Perimeter and value of x show all work

In the figure, mZRPZ = 95 and TU ||RQ|| VW. Find the measure of angle YSV.

madreJ [45]

Answer:

$m\angle YSV=85^o$

Step-by-step explanation:

The complete question in the attached figure

step 1

Find the measure of angle QPZ

we kno that

$m\angle RPZ+m\angle QPZ=180^o$ ---> by supplementary angles (form a linear pair)

we have

$m\angle RPZ=95^o$ ---> given value

substitute

$95^o+m\angle QPZ=180^o$

$m\angle QPZ=180^o-95^o$

$m\angle QPZ=85^o$

step 2

Find the measure of angle YSV

we know that

When two lines are crossed by another line, <em><u>Alternate Exterior Angles</u></em> are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. If the two lines are parallel then the alternate exterior angles are congruent.

In this problem

The transversal is the line XY

The two parallel lines are RQ and VW

therefore

$m\angle YSV=m\angle QPZ$ ---> by alternate exterior angle

we have

$m\angle QPZ=85^o$

therefore

$m\angle YSV=85^o$

5 0

4 years ago

A recent study of two vendors of desktop personal computers reported that out of 836 units sold by Brand A, 111 required repair,

iris [78.8K]

Answer:

Step-by-step explanation:

Hello!

The study variables are:

$X_A$ : The number of Brand A units sold that required repair.

$n_A= 836$

$x_A= 111$

$X_B$ : THe number of Brand B units sold that required repair.

$n_B= 739$

$x_B= 111$

1. Calculate the difference in the sample proportion for the two brands of computers, p^BrandA−p^BrandB =?.

The sample proportion of each sample is equal to the number of "success" observed xi divided by the sample size n:

^p $_A$ = $\frac{x_A}{n_A}= \frac{111}{836}= 0.1328$

^p $_B$ = $\frac{x_B}{n_B}= \frac{111}{739} =0.1502$

^p $_A$ - ^p $_B$ = 0.1328 - 0.1502= -0.0174

Note: proportions take numbers from 0 to 1, meaning they are always positive. But this time what you have to calculate is a difference between the two proportions so it is absolutely correct to reach a negative number it just means that one sample proportion is greater than the other.

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands?

A. H0:pA−pB=0 , HA:pA−pB<0

B. H0:pA−pB=0 , HA:pA−pB>0

C. H0:pA−pB=0 , HA:pA−pB≠0

If you want to test whether the proportion of computers of both brands is different, you have to do a two-tailed test, the correct option is C.

3. Calculate the pooled estimate of the sample proportion, ^p= ?

To calculate the pooled sample proportion you have to use the following formula:

^p= $\frac{x_A+x_B}{n_A+n_B}= \frac{111+111}{836+739}= 0.14095 = 0.1410$

4. Is the success-failure condition met for this scenario?

A. Yes

B. No

The conditions that have to be met are:

$n_A\geq 30$ ⇒ Met

$n_A*p_A\geq 5$ ⇒ 836 * 0.1328= 111.4192; Met

$n_A*(1-p_A)\geq 5$ ⇒ 836 * (1 - 0.1328)= 727.5808; Met

$n_B\geq 30$ ⇒ Met

$n_B*p_B\geq 5$ ⇒ 739 * 0.1502= 110.9978; Met

$n_B*(1-p_B)\geq 5$ ⇒ 739 * (1-0.1502)= 628.0022; Met

All conditions are met.

5. Calculate the test statistic for this hypothesis test. ? =

$Z_{H_0}= \frac{(p'_A-p'_B)-(p_A-p_B)}{\sqrt{p'(1-p')[\frac{1}{n_A} +\frac{1}{n_B} ]} } = \frac{-0.0174-0}{\sqrt{0.1410*0.859*[\frac{1}{836} +\frac{1}{739} ]} }= -0.9902$

6. Calculate the p-value for this hypothesis test, p-value = .

This hypothesis test is two-tailed and so is the p-value, since it has two tails you have to calculate it as:

P(Z≤-0.9902) + P(Z≥0.9902)= P(Z≤-0.9902) + ( 1 - P(Z≤0.9902))= 0.161 + (1 - 0.839) = 0.322

7. What is your conclusion using α = 0.05?

A. Do not reject H0

B. Reject H0

The decision rule using th ep-value is:

If p-value > α, the decision is to not reject the null hypothesis.

If p-value ≤ α, the decision is to reject the null hypothesis.

The p-value= 0.322 is greater than α = 0.05, so the decision is to not reject the null hypothesis.

8. Compute a 95 % confidence interval for the difference p^BrandA−p^BrandB = ( , )

The formula to calculate the Confidence interval is a little different, because instead of the pooled sample proportion you have to use the sample proportion of each sample to calculate the standard deviation of the distribution:

( $p'_A-p'_B$ ) ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_A(1-p'_A)}{n_A} +\frac{p'_B(1-p'_B)}{n_B} }$

-0.0174 ± 1.965 * $\sqrt{\frac{0.1328*0.8672}{836} +\frac{0.1502*0.8498}{739} }$

[-0.0520; 0.0172]

I hope it helps!

3 0

3 years ago

A square poster has a side length of 26 in. Drawn on the poster are four identical triangles. Each triangle has a base of 8 in.

Firdavs [7]

To find the probability of landing on a triangle, you will want find the combined areas of the triangles and the total area of the square target.

Divide the area of the combined areas and the total area to find the probability of landing on a triangle.

A = 1/2bh
1/2 x 8 x 8
A = 32 square inches
32 x 4
128 square inches (areas of triangles)

A = bh
26 x 26
A = 676 square inches

128/676 = 0.189

There is an approximate probability of 0.19 of hitting a triangle.

6 0

3 years ago

Read 2 more answers

In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Su

kykrilka [37]

Answer:

Step-by-step explanation:

Using the formula for calculating the confidence interval to estimate an interval for the mean rate of return on all real estate investments with 95% confidence;

Confidence Interval = xbar±(Z*S/√n)

xbar is the mean = 20%(assumed since we are not given)

n is the sample size = 200

S is the standard deviation = 2.25%

Z is the Z score at 95% confidence interval = 1.960

Confidence Interval = 20±(1.96*2.25/√200)

Confidence Interval = 20±(1.96*2.25/14.14)

Confidence Interval = 20±(1.96*0.159)

Confidence Interval = 20±0.312

Confidence Interval = (20-0.312, 20+0.312)

Confidence Interval = (19.688, 20.312)

Hence the interval for the mean rate of return on all real estate investments with 95% confidence is 19.688<x<20.312.

This means that the minimum rate of return on investment is 19.688% and the maximum rate of return on investment is 20.312%.(assuming 20% as the mean)

3 0

3 years ago

Last year, 140 people in a community had cell phones. This year, the number

ycow [4]

Answer:

Part B: 91 people

Step-by-step explanation:

<h3><em>Sorry i cant add a explanation, because im still learning about it.</em></h3>

3 0

3 years ago

Perimeter and value of x show all work​

Perimeter and value of x show all work