A theater has 41 rows of seats. If there are 22 seats in the 1st row, 26 in the 2nd row, 30 in the 3rd row . How many seats are there in total? Show and explain all work.

The measure of ∠XYZ is 112° if WXYZ is a rhombus.

A quadrilateral with four equal-length sides is known as a rhombus in plane Euclidean geometry (plural rhombi or rhombuses). Another term for this shape is an equilateral quadrilateral since all of its sides are equal in length. The rhombus is frequently referred to as a "diamond" after the diamonds suit in playing cards, which resembles the projection of an octahedral diamond.

Every rhombus is straightforward (does not self-intersect), and it is a particular instance of a parallelogram and a kite. Right-angled rhombuses are called square.

A rhombus's diagonals cut through two opposing angles:

∠YWZ=∠WYZ

Now, we have to substitute ∠YWZ=56° into ∠YWZ=∠WYX: 56°=∠WYX

We have to calculate 56°=∠WYX:∠WYX=56°

The angle addition postulate is, ∠XYZ=∠WYX+∠WYZ

Now, substitute ∠WYZ=56°, ∠WYX=56° into ∠XYZ=∠WYX+∠WYZ

∠XYZ=56°+56°

∠XYZ=112°

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The value of side JK in the Rhombus JKLM is 3√41.

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape.

Given that,

JKLM is a rhombus,

And side MN = 15 and diagonal JL = 24,

Since, In rhombus diagonal bisects each other at equally at 90°.

Therefore, ∠JNK = 90°, and JN = JL/2 = 12

Also, NK =MN = 15

Use Pythagorean formula to find side JK,

JK² = JN² + NK²

      = (12)² + (15)²

      = 144 + 225

JK² = 369

JK  = 3√41

The required value of side JK is 3√41.

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The Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5.

What is trigonometric function ?

Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate degree angle of a triangle.

The difference in y values from max to min = 15. 15/2 = a
max cosine = 1, min cosine =-1
7.5 x 1 - 1.5 = 6
7.5x -1 -1.5 = -7.5-1.5= -9
h(x) = 7.5cos(bx+c) -1.5
now just get a period or frequency that matches the x coordinates 3 and 6.5 to get b and c
at (3,6) cosine = 1 to get a maximum value. cosine is at a max when cos(bx+c) = 1 and bx+c=0, 360, 720...
if x=3, then 3b +c=0 and c=-3b
for (6.5,-9) to be a minimum h value, then cos(6.5b+c) =-1 that happens when the angle = 180. +n360 for any integer n. 6.5b+c = 180
c= 180-6.5b
c=-3b
180-6.5b =-3b
add 6.5b to both sides to get
180= 3.5b
b = 180/3.5 = 51 1/7
c=-3b = -153 3/7
h(x) = 7.5cos(51.4x - 154.3)-1.5
hence , Formula for h(x) is 7.5cos(51.4x - 154.3)-1.5

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120 will be the shape of the sampling distribution.

Quantitative data's distribution shape may be characterized as having a logical order to the numbers and allowing for the identification of the "low" and "high" end values on the histogram's x-axis. Since qualitative data are not numerical, the distribution shape cannot be specified.

Given that,

Sample size of A, n = 200

Sample size of B, n = 100

Proportion of adults in district A = 60%

Proportion of adults in district B = 45%

In the sample size of 200, the number of adults that support a new ballot measure is:

= (60%) × 200

= 120

Those that oppose is:

= 200 -120

= 80

If 45% supports a new ballot measure in district B, then 55% do not support. The difference between those that support and do not support is:

(55% - 45%) × 100

= 10

Hence, the sampling distribution of p(A) and p(B) is approximately normal, because the number of success in district A is 120.

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The triangle congruency theorem which can be used to prove

â–³ ≅ â–³onp is  ASA (angle  side angle)

Let the triangles be ONP and GHL

The congruence theorem, which will demonstrate that "GHL" and "ONP ," are congruent is to be discovered.

As can be seen, side lengths GH of GHL and ON of ONP are equal.

Furthermore, we are informed that mONP = mHKJ.

Since line segments GK and JL connect to produce them, we can see that GHL is the vertical opposite angle of ONP . Therefore, using the vertical angles theorem, mONP  congruence mKHJ.

We can see that both triangles contain two congruent angles and one congruent included side; as a result,

GHL ONP by ASA congruence.

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Answer:

x=6

Step-by-step explanation:

4(x+5) =9x+4x-34

1. we can simplifying the right hand side by adding 9x+4x

this gives us

           4(x+5)=13x-34

2. we expand the brackets to get

           4x+20=13x-34

3. we take the x on one side in this case we will subtract 4x from each side and add 34 on each side to get

          54=9x

4. we divide each side by 9 because we want to find the value of x this gives us

         6=x

This data collection may be characterized as numerical and univariate.

What is numerical and univariate?

If the collection of all potential values for a numerical univariate data is finite or countably infinite, the data is discrete. Usually, discrete univariate data are used in counting (such as the number of books read by a person). If the range of all potential values is a set of numbers, then a numerical univariate data is continuous.

Categorical data:

Categorical variables represent different sorts of data that may be categorized. Race, sex, age group, and educational level are some examples of categorical variables.

Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data.

Numerical data refers to the data that is in the form of numbers, and not in any language or descriptive form. Also known as qualitative data as it qualifies data before classifying it.

Over here we have the data for the average time spent reading per day for students in an 8th grade class.

Average Time is a numerical data

Bivariate data deals with two variables univariate data, which is one variable data we have numerical data and one variables so its Numerical and univariate.

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The difference in the areas of the signals based on the information given is 549.5km².

The formula to calculate the area of a circle will be:

= πr²

where r = radius

Mast 1 broadcast radio signals that can be heard within a radius of 15km. The area will be:

= πr²

= 3.14 × 15²

= 706.5km²

Mast 2 broadcast radio signals that can be hear within a radius of 20km. The area will be:

= πr²

= 3.14 × 20²

= 1256km²

The difference in the areas will be:

= 1256km² - 706.5km²

= 549.5km²

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Complete question

Mast 1 broadcast radio signals that can be heard within a radius of 15km.

Mast 2 broadcast radio signals that can be hear within a radius of 20km.

Calculate the difference in the areas of the signals.

The sum of the fractions (- 3/5 + 1/5) in simplest form is - 11/20.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Are two proper fractions - 3/4 and - 1/5, and we are required to take the difference which is,

= - 3/4 - (- 1/5).

Now the negative signs will distribute to positive which is,

= - 3/4 + 1/5.

Now, the LCM of 4 and 5 is 20.

= {(-3×5) + (1×4)}/20.

= (- 15 + 4)/20.

= - 11/20.

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Answer:

The amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.

Step-by-step explanation:

What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the tanks at the Georgia Aquarium hold approximately 8.4 × 10⁶ gallons of water. The tanks at the Audubon Aquarium of the Americas hold about 400,000 gallons of water.The number of the time will be calculated as below:-= 8.4 × 10⁶ / 400,000= 20.1

Therefore, the amount of water at the Georgia Aquarium is 20 times greater than the aquarium of the Americas hold.To know more about an expression followbrainly.com/question/15772941#SPJ2

One tablet weighs will be 1.93 pounds.​

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 combined weight of 4 identical tablet computers and a 4 3-pound laptop is 10.7 pounds.

Now,

Let the weight of 1 tablet = x

So, We can formulate;

⇒ 4x + 3 = 10.7

Solve for x as;

⇒ 4x = 10.7 - 3

⇒ 4x = 7.7

⇒ x = 7.7 / 4

⇒ x = 1.93 pounds

Thus, One tablet weighs = 1.93 pounds.​

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Length of AB in the cuboid is 20.784cm.

There are 6 faces, 12 edges, and 8 vertices on a cuboid.

All of the cuboid's faces have rectangular shapes.

The cuboid's opposing edges are parallel to one another.

The three dimensions of a cube are length, width, and height.

All of the angles created at the cuboid's vertices are 90 degree angles.

Length of Diagonal of cuboid is [tex]\sqrt{a^2+b^2+c^2}[/tex], where a,b,c are side lengths of cuboid,

Given:

AG=24cm;

AB=2BC;

CG=6m;

We know that diagonal of cuboid length is [tex]\sqrt{a^2+b^2+c^2}[/tex]

Here

Let AB=a, BC=b, CG=c;

So a=2b;

Now  

[tex]AG=\sqrt{a^2+b^2+c^2}=\sqrt{(2b)^2+b^2+6^2}=\sqrt{ 5b^2+36 }=24\\5b^2+36=576\\5b^2=540\\b=10.392cm\\AB=a=2b=20.784cm[/tex]

Length of AB in the cuboid is 20.784cm.

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The correct matrix representation is [tex]\left[\begin{array}{ccc}2&3\\3&-1\\\end{array}\right][/tex]

We can represent a vector pointing at a point by its x coordinate, and y coordinate, and Let us say there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(2,3) and P₂(3,-1)

Thus by the coordinates of the two vectors, we can represent  the matrix  

[tex]\left[\begin{array}{ccc}2&3\\3&-1\\\end{array}\right][/tex]

Hence, Option D) is the correct answer.

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Answer:

x=125,2x=250

Step-by-step explanation:

A hexagon sum of angles is 720 degrees.

The sum of the hexagon's angles is 345+3x

345+3x=720

3x=375

x=125

2x=250

From the sampling distribution we know:

a. will become more variable as the sample size increases.

A sampling distribution is the probability distribution of a statistic that was acquired from more samples taken from a certain population. The distribution of frequencies for a variety of potential outcomes that could happen for a population statistic makes up the sampling distribution of a specific population.

When it comes to the spread of all sample proportions, theory predicts behaviour far more accurately than just stating that larger samples have a smaller spread. In actuality, the sample size, n, and the standard deviation of each sample proportion.

Thus, option (a) correctly describe about sampling distribution of the sample proportion.

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L= 97

Step-by-step explanation:

The perimeter is all of the sides of the rectangular pool added up. We know the both widths are gonna be 54m. So to find both widths together you need to multiply 54 by 2 to give us 108. The we need to find both lengths together, so subtracting 302-108 will get us 194. Both lengths together, 194,  divided by 2 is 97, which is our length.  

No, The given table is not in proportional.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table is,

 Width of photo                              Height of photo

      2                                                     3

      4                                                     6

      5                                                     7

      8                                                     10

Now,

Since, The table is,

 Width of photo                              Height of photo

      2                                                     3

      4                                                     6

      5                                                     7

      8                                                     10

So, By definition of proportional, we get;

⇒ Width /Height = 2 / 3

⇒ Width /Height = 4 / 6 = 2 / 3

⇒ Width /Height = 5 / 7

⇒ Width /Height = 8 / 10 = 4 / 5

Clearly, All the proportion are not in same ratio.

Thus, The given table is not in proportional.

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Answer:8

Step-by-step explanation: isaid it is

Option D is correct since the side opposite the larger angle is larger and you know that MN>NP, so the angle O's measure is more than the angle Q's measure.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here,

The side that is opposite to the greater angle is greater.

you know that MN>NP.

Then the measure of angle O is larger than the measure of the angle Q.

Because the side opposing the greater angle is larger and you know that MN>NP, option D is true. As a result, the measure of angle O is larger than the measure of angle Q.

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According to the exchange rates £1 = €1. 18, £1 = $1. 72 the job in New York will pay Salma the higher salary.

In mathematics, the term "more than" refers to an inequality between two values, quantities, or numbers, where one is greater than the other. In other terms, we say that A is more than B when A is greater in contrast to B.

A job in Milan offer €70,000 per year;

And exchange rate are:

£1 = €1. 18

so she will get

£=70,000x1. 18

£=82600

on other hand job in New York offer $102,900 per year. The exchange rate are:

£1 = $1. 72

so she will get

£= 102,900x1. 72

£=176988

So the job in New York will pay her higher salary.

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Answer:

All are rational except 47.444...

Answer:

x = 2

Step-by-step explanation:

-2x - 48 ≥ 10x - 24

-48 + 24 ≥ 10x + 2x

24 = 12x

x = 2

From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°

Basic properties of triangles are:

1)A triangle's (of all varieties) total sum of angles is 180°.

2)The length of a triangle's two longest sides added together is longer than the third side.

3)Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

4)The longest of a triangle's three sides is the side that faces the larger angle.

5)A triangle's exterior angle is always equal to the product of its inner and exterior opposite angles. The outer angle attribute of a triangle refers to this characteristic.

As sum of angles in a triangle is 180° and sum of angles on a line is also 180°, both the figures are related.

Sum of angles=180°;

[tex]50+B+65=180;\\B=65[/tex]

∠B=65°

Similarly angle 2 is also 65°

From Properties of Triangles , both figures are connected and angle ∠B or ∠2 is 65°

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Answer:

Step-by-step explanation:

3

After 5 years the value of the farmhouse would be $23675 more than the value of the farmhouse when it was built.

What is the exponential function?

The exponential function is a mathematical function denoted by [tex]f(x)=e^{x}[/tex]. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices or Lie algebras.

The value of a farmhouse, in dollars, x years from the year it was built can be predicted by the function

               [tex]g (x) = 65500(1.05)^x[/tex]

Now the given table shows that the value of the farmhouse over the years

Now the value of the farmhouse when it was built = $70000

Now after 5 years, the cost would be

                [tex]g(x) = 65500(1.05)^x\\\\g(5)=65500(1.05)^5\\\\g(5) = 93675\\[/tex]

Now the difference would be = 93675 - 70000

                                                 = $23675.

Hence, After 5 years the value of the farmhouse would be $23675 more than the value of the farmhouse when it was built.

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The total number of pairs sold by SoccerWorld is 57

How to determine the total number of pairs sold by SoccerWorld?

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

SoccerWorld sold 3 as many boots as JP Sports

DirectSportz sold 5 more boots than JP Sports.

Cost of each pair = £70

Amount in sales = £7000

The above parameters means that

s = 3j

d = 5 + j

70(s + d + j) = 7000

Where

j = JP Sports

s = SoccerWorld

d = DirectSportz

Divide both sides of 70(s + d + j) = 7000 by 70

s + d + j = 100

Substitute s = 3j and d = 5 + j

3j + 5 + j + j = 100

Evaluate the like terms

5j = 95

Divide by 5

j = 19

Substitute j = 19 in s = 3j

s = 3 * 19

So, we have

s = 57

Hence, the number of pairs is 57

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Hello,

I hope you and your family are doing well!

The polynomial x^3-13x^2+25x+50 can be factored as (x+5)(x-5)(x+10).

The polynomial x^4+7x^3+13x^2+6x-45 can be factored as (x+5)(x-5)(x+3)(x-3).

So the correct match is:

(x+5) - x^3-13x^2+25x+50

(x-5) - x^3-13x^2+25x+50

(x+10) - x^3-13x^2+25x+50

(x-10) - x^4+7x^3+13x^2+6x-45

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Happy Holidays!

The value of y is 54 when x = -2

The value of y is 18 when x = -1.

The value of y is 6 when x = 0.

The value of y is 2 when x = 1.

The value of y is 2/3 when x = 2.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is

y = 6(⅓)^x

To find the value at x = -2, -1, 0, 1, 2, put the value of x in the given equation.

Putting x = -2 in the equation y = 6(⅓)^x

y = 6(⅓)⁻²

Applying index formula (1/a)^(-m) = a^m

y = 6(3)²

y = 6 × 9

y = 54

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁻¹

Applying index formula (1/a)^(-m) = a^m

y = 6(3)¹

y = 6 × 3

y = 18

Putting x = -1 in the equation y = 6(⅓)^x

y = 6(⅓)⁰

Applying a⁰ = 1

y = 6 × 1

y = 6

Putting x = 1 in the equation y = 6(⅓)^x

y = 6(⅓)¹

y = 6 × 1 /3

y = 2

Putting x = 2 in the equation y = 6(⅓)^x

y = 6(⅓)²

y = 6 × (1/9)

y = 6/9

Divide the denominator and numerator by 3:

y = 2/3

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Total number of seats for the center aisle z  = 400 + 10x + Y

The cafeteria would have a total of 3z = 1200 + 30 x + 3y chairs.

The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or full sum. In mathematics, adding two or more integers yields the sum. When you multiply 8 by 8, you get 16.

If z represents the total number of seats, then z=z1 + z2.

The equation for the first ten rows would be 10 (30 + x)= z1.

The equation for the final five rows would be 5 (20 + y) = z2.

Therefore, there would be z= z1+ z2  seats in the center aisle.

So total number of chairs in the middle aisle would be

z= z1+ z2

z= 10 ( 30 + x)+5 ( 20 + y)

z= 300 + 10x + 100 + y

z= 400 + 10x + y

The total number of chairs in the cafeteria would be z +z +z ( for the 3 aisle right , middle and left)

3z = 3(400 + 10x + y)

3z= 1200 + 30 x+ 3y

Total number of seats for the center aisle z  = 400 + 10x + Y

The cafeteria would have a total of 3z = 1200 + 30 x + 3y chairs.

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In order to increase the likelihood that a blue marble would be drawn at random to 3/4, we must thus add 32 more blue marbles.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Here,

Let the number of blue marbles added be x,

Probability=3/4

Total marbles=20

Number of blue marbles=7

(7+x)/(20+x)=3/4

4(7+x)=3(20+x)

28+4x=60+3x

x=60-28

x=32

So, we need to add 32 more blue marbles to make the probability of randomly drawing a blue marble be 3/4.

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