The figure shows a pair of parallel lines
intersected by another pair of parallel lines.
Are the measures of Z4 and 214 related in
the same way as the measures of 29 and
Z7? Show your work.

9514 1404 393

Answer:

  y = 55°

Step-by-step explanation:

You know the sum of angles in a triangle is 180°. So, ...

  25° +30° +x = 180°

And, you know a linear pair of angles totals 180°:

  x + y = 180°

Substituting for 180°, we have ...

  25° +30° +x = x + y

Subtracting x from both sides, we get a relation that is useful to remember:

  25° +30° = y

  y = 55°

_____

This relation is usually described as ...

  An exterior angle is equal to the sum of the remote interior angles.

Answer:

Step-by-step explanation:

The data set below shows the number of questions that each of the 20 students in the  sample answered correctly.

12 , 16 , 18,  17 , 18 , 33 , 41 , 44 , 38 , 35 , 19, 36, 19 ,13, 43, 8 ,16, 14, 10, 9

Arrange the data in ascending order:

8 ,9 ,10 ,12 ,13 ,14 ,16 ,16 ,17 ,18 ,18 ,19 ,19 ,33 ,35 ,36 ,38 ,41 ,43 ,44

a)

Key 0|8=08  number of questions answered correctly

0| 9 , 9

1| 0,2,3,4,6,6,7,8,8,9,9

2|

3| 3,5,6,8

4| 1,3,4

b)

The plot is divided into two groups

One is mid tens and other in the high 30's

There is no score in 20's

c) A measure of center might fall between the two groups i.e. mean is 22.95 where there is no data and would not provide an accurate picture of student performance

Answer:

1 a  [tex]p -value = 0.030054[/tex]

1b   [tex]p -value = 0.0029798[/tex]

1c  [tex]p -value = 0.0039768[/tex]  

2a  [tex]p-value = 0.00099966[/tex]

2b  [tex]p-value = 0.00999706[/tex]

2c  [tex]p-value = 0.0654412[/tex]

Step-by-step explanation:

Considering question a

  The alternative hypothesis is H1:μ>μ0

   The test statistics is  z =1.88

Generally from the z-table  the  probability of   z =1.88 for a right tailed test is

    [tex]p -value = P(Z > 1.88) = 0.030054[/tex]

Considering question b

  The alternative hypothesis is H1:μ<μ0

   The test statistics is  z=−2.75

Generally from the z-table  the  probability of   z=−2.75 for a left tailed test is

    [tex]p -value = P(Z < -2.75) = 0.0029798[/tex]

Considering question c

  The alternative hypothesis is H1:μ≠μ0

   The test statistics is  z=2.88

Generally from the z-table  the  probability of  z=2.88 for a right  tailed test is

    [tex]p -value = P(Z >2.88) = 0.0019884[/tex]    

Generally the p-value for the two-tailed test is

    [tex]p -value = 2 * P(Z >2.88) = 2 * 0.0019884[/tex]    

=> [tex]p -value = 0.0039768[/tex]  

Considering question 2a

    The alternative hypothesis is H1:μ>μ0

     The sample size is  n=16

     The  test statistic is  t =  3.733

Generally the degree of freedom is mathematically represented as

        [tex]df = n - 1[/tex]

=>     [tex]df = 16 - 1[/tex]

=>     [tex]df = 15[/tex]

Generally from the t distribution table  the probability of   t =  3.733 at a degree of freedom of  [tex]df = 15[/tex] for a right tailed test is  

       [tex]p-value = t_{3.733 , 15} = 0.00099966[/tex]

Considering question 2b

    The alternative hypothesis is H1:μ<μ0

     The degree of freedom is df=23

     The  test statistic is ,t= −2.500

Generally from the t distribution table  the probability of   t= −2.500 at a degree of freedom of  df=23 for a left  tailed test is  

       [tex]p-value = t_{-2.500 , 23} = 0.00999706[/tex]

Considering question 2c

    The alternative hypothesis is H1:μ≠μ0

     The sample size is  n= 7

     The  test statistic is ,t= −2.2500

Generally the degree of freedom is mathematically represented as

        [tex]df = n - 1[/tex]

=>     [tex]df = 7 - 1[/tex]

=>     [tex]df = 6[/tex]

Generally from the t distribution table  the probability of   t= −2.2500 at a degree of freedom of  [tex]df = 6[/tex] for a left   tailed test is  

       [tex]t_{-2.2500 , 6} = 0.03272060[/tex]

Generally the p-value  for t= −2.2500 for a two tailed test is

     [tex]p-value = 2 * 0.03272060 = 0.0654412[/tex]

Answer:

4.9 feet

Step-by-step explanation:

First, we need to determine the height of the building using the following:

[tex]L^2 = H^2 + B^2[/tex]

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

[tex]20^2 = H^2 + 10^2[/tex]

[tex]400 = H^2 + 100[/tex]

[tex]H^2 = 400 - 100[/tex]

[tex]H^2 = 300[/tex]

[tex]H = \sqrt{300[/tex]

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

[tex]L_2^2 = H^2 + B_2^2[/tex]

Where

[tex]L_2 = 18[/tex] --- Length of the second ladder

[tex]H = \sqrt{300[/tex] ----- Height of the building

So, we have:

[tex]18^2 = \sqrt{300}^2 + B_2^2[/tex]

[tex]324 = 300 + B_2^2[/tex]

[tex]B^2_2 = 324 - 300[/tex]

[tex]B^2_2 = 24[/tex]

Solving for B2, we have:

[tex]B_2 = \sqrt{24[/tex]

[tex]B_2 = 4.9[/tex]

Answer:

The value is  [tex]\sigma _x = 1.1832[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is [tex]\mu = 25[/tex]

    The population standard deviation is  [tex]\sigma = 7[/tex]

    The sample size is  n =  35

Generally the standard deviation of the sampling distribution is mathematically represented as

       [tex]\sigma _x = \frac{\sigma}{\sqrt{n} }[/tex]

=>    [tex]\sigma _x = \frac{7}{\sqrt{35} }[/tex]

=>    [tex]\sigma _x = 1.1832[/tex]

Answer:

[tex]a = 1[/tex]

Step-by-step explanation:

Given

[tex]4x - 3(x + a) = 2[/tex]

[tex]x = 5[/tex]

Required

Determine the value of a

[tex]4x - 3(x + a) = 2[/tex]

Substitute 5 for x

[tex]4(5) - 3(5 + a) = 2[/tex]

Open all brackets

[tex]20 - 15 - 3a = 2[/tex]

[tex]5 - 3a = 2[/tex]

Collect Like Terms

[tex]-3a = 2 - 5[/tex]

[tex]-3a = -3[/tex]

Solve for a

[tex]a = -3/-3[/tex]

[tex]a = 1[/tex]

Answer: The product of two consecutive even numbers is 12 more than the square of the smaller number. The product of the numbers is 6 and 8 is 48. Square of the smaller number (here 6) is 36. so, 12 + 36 = 48.

hope this helps:)

Step-by-step explanation:

Answer:

$0.4 / pds

Step-by-step explanation:

Total amount paid divided by total number of pounds bought

12/30

= 0.4

Answer:

Rita earns 10 points at the end of the play.

Bernie losses 35 points.

Step-by-step explanation:

Rita earns 6 points 3 time and loses 4 points twice

6 * 3 = 18

4 * 2 = 8

18 - 8 = 10 points

Bernie get bonus of 15 points

looses 25 points twice

15 -  (25 * 2) = -35 points

Answer:

The p- value  is [tex]p-value  =  0.2033[/tex]

Its interpretation is  

As  [tex]p-value > \alpha[/tex]

The decision rule is

Fail to reject the null hypothesis

 The conclusion is  

There is no  sufficient evidence to support the  company claims at a level of  sign9ificance of 0.05

Step-by-step explanation:

From the question we are told that

  The mean is  [tex]\mu =  30 \  inches[/tex]

  The standard deviation is   [tex]\sigma  =  1.2 \  inches[/tex]

  The sample size is  n  =  100

  The sample mean is  [tex]\= x  =  30.1[/tex]

Let assume the level of significance is  [tex]\alpha = 0.05[/tex]

The null hypothesis is [tex]H_o  :  \mu \le 30[/tex]

The alternative is  [tex]H_a : \mu > 30[/tex]

Generally the test test is mathematically represented as

    [tex]z =  \frac{\= x- \mu }{\frac{\sigma}{\sqrt{n} } }[/tex]

=>  [tex]z =  \frac{30.1- 30 }{\frac{1.2}{\sqrt{100} } }[/tex]

=>  [tex]z =  0.83[/tex]

Generally from the z-table  the  probability of (Z > 0.83 ) is

   [tex]p-value  =  0.2033[/tex]

From the value obtained we see that  [tex]p-value > \alpha[/tex] hence

 The decision rule is

Fail to reject the null hypothesis

 The conclusion is  

There is no  sufficient evidence to support the  company claims at a level of  sign9ificance of 0.05

Answer:

¾(y + 3) + 9w

Step-by-step explanation:

Let's write it step by step:

Step 1: Three fourths of the sum of y and 3 is; ¾(y + 3)

Step 2: plus the product of 9 and w is;

¾(y + 3) + 9w

Thus,the final algebraic expression of the statement given in the question is;

¾(y + 3) + 9w

Answer:

The answer is c

Step-by-step explanation:

Beacuse when u the shape is transfrromed that what u get

Answer:

8x8

Step-by-step explanation:

Answer:

I have multiple.

Step-by-step explanation:

16x4=64

8x8=64

4x16=64

Answer:

[tex]7x\leq x-24[/tex]

Here, [tex]x[/tex] denotes the required number.

Step-by-step explanation:

Let [tex]x[/tex] denotes the required number that satisfies the following condition.

''seven times a number is less than or equal to a quantity that is 24 less than that same  number''

Seven times a number is equal to [tex]7x[/tex]

Quantity that is 24 less than that same  number is equal to [tex]x-24[/tex]

Now find the inequality.

As seven times a number is less than or equal to a quantity that is 24 less than that same  number,

[tex]7x\leq x-24[/tex]

Answer:

Step-by-step explanation:

You can fold the two big rectangles together and make a kinda box like thing, with the triangles as faces, but... there's no top!

Answer:

-7

Step-by-step explanation:

Answer:

3.75 cups of sugar. I think

Answer:

3 3/4

Step-by-step explanation:

3/5 times 5

1.multiiply the numerator by 5

The numerator is the top number which is 3 in this case

So 3x5 is 15

You keep the denominator 4

so 15/4 that is an improper fraction now divide 15 by 4

or count by fours

4,8,12,16

16 is more than 15 so the new numerator is 12 and how many times did we count to fours? 3 times

so 3 is a whole now subtract the 12 you already took with 15. 3 is the extra so 3 wholes and 3 extras which is 3 3/4

*remember you keep the denominator the same

Answer:

h. x=11

i. x=4 1/6 (1/6 is a fraction)

k. x=-8

l. x= 3 1/2 (1/2 is a fractio)

Step-by-step explanation:

Answer:

25.6-14.07= 11.53

Step-by-step explanation:

Answer:

11.53

Step-by-step explanation:

25.6-14.07=11.53

Answer:

2x6/4=3

Step-by-step explanation:plz mark brainliest

Answer:

The answer is 1/12

Step-by-step explanation:

Divide: 2/6 : 4 = 2/6 · 1/4= 2 · 1/6 · 4 = 2/24 = 2 · 1 / 2 · 12 = 1 /12

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step , cancel by a common factor of 2 gives 1/12

.

In words - two sixths divided by four = one twelfth.

Answer:

60 hope this helps

Step-by-step explanation:

15 divided by 5 =3

20 multiplied by 3 =60

Answer:

The slope is 0

Step-by-step explanation:

Step-by-step explanation:

Since we are not told what to look for, we can as well look for the value of x, m∠SQT and  m∠RQS

Given

m∠RQS=(4x-20)°

m∠SQT=(3x+14)°

m∠RQT=155°

The addition postulate is true

m∠RQT= m∠RQS + m∠SQT

Substitute the given parameters into the formula

155 = 4x-20+3x+14

155 = 7x-6

7x = 155+6

7x = 161

x = 161/7

x = 23

Solve for m∠RQS

m∠RQS = 4x-20

m∠RQS = 4(23)-20

m∠RQS = 92-20

m∠RQS = 72°

Solve for m∠SQT

m∠SQT = 3x+14

m∠SQT = 3(23)+14

m∠SQT = 69+14

m∠SQT = 83°

Answer:

Step-by-step explanation:

What happens to

- the angles on a shape

- the lines on the shape

- the shape itself

when the shape is transformed?

ANSWER:

- When a shape is transformed, the angles on the shape either increase or reduce in size

- When a shape is transformed, the lines on the shape change direction. They could also be shorter, longer, more curved, or more flattened.

- When a shape is transformed, the shape itself becomes another one.

The difference of 8.026 is given by the expression 9.947 − 1.921. The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The expression will be solved as below:-

E = 9.947 − 1.921

Subtract the smaller value from the bigger value,

E = 9.947 − 1.921

E = 8.026

Hence, option C is showing the right difference.

To know more about an expression follow

https://brainly.com/question/5034267

#SPJ2

Answer:

10:21

Step-by-step explanation:

Step-by-step explanation:

for the first one -6/3=3/(-6)

is false

The left side  − 2  does not equal to the right side  − 0.5 , which means that the given statement is false.

False

-8*9=9*(-8)

is true

The left side  − 72  is equal to the right side  − 72 , which means that the given statement is always true.

True

Answer:

Yes its less than 0

Step-by-step explanation:

it would go behind the 0 on a number line