63^\circ

The dimensions given in \triangle WXY are:

\angle Y = 63^\circ\\\angle X = 90^\circ

We know that the sum of three angles in a triangle is equal to 180^\circ.

\angle W+\angle X+\angle Y = 180^\circ\\\Rightarrow \angle W+90+63=180^\circ\\\Rightarrow \angle W = 27^\circ

Now, if we compare the angles of the two triangles:

\angle A = \angle W = 27^\circ\\\angle B = \angle X= 90^\circ\\\angle C = \angle Y= 63^\circ

So, by AA postulate (i.e. Angle - Angle) postulate, the two triangles are similar.

\triangle ABC \sim \triangle WXY by <em>AA theorem.</em>

<em>So, correct answer is option B. AA </em>

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There are 21 students in a class. The median age of the students is 23. The oldest student is 29.
Varvara68 [4.7K]

Answer:

1) At least one (the 11th) student is 23 (years old), <u>Must be true</u>

2) Some students are younger than 15 <u>Could be true</u>

Step-by-step explanation:

1) The given parameters are;

The number of student in the class = 21

The median age of the student = 23

The age of the oldest student = 29

Therefore, given that the median age = The age of the (n + 1)/2 th student

Where;

n = The number of student in the class = 21

∴ The median age = The age of the (21 + 1)/2 th = 11 th student, when the age of the students are arranged in increasing order, therefore, we have;

At least one (the 11th) student is 23 (years old), <u>Must be true</u>

2) Given that there are 10 students with ages equal to or lower than the  median age, and the difference between the median age and the age of the oldest student = 29 - 23 = 6 years, we have;

Some students are younger than 15 <u>Could be true</u>

5 0
3 years ago
Tell how you rename fractions greater than 1 as mixed numbers as fractions greater than 1.
alex41 [277]
For example...
 if you have a mixed fraction 1 1/2, and change it to fraction greater than one, it would be  3/2  (which is 1 or 2/2 + 1/2)
8 0
3 years ago
Identify the sampling designs that use convenience sampling. Check all that apply.
vazorg [7]

Answer:

1,2,5

Step-by-step explanation:

I did the assignment

8 0
3 years ago
In a certain town in the united states, 40% of the population are democrats and 60% are republicans. The municipal government ha
mixer [17]

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

4 0
3 years ago
If g(x) is the inverse of f(x)=4x+12 and f(x)=, what is g(x)
Nitella [24]
Hello,
f(x)=y=4x+12

x=4y+12
==>4y=x-12
==>y=x/12- 3

g(x)=x/12 -3


6 0
3 years ago
Read 2 more answers
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