1.
What is the area of this figure?

We have proved that the ray FE is parallel to the ray GC.

What is meant by parallel lines?

In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

Angle DEF intersects at B

which results in angle DEF corresponding to the angle  ACG.

As DEF = 45 so angle ACG = 45

So by the above discussion, we can say that the ray FE is parallel to the ray GC.

Hence, we have proved that the ray FE is parallel to the ray GC.

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Answer:

the answer is < explanation at the step by step

Step-by-step explanation:

Do the Basic equation

2.18 x 10 - 6= 15.8

4.36 x 10 - 7= 36.6

Answer:

[tex]x = \frac{26 + 8 \sqrt{10} }{9} [/tex]

or

[tex]x = \frac{26 - 8 \sqrt{10} }{9} [/tex]

Step-by-step explanation:

I apologise for my messy explanation.

The solution of the expression will be;

⇒ x = 5.7

or ⇒ x = 0.07

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Now,

Since, The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Solve as;

⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3

⇒ log ₂ (3x + 2) - log ₂ √(x) = 3

⇒ log ₂ (3x + 2) / (√x) = 3

⇒ (3x + 2) / √x = 2³

⇒ (3x + 2) / √x = 8

⇒ (3x + 2) = 8√x

Taking square both side, we get;

⇒ (3x + 2)² = (8√x)²

⇒ 9x² + 12x + 4 = 64x

⇒ 9x² + 12x - 64x + 4 = 0

⇒ 9x² - 52x + 4 = 0

By applying quadratic formula, we get;

⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9

⇒ x = 52 ± √ 2704 - 144 / 18

⇒ x = 52 ± √2560 / 18

⇒ x = 52 ± 50.6 / 18

This gives two solution as;

⇒ x = (52 + 50.6) / 18

⇒ x = 102.6/18

⇒ x = 5.7

And, We get;

⇒ x = 52 - 50.6 / 18

⇒ x = 1.4 / 18

⇒ x = 0.07

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Answer: x = 11

Step-by-step explanation: set both angles equal to 90 bc a triangle is 180 minus the 90 degree angle

The distance between  Bowtown to Dovebury is 39.

The total distance Dave will drive is 54 miles.

What is meaning of  total distance?

Total distance refers to the actual travel distance between the origin and destination locations of the material.

Given table is

Aranville

24                 Bowtown

37                        20           Cliffton

18                         39               17           Dovebury

From the table, the distance from Bowtown to Dovebury is 39miles.

The distance between Aranville to Cliffton is 37 miles.

The distance between Cliffton to Dovebury is 17 miles.

Dave wants to drive from Aranville to Cliffton and then from Cliffton to Dovebury.

Total distance is (37 + 17) miles = 54 miles

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The hypothesis, at the 0.05 significance level,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

we conclude p-Value > α so, cannot reject null hypothesis. The observed distribution of X may be fitted by the geometric distribution g(x ; 1 / 2), x=1,2,3

A coin is thrown until a head occurs and the number X of tosses recorded.

The probability that head occur on toss ,p = 0.5

Consider the null and alternative hypothesis,

H₀ : the observed distribution of X may be fitted by the geometric distribution

Hₐ : the observed distribution of X may not be fitted by the geometric distribution

The chi square test statistic here as:

χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

where Oᵢ--> observed value

Eᵢ --> expected value

and the expected frequencies for each X here E(x) = P(X = x) = 256×g(x)

The probability mass function of geometric distribution with parameter 1/2 is g(x) = (1/2)(1 - 1/2)⁽ˣ⁻¹⁾

where x = 0, 1,2 ,3,......

Observed values are f :136 60 34 12 9 1 3 1

Using the data,we calculate the expected values

E₁ = P( x = 1) = 256×g(1) = 256×(1/2)(1/2)⁰

= 128

E₂ = P( x =2) = 256×g(2) = 256×(1/2)(1/2)¹

= 64

E₃ = P( x = 3) = 256×g(3) = 256×(1/2)(1/2)² = 32

E₄ = P( x = 4) = 256×g(4) = 256×(1/2)(1/2)³

= 16

E₅ = P( x = 5) = 256×g(5) = 256×(1/2)(1/2)⁴

= 8

E₆ = P( x = 6) = 256×g(6) = 256×(1/2)(1/2)⁵

= 4

E₇ = P( x = 7) = 256×g(7) = 256×(1/2)(1/2)⁶

= 2

E₈ = P( x = 8) = 256×g(8) = 256×(1/2)(1/2)⁷

= 1

Hence, χ² = ∑( Oᵢ - Eᵢ)²/Eᵢ

= (136 - 128)²/128 + (60 - 64)²/64 + (34 - 32)²/32 + (12-16)²/16 +(9 - 8)²/8 + (1 - 4 )²/4 + (3 - 2)²/2 +(1 - 1)²/1

= 0.5 + 0.25 + 0.125 + 1 + 0.125 + 2.25 + 0.5 =4.75

Significance level is α =0.05

Using the χ² table, the p- value for χ² is 0.6290 .. Now P value > 0.05 , therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we have sufficient evidence here that the frequencies given are fitted by the geometric (p = 0.5) distribution.

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Answer:

84 copies

Step-by-step explanation:

18 copies: $6 ==> 18:6

18:6 ==> 18/6 = 3

18 copies: $6 = 3 copies: $1  ==> common ratio of copies to cost

3 copies: $1 =

(3 copies: $1)*28 =  ==> multiply by 28 to get the number of copies for $28

3*28 copies: $28 = 84 copies: $28

Answer: 84 copies

Answer:

(18 copies for $6 = x copies for $28)

18:6 = x:28

6x = 18(28)

6x = 504

x = 84 copies

Copies       |     Dollars

  18             |       $6

  84           |      $28

Step-by-step explanation:

The mean number of misprints per page on manuscript is 0.5 and If a page is selected then the probability that it has 3 misprints is 0.0126..

The Poisson distribution is a theoretical discrete probability, also known as the Poisson distribution probability mass function. It is used to find the probability that independent events occur at regular time intervals and have a constant average rate. λ is the Poisson rate parameter, the expected average number of events over a given time interval.

Using the Poisson distribution formula:

P(X = x) = (e-λ (λˣ) )/x!

where λ is mean number or poisson rate parameter ; x = 0, 1, 2, 3...

e is the Euler's number(e = 2.718)

We have given that,

Total number of Manuscript Pages = 400

total misprinted pages = 200

let X be random variable that the page is misprinted .

Mean number, λ = 200/400 = 0.5

the probability that it has 3 misprints, P(X= 3) = (e⁻⁰·⁵ (0.5)³ )/3!

= e⁻⁰·⁵ ( 0.125 )/6 =0.075816/6 = 0.0126

Hence, the required probability is 0.0126..

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Complete question:

Misprints on Manuscript Pages In a 400-page manuscript, there are 200 randomly distributed misprints Part 1 of 2 Find the mean number of misprints per page. Round the answer to one decimal place as needed. If a page is selected, find the probability that it has 3 misprints.

The values of the angles x, y, z are x=56°, y=124°, z=56°

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

From the given figure,

∠y=124°

∠x+124°=180°

∠x=180°-124°

∠x=56°

∠x=∠z=56°

Therefore, The values of the angles x, y, z are x=56°, y=124°, z=56°

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Therefore , the solution to the given problem of equation that the estimated rent comes out o be $1600.

The equivalent sign connects two expressions to form a mathematical statement known as an equation. An equation is, for instance, 2x - 5 = 15. By solving this equation, we can determine that the value of the variable x is 5.

Here,

In 2020, a one-bedroom apartment in New York City will cost $1600.

The formula for a straight line graph is often y = mx + c, where;

m = gradient

c is the vertical intercept.

With this knowledge, the graph clearly shows that the ideal line of fit for the data plot is y = 40x + 800.

This means that a one bedroom flat in New York City will cost; in the year 2020, which is 20 years after the year 2000;

y = 40(20) + 800 = $1600

Therefore , the solution to the given problem that the estimated rent comes out o be $1600.

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Answer:

Doing the math, it should be 7.25/1

The graph which correct shows an image and pre-image after reflecting across the line; y = -x as required in the task content is; Option 1.

It follows from the task content that the answer choice which correctly represents an image ajd pre-image after reflecting across the line; y = -x.

First it is noteworthy to know that the line; y = -x is one which passes through the origin and has a negative slope of; -1.

On this note, by observation; when the line y = -x is drawn; the graph which represents the image and pre-image after reflecting across the line; y = -x is; Option 1.

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Using the Leading Coefficient Test the end behavior of the function  f(x) = 1234999x as the values of x increase towards infinity, ∞ is the functin also tends to infinity

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = 1234999x

The end behavior is determined by the leading Coefficient = 1234999, the problem has only one variable and hence the leading coefficient

x ⇒ ∞ f(x) ⇒ ∞

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The equation is y = 15x + 90. The initial value is 90. Rate of change is: 15.

To host a party at a local restaurant, you must pay $90 to rent it and $15 per guest.

To write a linear equation that models a situation in slope-intercept form, y = mx + b, find the following:

Given the table above, the value of y when x = 0 is 90. This means the initial value (b) = 90.

Using two pairs of values from the table, (0, 90) and (6, 180):

Rate of change (m) = (180 - 90) / (6 - 0) = 15

Substitute m = 15 and b = 90 into y = mx + b, to write the equation:

y = 15x + 90.

The graph of y = 15x + 90 is shown below.

The complete table is:

x   |  y  

0    90

3    135

6    180

9    225

12   270

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Answer:

693.2

Step-by-step explanation:

6.932 · 100

Move the point two times to the right

693.2

Answer:

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 110.5° is added to the data, how does the mean change and by how much?

80.41 to 82.7

The mean increases by 2.7°.

The means stays at 80.4°.

The mean stays at 82.7°.

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 58° is changed to 101°, which of the following measures changes the most and what is the new value?

Mean 84°

Range 48°

IQR 32°

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 101° is added to the data, how does the mean change?

80.42 to 82

The mean decreases by 1.6°.

The mean decreases by 8.4°.

The mean increases by 8.4°.

Step-by-step explanation:

Assume the account earns 7% simple interest. in your account now. You would need to deposit $3,007.52 in your account.

1541 days = 4.2219 years

Hence,

Time = 4.2219 years

Interest rate = 7%

Principal = $4,000

Hence,

4000=Po(1+.07)^4.2219 years

4000=1.33×Po

Po = 4,000 /1.33

Po = $3,007.52

Therefore the amount you need to deposit is  $3,007.52.

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The perimeter of the rectangle 24x + 1 feet. The perimeter of a geometric figure is the total length of its sides.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

To find the perimeter of a rectangle, you need to add the lengths of all four sides of the rectangle.

The width of the rectangle is 4x-7.5 feet and the length is 7.5x+8 feet.

The perimeter is therefore equal to 2 times the sum of the width and the length,

= 2 * (4x-7.5 + 7.5x + 8) feet.

This simplifies to 2 * (12x + 0.5) feet,

which is equal to 24x + 1 feet.

The perimeter of the rectangle 24x + 1 feet

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Answer:

Step-by-step explanation:

You split it up into two 3-D triangles.

One of them has a volume of ((6*(5+5))/2)*8 = (60/2)*8=240

For the other one, you are missing a side on the 2-D face, so in order to apply pythagorean's theorem you need to split it into two more triangles. You know that 13^2=5^2+x^2    169-25=x^2         144=x^2  x=12

now that you know the missing side of the triangle you can recombine them. The volume of the remaining 3-D triangle is (((5+5)*12)/2)*8 = 60*8=480

480+240=720 meters cubed

Answer:

x = 6

Explanation:

If x is reserved for the number of hours it'll take, then the first equation is saying that $6 is being multiplied by an x amount of hours, which is then added by $30. The second equation states that $11 is being multiplied by an x amount of hours, but there is no flat fee. This makes the equation:

6x + 30 = 11x

The steps to solving this are:

1) Make the variables on one side. In this case, it is easier to put them on the right.

11x - 6x = 5x

5x = 30

2) Divide both sides by 5.

5x / 5 = 30 / 5

x = 6

This means it will take 6 hours for them to charge the same amount of money.

The fourth term of the recursive sequence in this problem is given as follows:

[tex]a_4 = 15[/tex]

The nth term of a recursive sequence is obtained applying the recursive rule n times, considering that the first term of the sequence is given.

The recursive rule for this problem is given as follows:

[tex]a_n = 2a_{n - 1} + 1[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 1[/tex]

Then the second term of the sequence is given as follows:

[tex]a_2 = 2(1) + 1 = 2 + 1 = 3[/tex]

The third term of the sequence is given as follows:

[tex]a_3 = 2(3) + 1 = 6 + 1 = 7[/tex]

The fourth term of the sequence is given as follows:

[tex]a_4 = 2(7) + 1 = 14 + 1 = 15[/tex]

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The equation of line that passes through point (-8, 1) and parallel to x - 4y = 4 is x - 4y + 12 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given equation is,

x - 4y = 4.

The slope of the given equation,

m = 1/4

The slope of the required line will be equal to given line if line is parallel.

The equation of line that passes through point (-8, 1) and parallel to line x - 4y = 4.

y - 1  = m (x - (-8))

y - 1 = 1/4.(x + 8)

4y - 4 = x + 8

x - 4y + 12 = 0

The required equation of line is x - 4y + 12 = 0.

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The sampling methods here that are not examples of simple random sampling are;

A) Select the first 10 people from a list of members.

B) Ask 10 members in the gym on a Monday morning

E) Select every 20th person from a list of members until she has 10 .

F) Ask all members of the gym

A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.

The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.

A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.

B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.

C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.

D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.

E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.

F) Ask all members of the gym; This is not random selection.

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The associative property states that the order in which three or more numbers are added or multiplied does not affect the result of the operation. You can apply the associative property to the expressions A. 9-5-2, B. 5+3-2, and D. 7+3+1.

In expression A, 9-5-2, you can rearrange the numbers as follows: 9-5-2 = (9-5)-2 = 4-2 = 2.

In expression B, 5+3-2, you can rearrange the numbers as follows: 5+3-2 = (5+3)-2 = 8-2 = 6.

In expression D, 7+3+1, you can rearrange the numbers as follows: 7+3+1 = (7+3)+1 = 10+1 = 11.

You cannot apply the associative property to expression C, 8÷4÷1, as this is a division expression, and the associative property does not apply to division.

Overall, the associative property allows you to rearrange the order of addition or multiplication of three or more numbers without affecting the result of the operation.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A mathematical principle that states the product of a multiplication issue is unaffected by the way the elements are organized.

The associative property for addition and multiplication is valid but not for division.

The expressions that you apply the associative property to will be (9 - 5 - 2), (5 + 3 - 2), and (7 + 3 + 1). Then the correct options are A, B, and D.

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David's three exam scores are B. 84, 88, 98

From the information, David took three exams. The median score of his exams was 88, the mean score was 90, and the range was 14.

The scores are 84, 88, and 98. The middle number is 88. It's the median.

The mean is:

= (84 + 88 + 98) / 3

= 270 / 3.

= 90

Range will be:

= Highest number - Lowest number

= 98 - 84

= 14

In conclusion, the correct option is B.

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Measure of angle AKQ is 90°.

There are several different kinds of angles in geometry. Angle is one of the most significant and fundamental units. When two rays or lines are connected at their common terminus, an angle is created. Angles are used in many facets of daily life, including the construction of buildings, dams, and statues, starting with a pizza slice. Angle has a crucial role in civil engineering. A pair of rays (half-lines) with a shared terminal are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Given

Measure of angle AKQ is 90°.

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The amount of money earned by Zach each week will be equal to $9 per week.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

Total amount earned by Zach = $36

The time taken to earn the amount = 4 weeks

Then, the amount earned each week will be.

= $36/4

= $9 per week

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Answer:

x = 9

Step-by-step explanation:

Use Vertical Angles and Supplementary Angles to put all the given information inside the triangle.

Then use the idea that the three angles in a triangle add up to 180° to write an equation.

see image.

Actually also--shortcut! The 150° is an exterior angle, so it is equal to the

90° + 5x+15

90 + 5x + 15 = 150

this calculation comes out the same as the other.

Answer:

  x = 9

Step-by-step explanation:

Given a right triangle with an exterior angle of 150°, and a vertical angle to the other acute angle marked as 5x+15, you want to solve for x.

The exterior angle is equal to the sum of the remote interior angles. One of those is the right angle; the other is a vertical angle with respect to the one marked 5x+15. So, we have ...

  150 = 90 + (5x +15)

  45 = 5x . . . . . subtract 105

  9 = x . . . . . . divide by 5

The value of x is 9.

Answer:

The inverse of f is x=8

Step-by-step explanation:

I did it