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aivan3 [116]
2 years ago
12

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

elow is equal to the measure of the exterior angle. Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle) Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
I know its one of the step two answers but which one?
Mathematics
1 answer:
Goshia [24]2 years ago
4 0

Given steps  :

Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle)

Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) : <em>It's incorrect step because m<p and m<0 are on a common point on a line and make a linear pair. Therefore, m<p and m<0 are supplementary angles.</em>

Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p.

Step 4: So, m∠m + m∠n = m∠p.

<h3>Therefore, student did mistake in 2nd step and correct step should be  Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles).</h3>
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2. In a given country, records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are independe
Kitty [74]

Answer:

P(R) = 0.14

P(I) = 0.16

P(D) = 0.315

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Let Democrat = D

Republican = R

Independent = I

If 45% are Democrats, 35% are Republicans, and 20% are independents, then

Total registered voters = 100

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D = 0.7 × 45 = 31.5

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I = 0.8 × 20 = 16

 If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is

a Republican:

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6 0
2 years ago
A test has 50 questions. each right answer is worth 2 points; each wrong answer deducts 0.5 points; blank answers are not counte
mestny [16]

ANSWER: There are 2 blank answers

 

EXPLANATION

 

Let

The number of right answers be ‘r’

The number of wrong answers be ‘w’

The number of blank answers be ‘b’

 

r + w + b = 50

This means r + w ≤ 50

 

Then we know,

Right answers = 2 marks

Wrong answers = -0.5 mark

Blank Answers = 0 marks

 

2r – 0.5w = 88.5

2r = 88.5 + 0.5w                               … (Equation I)                   

 

Since the score as .5, we know that there is at least one wrong answer, and the number of wrong answers is an odd number.

 

Since the score is 88.5, and each right answer gives 2 marks

There are at more than 44 (i.e. 88/2) right answers

 

Since r + w ≤ 50, and possible values of w are odd numbers

If r = 45, Possible values of w are 1, 3, and 5

If r = 46, Possible values of w are 1, 3

If r = 47, Possible values of w are 1, 3

If r = 48, The only possible value of w is 1

If r = 49,The only possible value of w is 1

 

 

Since 2r = 88.5 + 0.5w  (Equation I)

We test for possible values:

 

If r = 45

2r = 88.5 + 0.5w  

2(45) = 88.5 + 0.5w  

90 = 88.5 + 0.5w

0.5w = 90 – 88.5

0.5w = 1.5

w = 3

 

So,

If there are 45 right answers

There are 3 wrong answers

r + w + b = 50

45 + 3 + b = 50

48 + b = 50

b = 50 – 48

b = 2

Then, there are 2 blank answers.

 

If r = 46

2r = 88.5 + 0.5w

2(46) = 88.5 + 0.5w

92 = 88.5 + 0.5w

0.5w = 92 – 88.5

0.5w = 3.5

w = 7

 

So,

If there are 46 right answers

There are 7 wrong answers

We know that r + w ≤ 50

46 + 7 = 53

So 46 and higher numbers are not possible solutions.

 

The only possible solution is:

There are 45 right answers

There are 3 wrong answers

<span>There are 2 blank answers</span>

6 0
3 years ago
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