All categories

3 years ago

Which of the following theorems cannot be used to prove two lines are parallel?

Mathematics

1 answer:

mariarad [96]3 years ago

6 0

Answer:

Option H

Step-by-step explanation:

Option F

If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

True.

Option G

If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

True

Option H

If two line are cut by a transversal so that a pair of vertical angles are congruent, then the lines are parallel.

Since, vertical angles don't prove the lines cut by a transversal are parallel.

So the statement is False.

Option J

If two lines are are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.

True.

You might be interested in

1. Which of the following triangles is classified as a right triangle?

Sergio039 [100]

Answer:

a triangle witih side lengths of 12,16,20

7 0

3 years ago

We would like to create a confidence interval.

Vlada [557]

Answer:

c.A 90% confidence level and a sample size of 300 subjects.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level $1-\alpha$ , we have the confidence interval with a margin of error of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

In this problem

The proportions are the same for all the options, so we are going to write our margins of error as functions of $\sqrt{\pi(1-\pi)}$

a.A 99% confidence level and a sample size of 50 subjects.

$n = 50$

99% confidence interval

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.3642\sqrt{\pi(1-\pi)}$

b.A 90% confidence level and a sample size of 50 subjects.

$n = 50$

90% confidence interval

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{50}}\sqrt{\pi(1-\pi)} = 0.2623\sqrt{\pi(1-\pi)}$

c.A 90% confidence level and a sample size of 300 subjects.

$n = 300$

90% confidence interval

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{1.645}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.0950\sqrt{\pi(1-\pi)}$

This produces smallest margin of error.

d.A 99% confidence level and a sample size of 300 subjects.

$n = 300$

99% confidence interval

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The margin of error is

$M = z\sqrt{\frac{\pi(1-\pi)}{n}} = \frac{2.575}{\sqrt{300}}\sqrt{\pi(1-\pi)} = 0.1487\sqrt{\pi(1-\pi)}$

6 0

3 years ago

The 4th and 8th term of a G.P. are 24 and 8/27 respectively. find the 1st term and common ratio

beks73 [17]

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric progression is

• $a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

given a₄ = 24, then

a₁ $r^{3}$ = 24 → (1)

Given a₈ = $\frac{8}{27}$ , then

a₁ $r^{7}$ = $\frac{8}{27}$ → (2)

Divide (2) by (1)

$r^{4}$ = $\frac{\frac{8}{27} }{24}$ = $\frac{1}{81}$

Hence r = $\sqrt[4]{\frac{1}{81} }$ = $\frac{1}{3}$

Substitute this value into (1)

a₁ × ( $\frac{1}{3}$ )³ = 24

a₁ × $\frac{1}{27}$ = 24, hence

a₁ = 24 × 27 = 648

4 0

3 years ago

Which Data set has the smallest IQR ?

mel-nik [20]

Answer:

<h2 /><h2>The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers. Interquartile Range. 25% of values.</h2>

<h2 />

<h2>here your answer </h2>

8 0

3 years ago

TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a c

Blababa [14]

(35x+18)=126. I think this is right not for sure

4 0

3 years ago

Read 2 more answers