The figure shown has two parallel lines cut by a transversal:

A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Use the figure to complete the sentence. (4 points)

∠3 and ____ are alternate interior angles.

∠2
∠6
∠5
∠8

Answer:

20c

Step-by-step explanation:

if the temperature rises 2c every hour u count from 6 to 3 and it would be 10 hours

then u do 10×2=20 or 10×2=20c

Answer: D.

Step-by-step explanation:

-2/20 = -0.1, 0.1 is the closet one to -3

The expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .

In the question ,

it is given that

the diameter of the cylindrical metal pipe = 20mm

so the radius of the cylindrical pipe = 10 mm

height of the cylindrical metal pipe = 21mm

Using the formula of Volume of Cylinder = π*r²*h  

the volume of cylindrical metal pipe = π*(10)²*21     .....(i)

the height of smaller cylinder = 21mm

radius of the smaller cylinder = 6mm

So, Volume of the smaller cylinder = π*(6)²*21     .....(ii)

the volume of metal needed to make the pipe = Volume of cylindrical metal pipe - Volume of the smaller cylinder .

Substituting the values from (i) and (ii) , we get

volume of metal needed = π*(10)²*21 - π*(6)²*21

= 21*π*(10)² - 21*π*(6)²

hence , option(a) is correct .

Further Simplifying , we get

= 21*100*π - 21*36*π

= 2100π - 756π

hence , option(c) is also correct

Therefore , the expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .

The given question is incomplete , the complete question is

A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters and the the radius of the smaller cylinder is 6 millimeters.

Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.

(a) 21*π*(10)² - 21*π*(6)²

(b) π*(20)²*(21) – π*(6)²

(c) 2100π - 756π

(d) 7,644π

(e) 1,344

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Answer: A & C

Step-by-step explanation: Just did it

Answers:    

15)  x= −1 and y=2

16)  x=2 and y= −1

Step-by-step explanation:

15) Solve the system by elimination:

Multiply the first equation by 2 and the second equation by 1.

2(8x−6y=−20)

1(−16x+7y=30)

They then become:

16x−12y=−40

−16x+7y=30

Add the two equations to eliminate x:

−5y=−10

Then solve for y by dividing both sides by -5:

−5y/−5 = −10/−5

The answer for y is y=2

Now Substitute 2 for y in the equation 8x−6y=−20:

8x−(6)(2)=−20

8x−12=−20

Add 12 to both sides:

8x−12+12=−20+12

8x=−8

Divide by 8:

8x/8 = −8/8

The answer for x is x=−1

16) Solve the system by elimination:

Multiply the second equation by 6 and merge the equations together.

(6x−12y=24)

6(−x−6y=4)

They then become:

6x−12y=24

−6x−36y=24

Add the two equations to eliminate x:

−48y=48

Then solve for y:

−48y=48

−48y/−48 = 48/−48

The answer for y is y= −1

Now substitute −1 for y in 6x−12y=24:

6x−(12)(−1)=24

6x+12=24

Add -12 to both sides:

6x+12+−12=24+−12

6x=12

6x/6 = 12/6

The answer for x is x=2

Solved! Please don't forget the Brainliest!!

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Problem 15.) The two equations are :

Let's multiply whole equation (1) by 2

[tex]\qquad \sf  \dashrightarrow \: 16x - 12y = - 40 \: \: \: \: \: \: - (3)[/tex]

Now, Add equation (3) and equation (2)

[tex]\qquad \sf  \dashrightarrow \: 16x - 12y - 16x + 7y = - 40 + 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 5y = - 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 10 \div - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 2[/tex]

Plug the value of y in equation (1) :

[tex]\qquad \sf  \dashrightarrow \: 8x - 6y = - 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x - 6(2) = - 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x - 12 = - 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x = - 20 + 12[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 8 \div 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = - 1[/tex]

So, the required values are : x = -1 and y = 2

Problem 16.) The two equations are :

Multiply equation (2) by 2 :

[tex]\qquad \sf  \dashrightarrow \: - 2x - 12y = 8 \: \: \: \: \: \: - (3)[/tex]

Now, subtract equation (3) from equation (1)

[tex]\qquad \sf  \dashrightarrow \: 6x - 12y - ( - 2x - 12y) = 24 - 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x - 12y + 2x + 12y= 16[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8x = 16[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 16 \div 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 2[/tex]

Now, plug x = 2, in equation (2) :

[tex]\qquad \sf  \dashrightarrow \: - x - 6y = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 2 - 6y = 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 6y = 4 + 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 6y = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = 6 \div - 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 1[/tex]

So, the required values are : x = 2 and y = -1

Answer:

B is the answer.

Step-by-step explanation:

X is the number of hours the plumber worked.

Answer: B

Step-by-step explanation:

Answer: q = -216

Step-by-step explanation:

multiply both sides

90 + q = -126

move the constant to the right

q = -126 = 90

calculate

q = -216

have a GREAT day!!

Answer:

Step-by-step explanation:

The answer will be: 200/300 of scarves are blue. 200/300 also is equal to 2/3. The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

Reduce the fractions if they aren't already in the lowest terms. Then, all that is required is to multiply the denominator by the denominator and the numerator by the numerator. For instance, multiplying 2 by 7 yields the new numerator, which is 14, when multiplying 2/3 and 7/8. The result of multiplying 3 by 8 is 24.

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In the quadrilateral KITE,

The value of side KI = [tex]\sqrt{17}[/tex]

The value of side KE = [tex]\sqrt{17}[/tex]

The value of side IT = [tex]3\sqrt{5}[/tex]

The value of side TE = [tex]3\sqrt{5}[/tex]

The quadrilateral KITE is a kite because , KI = KE and IT = TE

How are the values of the quadrilateral sides calculated?

K (0,-2) , I(1,2) ,T(7,5) , E(4, -1)

KI = [tex]\sqrt{17}[/tex]

What is the value of side KE ?

K (0,-2) and E(4, -1)

The distance formula is:

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\KE =\sqrt{(4-0)^{2} + (-1 +2)^{2} }\\\\KE = \sqrt{(4)^{2} + (1)^{2} }\\\\KE = \sqrt{16+1} \\\\KE = \sqrt{17}[/tex]

The value of side KE of the quadrilateral = [tex]\sqrt{17}[/tex]

What is the value of  side IT ?

I(1,2)  and T(7,5)

The distance formula  is:

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\IT =\sqrt{(7-1)^{2} + (5-2)^{2} }\\\\IT = \sqrt{(6)^{2} + (3)^{2} }\\\\IT = \sqrt{36+9} \\\\IT = \sqrt{45} =3 \sqrt{5}[/tex]

The value of  side IT of the quadrilateral =[tex]3\sqrt{5}[/tex]

What is the value of side TE  ?

T(7,5) and E(4, -1)

The distance formula is :

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\TE =\sqrt{(4-7)^{2} + (-1-5)^{2} }\\\\TE = \sqrt{(-3)^{2} + (-6)^{2} }\\\\TE = \sqrt{9+36} \\\\TE = \sqrt{45} =3 \sqrt{5}[/tex]

The value of side TE of the quadrilateral = [tex]3\sqrt{5}[/tex]

The quadrilateral KITE is a kite because :

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Answer:

The answer is in the picture.

Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

4^-2 * 7^-2

= 1/4^2 * 1/7^2

= 1/16 * 1/49

- 1/784

Answer:

a

Step-by-step explanation:

Since the point B is between points A and C, the length BC is 22.25 units

From the question, we have the following parameters that can be used in our computation:

Length AB = 6x - 9

Length BC = 3x + 17

Length AC = 5x + 16

The above implies that the point B is between points A and C

So, we have the following equation

AC = AB + BC

Substitute the known values in the above equation

So, we have the following equation

5x + 16 = 6x - 9 + 3x + 17

Collect the like terms

So, we have the following equation

5x - 6x - 3x = -9 + 18 - 16

Evaluate the like terms

So, we have the following equation

-4x = -7

Divide by -4

x = 7/4

Substitute x = 7/4 in the equation BC = 3x + 17

So, we have the following equation

BC = 3 x 7/4 + 17

Evaluate

BC = 22.25

Hence, the numerical length of BC is 22.25 units

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 m = 1/4  is the slope of the line .

What is slope in plain English?

The slope of a line passing through points ( x₁ , y₁ ) ( x₂ , y₂ )  is defined as

   m = y₂ - y₁/x₂ - x₁

if the x coordinates are not equal. The slope is not defined if the x

coordinates are equal because that would require dividing by zero.

here ,

      ( x₁ , y₁ ) = (0, 5)

      ( x₂ , y₂ ) = ( -12 , 2 )

   m = y₂ - y₁/x₂ - x₁

    m =  2 - 5/-12 - 0

   m = -3/-12

  m = 1/4

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It will cost 140 dollars to buy enough carpet for the living room.

A rectangle is a four-sided figure in which opposite sides are equal and the diagonals are also of the same length.

Given Ed's living room is 4 yards wide and 7 yards long.

We know that the area of a triangle is the product of its length and width.

∴ The area of  Ed's living room is (4×7) sq yards = 28 sq yards.

Also given to install yellow carpet that costs $5.00 per square yard,

∴ For 28 sq yards, the cost of installing a yellow carpet will be,

= (28×5) dollars.

= 140 dollars.

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Answer:

Step-by-step explation:

if the ratio of 9 contains 63 men then what about the ratio of 5 u do cross multiplication it will be 5 ×63 the answer you get multiply by 9 answer will be 35

Answer: x= -16

Step-by-step explanation:

The cost of 8 pounds of oranges based on the total cost of 5 pounds bought is 12.00

What is the cost for a pound of oranges?

The cost of a pound of oranges based on the rate at which 5 pounds were bought and 8 pounds would also be bought is determined as the amount paid for 5 pounds of oranges divided by the number of pounds of oranges bought

cost per pound of oranges=cost of 5 pounds/5 pounds

cost per pound of oranges=7.50/5

cost per pound of oranges=1.50

Based on the 1.50 per pound, the cost of 8 pounds is the cost per pound multiplied by 8 pounds

cost of 8 pounds of oranges=1.50*8pounds

cost of 8 pounds of oranges=12.00

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There is insufficient evidence to prove that the dice are loaded because every number on them has a probability of 1/6.

The likelihood of any number appearing on a six-sided die is 1/6.

It will not be 1/6 if it is loaded.

In order to determine whether the provided distribution complies with the idealized distribution of the dice throw, we do a chi-square test.

Step 1: Form the hypothesis.

H₀ = The likelihood of rolling any number on a six-sided die is one-sixth.

H₁ = The likelihood of getting any number on a six-sided die is not one in six.

Step 2: Indicate the degree of significance.

Alpha = 0.5

Step 3: computation of the chi-square test statistic (Image is attached for this step)

Step 4: Discover the important value.

Critical Value ⇒ 12.8325 =CHISQ.INV[1 - (0.05 / 2), 5]

Step 5: Determine the p-value.

p-value ⇒ 0.853 =1 - CHISQ.DIST(1.97,5,TRUE)

Step 6: Make a choice regarding whether or not to reject H₀

We are unable to reject the null hypothesis since the p-value is higher than 0.05.

As a result, we draw the conclusion that there is a 1/6 chance of getting any number on a six-sided die.

Note: Since the chi-square value is below the threshold, the null hypothesis cannot be rejected.

Because every number on the dice has a probability of 1/6, there is insufficient evidence to support the assertion that the dice are loaded.

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Answer:

x-intercept- (-1.2,0)

y-intercept- (0,6)

Step-by-step explanation:

To find the slope-intercept form, we have to find x and y.

First, find x. Get rid of the 2y, and the equation will look like this.

-10x=12

Now, divide both sides by -10.

12/-10=-1.2

The x-intercept would be (-1.2,0)

To find the y-intercept form, do the same thing.

Get rid of the -10x.

2y=12

Divide by 2 on both sides.

y=6

The y-intercept form would be (0,6)

Hope this helps! :D

The answers to all the equations are:

So, f(x):

(A) f(x) = x + 3 when f(4)

(B) f(x) = 2x - 9 when f(5)

(C) f(x) = -6x + 2 when f(-3)

Therefore, the answers to all the equations are:

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The test is one of the form  Hₐ <  ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀

According to problem ststement : We need to solve  an Hypotesis test proportion so:

H₀    P₀ = 0,4              and    Hₐ  < 0,4   ( Alternative hipotesis)

From a random sample of 700 employes 305 are determined to earn more than $ 50000

Proportion                    pₐ = 305/700 = 0,4357     pₐ  = 0,4357

proportions are p = 0.4  and q = 0,6

We will asume a confidence level of 95 % hence α=  1-0,95     α = 0,05

so from z table we find z(c) = 1,64

Therefore we must calculate our z(p) = ( pₐ-p₀) ÷√(p*q)/n

Calculating   z(p)  =  0,0357 /0,01851   ⇒  z(p) 1.9286

Our test is one of the form  Hₐ <  ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀

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The ratio of a new-second to an ordinary second regarding the values given is 125 : 108

The term ratio refers to a comparison of two or more numbers. ratio sometimes appear in the form x : y and is this is said to be x is to y

In the question, converting the units of days, hours, and minutes to seconds we have

= 1 day * 24 hours * 60 minutes * 60 seconds

= 86400

converting the units of days, new-hours, and new-minutes to new-seconds we have

= 1 day * 10 new-hours * 100 new-minutes * 100 new-seconds

= 100 000

The ratio of the new-seconds to ordinary seconds is calculated by

= 100 000 : 86400

= 125 : 108 (in least form)

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Mathematically we write this as:

=362+(302×q)

The expression is 362+302q

Goodluck.

The expected value of the discrete distribution, for each case, is given as follows:

a) Amount won by one entry: $0.075.

b) If the cost is the cost of a postage stamp:  -$0.525.

The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.

In this problem, the distribution for the prizes is given as follows:

Hence the expected value for the prizes is:

E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.

The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:

0.075 - 0.6 = -$0.525.

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