(3 × 2)^2 + 6 ÷ 3 × 2

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines

lisabon 2012 [21]

To enable the completion of the proof that line l is parallel to line m, a

diagram showing the lines and their common transversal is attached.

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ∠1 and ∠2 are supplementary angles ${}$ 1. Given

2. m∠1 + m∠2 = 180° ${}$ 2. Definition of supplementary ∠s

3. ∠1 and ∠3 are supplementary angles ${}$ 3. Exterior sides in opposite rays

4. m∠1 + m∠3 = 180° ${}$ 4. Definition of supplementary ∠s

5. m∠1 + m∠2 = m∠1 + m∠3 ${}$ 5. Transitive property of equality

6. m∠2 = m∠3 ${}$ 6. Subtraction property of equality

7. l ║ m ${}$ 7. Converse of alternate interior

${}$ angles postulate

Reasons:

Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°

Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)

Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles

Reason for statement 5: Transitive property of equality describes the property that if a number x = y, and z = y, then x = z.

Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality

Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.

Learn more here:

brainly.com/question/25178453

6 0

2 years ago

Mr Ruiz drove 305 miles in 5 hours on Saturday and 190 miles in 4 hours on Sunday what is his average speed in miles per hour fo

Snezhnost [94]

Add the mileage together to find total miles.

Add the hours together.

Divide total miles by total hours.

305 + 190 = 495 miles

5 + 4 = 9 hours.

495 / 9 = 55 miles per hour.

The average speed was 55 miles per hour.

4 0

3 years ago

A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remed

KiRa [710]

Answer:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed. So we can say that the 3 remedies ar approximately equally effective.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

NyQuil Robitussin Triaminic Total

No relief 11 13 9 33

Some relief 32 28 27 87

Total relief 7 9 14 30

Total 50 50 50 150

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference in the three remedies

H1: There is a difference in the three remedies

The level os significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*33}{150}=11$

$E_{2} =\frac{50*33}{150}=11$

$E_{3} =\frac{50*33}{150}=11$

$E_{4} =\frac{50*87}{150}=29$

$E_{5} =\frac{50*87}{150}=29$

$E_{6} =\frac{50*87}{150}=29$

$E_{7} =\frac{50*30}{150}=10$

$E_{8} =\frac{50*30}{150}=10$

$E_{9} =\frac{50*30}{150}=10$

And the expected values are given by:

NyQuil Robitussin Triaminic Total

No relief 11 11 11 33

Some relief 29 29 29 87

Total relief 10 10 10 30

Total 50 50 50 150

And now we can calculate the statistic:

$\chi^2 = \frac{(11-11)^2}{11}+\frac{(13-11)^2}{11}+\frac{(9-11)^2}{11}+\frac{(32-29)^2}{29}+\frac{(28-29)^2}{29}+\frac{(27-29)^2}{29}+\frac{(7-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(14-10)^2}{10} =3.81$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(3-1)=4$

And we can calculate the p value given by:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(3.81,4,TRUE)"

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed.

4 0

3 years ago

Can some one help me find x?

Gnom [1K]

Answer:

x = 20

Step-by-step explanation:

Exterior angles are equal.

7x - 3 = 6x + 17

Add 3 and subtract 6x to both sides.

x = 20 is the answer.

4 0