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zhannawk [14.2K]
3 years ago
15

Match the following reasons with the statements in the given proof. Prove that if two angles are complementary to the same angle

then they are equal in measure. 1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.
a) Substitution
2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90
b) Definition of complementary
3. m∠1 + m∠2 = m∠3 + m∠2
c) Subtraction property of equality
4. m∠1 = m∠3
d) Given
Mathematics
2 answers:
yulyashka [42]3 years ago
4 0

1. --> d

2. --> b

3. --> a

4. --> c

1 is d because that is the only piece of information that sounds like a given.

2 is b because we know that from the given, m∠1 is complementary to m∠2 and in the first problem, m∠1 + m∠2 = 90, they are added together. The definition of complementary angles is "Two angles with measures that, when added together, equal 90 degrees". Same thing with m∠3 and m∠2.

3 is a because since both of the problems equal 90 degrees, you can just take away the 90 and put an equal sign in between the two problems because they equal the same thing.

4 is c because you are subtracting m∠2 from the problems and ending up with just m∠1 = m∠3.

Hope this helps! :)

Elza [17]3 years ago
4 0

Answer:

1.   ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2.-->Given(A)

2.   m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90-->Definition of complementary(D)

3.   m∠1 + m∠2 = m∠3 + m∠2-->Substitution(C)

4.   m∠1 = m∠3-->Subtraction property of equality(B)

Step-by-step explanation:


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The University of Washington claims that it graduates 85% of its basketball players. An NCAA investigation about the graduation
Nonamiya [84]

Probabilities are used to determine the chances of events

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<h3>(a) What is the probability that 11 out of the 20 would graduate? </h3>

Using the binomial probability formula, we have:

P(X = x) = ^nC_x p^x(1 - p)^{n -x}

So, the equation becomes

P(x = 11) = ^{20}C_{11} \times (85\%)^{11} \times (1 - 85\%)^{20 -11}    

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<h3>(b) To what extent do you think the university’s claim is true?</h3>

The probability 0.11% is less than 50%.

Hence, the extent that the university’s claim is true is very low

<h3>(c) What is the probability that all  20 would graduate? </h3>

Using the binomial probability formula, we have:

P(X = x) = ^nC_x p^x(1 - p)^{n -x}

So, the equation becomes

P(x = 20) = ^{20}C_{20} \times (85\%)^{20} \times (1 - 85\%)^{20 -20}    

This gives

P(x = 20) = 1 \times (0.85)^{20} \times (0.15\%)^0

P(x = 20) = 0.0388

Express as percentage

P(x = 20) = 3.88\%

Hence, the probability that all 20 would graduate is 3.88%

<h3>(d) The mean and the standard deviation</h3>

The mean is calculated as:

\mu = np

So, we have:

\mu = 20 \times 85\%

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\sigma = np(1 - p)

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Hence, the mean and the standard deviation are 17 and 2.55, respectively.

Read more about probabilities at:

brainly.com/question/15246027

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