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2 years ago

PLEASE HELP (look at pictures)

Mathematics

1 answer:

Vladimir [108]2 years ago

6 0

<h2>Answer:</h2>

This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,

Reason: Given

Statement: $\angle1\cong\angle2$

Reason: Def of vertical $\angle s$

Statement: $\angle1\:and\:\angle3 \ are \ vertical$

Reason: Def of vertical $\angle s$

Statement: $\angle1\cong\angle3$

Reason: Transitive Property

Statement: $\angle2\cong\angle3$

Reason: corresponding Angles Converse Postulate

Statement: $p\parallel q$

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Assume that women's heights are normally distributed with a mean given by mu equals 62.3 in, and a standard deviation given by

Salsk061 [2.6K]

Answer: a) 0.6141

b) 0.9772

Step-by-step explanation:

Given : Mean : $\mu= 62.3\text{ in}$

Standard deviation : $\sigma = \text{2.4 in}$

The formula for z -score :

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

a) Sample size = 1

For x= 63 in. ,

$z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{1}}}=0.29$

The p-value = $P(z$

$0.6140918\approx0.6141$

Thus, the probability is approximately = 0.6141

b) Sample size = 47

For x= 63 ,

$z=\dfrac{63-62.3}{\dfrac{2.4}{\sqrt{47}}}\approx2.0$

The p-value = $P(z$

$=0.9772498\approx0.9772$

Thus , the probability that they have a mean height less than 63 in =0.9772.

8 0

3 years ago

Someone explain!! geometry

ikadub [295]

Step-by-step explanation:

sin 0 = opposite ÷ hypothenus

sin 0 = 3 / 5

3 / 5 = x / 15

5 × n = 15

n = 3

x = 3 × 3 = 9

y = use pythagoras

= 12

tan 0 = opposite ÷ adjacent

tan 0 = 9/12

4 0

3 years ago

Remo needs to buy a countertop for a bathroom. He calculated the area as 10 square feet. The actual area is 9.5 square feet. Wha

Digiron [165]

Answer:

The answer is either 5.26 or 5 I think its 5.26

Step-by-step explanation: The reason why I think its the two answers I said is because 10 is 10 percent of 100 so 9.5 is 9.5 percent which makes me think that

4 0

3 years ago

Read 2 more answers

The local branch of the Internal Revenue Service spent an average of 21 minutes helping each of 10 people prepare their tax retu

AURORKA [14]

Answer:

The confidence Interval is [- 0.7053 10.4521]

a: The hypotheses are

H0: μ1=μ2 against the claim Ha :μ1≠μ2

b. The critical value for t∝/2 for 17 d.f t > 2.508 and t < -2.111

c. t= -2.8422

d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means.

Step-by-step explanation:

When the standard deviations are not the same then the confidence intervals for mean differences are calculated as

(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2

x1`= 21 x2`= 27

n1= 10 n2= 14

s1= 5.6 s2= 4.3

The degrees of freedom is calculated using

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= 17

The t∝/2 for 17 d.f = 2.11

Putting the values

(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2

(21-27) - 2.11√5.6²/10+ 4.3²/14 < u1-u2 <(21-27) +2.11√5.6²/10+4.3²/14

6- 2.11*2.111 < u1-u2 < ( 6 ) +2.11*2.111

6- 4.4521 < u1-u2 < ( 6 ) +5.294

- 1.5479 < u1-u2 < 10.4521

The confidence Interval is [- 0.7053 10.4521]

a: The hypotheses are

H0: μ1=μ2 against the claim Ha :μ1≠μ2

The claim is that there is a difference in the average time spent by the two services

b. The critical value for t∝/2 for 17 d.f t > 2.508 and t < -2.111

The degrees of freedom is calculated using

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= 17

c. The test statistic is

t= (x1`-x2`) /√s1²/n1 + s2²/n2

t= (21-27) /√5.6²/10+ 4.3²/14

t= -6/2.111

t= -2.8422

d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means.

5 0

3 years ago

Hey all!

Rainbow [258]

Answer:

65°

Step-by-step explanation:

<u>Use the law of cosines:</u>

cos C = (25² + 27² - 28²)/(2*25*27)
cos C = 0.4222
m∠C = arccos 0.4222
m∠C = 65°

8 0

2 years ago