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3 years ago

Provide the missing statements and reasons for the following proof:

Mathematics

1 answer:

LuckyWell [14K]3 years ago

7 0

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

R2: Definition of corresponding angles
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

<h3>What are Supplementary Angles?</h3>

Supplementary angles, when added together will give us a sum of 180°.
Linear pair angles and corresponding angles are supplementary.

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

R2: Definition of corresponding angles
R3: Corresponding angles postulate
R5: Supplement Postulate
S7: m∠1 + m∠3 = m∠2 + m∠3
S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)

Learn more about supplementary angles on:

brainly.com/question/8992900

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netineya [11]

Answer:

See Explaination

Step-by-step explanation:

Looking at the question, The proportion of beer drinkers who preferred Budweiser to Schlitz as obtained from the sample is 54/100 = 0.54.

Let X be a random variable representing the number of drinkers who prefer Budweiser to Schlitz with total number of drinkers being n.

X \sim Bin(n, p)

From the sample, \hat{p} = 0.54

Therefore, the 95% confidence interval for p is given by,

(\hat{p}-z_{1-\alpha/2}\sqrt{\frac{1}{n}\hat{p}(1-\hat{p})}, \hat{p}+z_{1-\alpha/2}\sqrt{\frac{1}{n}\hat{p}(1-\hat{p})})

where z_{1-\alpha/2} is the upper \alpha/2 point of standard normal variate.

Here, \alpha = 0.05

Therefore, z_{1-\alpha/2} = z_{0.975} = 1.96

The required confidence interval for p is given by

(0.54 - 1.96\times \sqrt{\frac{0.54\times 0.46}{100}}, 0.54 + 1.96\times \sqrt{\frac{0.54\times 0.46}{100}}) = (0.442, 0.638)

Since the lower bound of the interval is less than 0.50 and upper bound is more than 0.50, therefore the two parties will use these bounds to glorify their brand. Budweiser will use the upper bound = 0.638 to say that the true proportion may be more than 0.5 indicating their beer is more preferred by the people. On the other hand, the lower bound = 0.442 will be used by the Schlitz to show that the true proportion may have values less than 0.5 indicating higher proportion of people favors their brand.

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3 years ago

A car is traveling on a highway at a constant speed, described by the equation d = 70t, where d represents the distance, in mile

almond37 [142]

Answer:

84miles

Step-by-step explanation:

Step one:

given data

we are told that the equation that describes the car's speed is

d = 70t-----------1

<em>From the equation, we can see that the speed with which the car is traveling is 70miles per hour, while we are expected to find the distance d when the time is 1.2 hours.</em>

<em />

Required

The distance d at 1.2 hours

Step two:

substituting in the expression we have

d= 70*1.2

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3 years ago

What is 3/9 and 123/999 as a decimal

Nutka1998 [239]

To convert fractions to decimals, divide the denominator into the numerator

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hope this helps

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4 years ago

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vitfil [10]

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Sedbober [7]

Answer:

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