A middle school took all of its 6th-grade students on a field trip to see a ballet at a theater that has 1500 seats. The students filled 1320 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?

The solution of the given equation is, y = -3.

what is solving an equation?

An effective method for solving linear equations can be found in the steps that follow. By deleting parentheses and combining like terms, each side of the equation can be made simpler. The variable term on one side of the equation can be separated using addition or subtraction. To find the variable, use multiplication or division.

Consider, the given equation

[tex]\frac{y}{y}-5 + \frac{5}{5}-y =0[/tex]

Since, If a/a then it is 1.

⇒ 1 - 5 + 1 - y = 0

-3 - y = 0

Add y on both sides,

-3 - y + y = 0 + y

-3 = y

y = -3

Hence, the solution of the given equation is, y = -3.

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Answer:

The perimeter of the quadrilateral is the sum of the four side lengths. If the perimeter is 92 feet, then we can write the equation $x + (x+2) + (x+4) + (x+6) = 92$, where $x$ is the length of the shortest side. Solving this equation, we find that $x = 20$. This means that the side lengths are 20 feet, 22 feet, 24 feet, and 26 feet, so the longest side is 26 feet.

(y2 - y1) / (x2 - x1) is the slope of the line passing through the points P1 x1 y1 and P2 x2 y2.

The slope of the line passing through the points P1 (x1, y1) and P2 (x2, y2) is calculated by: (y2 - y1) / (x2 - x1).

1. Subtract the y-coordinates of the two points: y2 - y1.

2. Subtract the x-coordinates of the two points: x2 - x1.

3. Divide the two results from steps 1 and 2: (y2 - y1) / (x2 - x1).

For example, if the two points are P1 (1, 5) and P2 (3, 8), then the slope is calculated by: (8 - 5) / (3 - 1) = 3 / 2 = 1.5. This means that the line has a slope of 1.5, which means that for every 1 unit increase in x, the y-coordinate increases by 1.5 units. So, for every 2 units increase in x, the y-coordinate increases by 3 units.

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The number of possible outcomes when she spins and flips a coin is 8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of sections in the spinner = 4.

The number of possible outcomes in the coin = 2

Now,

The number of possible outcomes when she spins and flips a coin.

= 4 x 2

= 8

i.e

{Red, Green, Blue, Orange} x {H, T}

{Red:H, Red:T, Green:H, Green:T, Blue:H, Blue:T, Orange:H, Orange:T}

______(A)

Thus,

The number of possible outcomes from (A) is 8.

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Step-by-step explanation:

16-5= 11

hope it's helpful

Bubble cost = $1.49

Beach ball cost = $2.00

Sand bucket cost = $3.50

Bubble = B

Beach Ball = A

Sand bucket = S

total cost = 6B + 2A + 3S

total cost = 6(1.49) + 2(2) + 3(3.5) = 23.44

Hope this helps :)

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- Jeron

The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

3, 5, 7, 9, 11, ...

The first term is 3. And the common difference is given as,

d = 5 - 3

d = 2

Then the position in the sequence for the given sequence will be given as,

aₙ = 3 + (n - 1) · 2

aₙ = 3 + 2n - 2

aₙ = 1 + 2n

The position in the sequence for the given sequence will be 2n + 1. Then the correct option is C.

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The formula for the exponential function is V = 5000 (2)^(−t/4).

What is an exponential function?

A function whose value is a constant raised to the power of an argument is called an exponential function.

Here, we have

The value of an item initially worth $5000 loses half its value every 5 years.

V = V₀eˣⁿ

At t = 0,V = V₀

So, V = 5000eˣⁿ

At t = 4,V = V₀/2 = 2500

Substituting these into our equation, we have

5000e^(4k) = 2500

e^(4k) = 12

4k = −ln2

k = −ln2/4

Finally, we have our equation

V = 5000e^(−tln2/4 )

V = 5000(e^ln2)^(−t/4)

V = 5000 (2)^(−t/4)

Hence, the formula for the exponential function is V = 5000 (2)^(−t/4).

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By studying the graph, it can be concluded that

Todd has done three mistakes

He has y increasing when x is between -5 and 0 instead of decreasing.

He has y decreasing when x is between 0 and 5 instead of increasing.

He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.

What is graph of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of points of the form (x, f(x))

Original specifications of the graph

y is decreasing when x is between -5 and 0

y is increasing when x is between 0 and 5

The relationship between x and y is non-linear from x = - 5 to x = 0

The relationship between x and y is linear from x = 0 to x = 5

From the graph it can be seen that Todd has done three mistakes

He has y increasing when x is between -5 and 0 instead of decreasing.

He has y decreasing when x is between 0 and 5 instead of increasing.

He has a non-linear relationship from x = 0 to 5 instead of a linear relationship.

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The Volume of the Pyramid=19.19in³

Surface Area of  the Pyramid=48.65in²

Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.

First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers. Calculating the volume of numerous common three-dimensional forms is made simple by arithmetic formulas. The volumes of increasingly complicated shapes can be calculated using integral calculus.

Given that,

Height of the pyramid =4.7

Pyramid's slant height= 5.2

Base of pyramid is a square with side=3.5

Volume of the pyramid=(1/3)(3.5×3.5)×(4.7)

=19.19 in³

The surface area of a pyramid=((1/2)×(4×3.5)×5.2)+(3.5×3.5)

=18.65in²

Therefore, the volume of the pyramid=19.19 in³

And the surface area of the pyramid=18.65in²

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The value of all the missing angles in the triangles are;

∠1 = 37°

∠6 = 30°

∠4 = 63°

∠3 = 133°

We know that the sum of angles in a triangle is equal to 180 degrees. Thus, with this knowledge, we can find the angles 1 and 6.

Therefore;

∠1 = 180 - (70 + 73)

∠1 = 180 - 143

∠1 = 37°

∠6 = 180° - (107° + 43°)

∠6 = 180° - 150°

∠6 = 30°

Now, we know that sum of angles on a straight line is 180 degrees. Thus, we can find angle 4 as follows;

∠4 = 180° - (65° + 42°)

∠4 = 180° - 117°

∠4 = 63°

∠3 = 90 + 43

∠3 = 133°

Thus, the conclusion is that the missing angles are ∠1 = 37°, ∠6 = 30°, ∠4 = 63°, ∠3 = 133°

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A linear function can only have one degree at most but the range of linear function is infinite.

In the given question, we have to explain what is the range of linear function.

A linear function can only have one degree at most. Therefore, it has at least most one x increased by one. The formula for them is f(x) = mx + b.

Nearly invariably, the domains and ranges of linear functions are infinite. When the graph is a horizontal line, there is an exception. This occurs when a function, like f(x) = b, equals a constant. These functions' domains are unlimited, but their range only contains the value b.

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Answer: 1. 2, 4, 8, 16, 32, 64,  and 128,...... I don't know if I should keep going.

2. 5, 11, 17, 23, 29, 35, 41, and 47

Answer: 2.

Step-by-step explanation:

11+3=14

14+3=17

17+3=20

20+3=23

2. 5,11,17,23

Answer:

2 inches

Step-by-step explanation:

volume of a cone: 1/3 π r^2 h

h = 12

1/3 π r^2 (12) = 16π

4πr^2 = 16π

r^2 = 16π/4π

r^2 = 4

r = 2

S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7), We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).

The link between lines and points is described by a graph, which is a mathematical description of a network.

The link between lines and points is described by a graph, which is a mathematical description of a network.

Plotting a graph based on the provided data is shown in the attachment.

Given, \s (x,y)=(x+7,y-9)

For example, S(-3,6)=S'(x+7,y-9)=S'(-3+7, 6-9)=S' (4,-3)

T(0, 7) = T' (x+7, y-9) = T' (0+7, 7-9) = T' (7,-2)

According to U(1,4)=U'(x+7,y-9)=U'(1+7, 4-9)=U' (8,-5)

Considering that V(-5,2)=V'(x+7,y-9)=V'(-5+7,2-9)=V' (2,-7)

To create the graph, we must plot the points S'(4,-3), T'(7,-2), U'(8,-5), and V'(2,-7).

S'(4,-3),T'(7,-2),U'(8,-5),V'(2,-7)

We must plot the graph using the above data for S(-3,6), T(0,7), U(1,4), and V(-52).

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Answer:

A, C, and E

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of [tex]\frac{1}{3}[/tex]

(- 3, 6 ) → ([tex]\frac{1}{3}[/tex] (- 3), [tex]\frac{1}{3}[/tex] (6) ) → (- 1, 2 )

Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data is a true statement.

Therefore, it is true that extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that outside the x-range.

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Answer:

To find out how much money is in Alex's account at the end of the week, we need to add up all of the transactions that he made over the course of the week.

We start by adding the initial amount that Alex had in his account before making any transactions, which is $170.42.

Then we add the first transaction, which is $50.73. This brings the total to $221.15.

Next, we add the second transaction, which is $114.13. This brings the total to $335.28.

Then we add the third transaction, which is $119.69. This brings the total to $455.97.

Finally, we add the fourth and last transaction, which is $226.71. This brings the total to $682.68.

Therefore, at the end of the week, Alex has $682.68 in his account.

Step-by-step explanation:

Answer: n+575= total

or n+575=t

Step-by-step explanation:

n is what we start with, plus what she has this year. the total is unknown.

The formula for the area of the trapezoid is A = 1/2(b₁ + b₂)h and the formula for height will be (2A)/(b₁ + b₂).

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

The area of a trapezoid is given as,

A = 1/2(b₁ + b₂)h

The formula for height h will be as,

A = 1/2(b₁ + b₂)h

h = (2A)/(b₁ + b₂)

Hence "The trapezoid's area is calculated using the calculation A = 1/2(b1 + b2)h, and its height is calculated using the formula (2A)/(b1 + b2).".

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The probability that Jeff wins exactly 1 prize is (3/4)³

According to the question,

A fast-food restaurant runs a promotion in which certain food items come with game pieces

Let the event of winning the game piece be A and x be the random variable for winning prize

So, Probability of Winning the game = P(A) = p = 1/4

Probability of not winning = q = 1 - 1/4

=> q = 3/4

Using Binomial distribution,

The Probability that he wins exactly 1 prize = P(x = 1)

=> P(x) = ⁿCₓ pˣ qⁿ⁻ˣ

Here, n = 4 , x = 1

P(1) = ⁴C₁ p¹ q³

=> 4 × (1/4)( 3/4)³

=> (3/4)³ is probability that jeff wins exactly 1 prize

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From the given combination, there are 280 ways to select a three-course meal.

What is the combination?

Combinations are ways of choosing things from a collection when the order of the choices does not matter. The number of selections is denoted by [tex]^{n} C_{r}[/tex] if you have to choose "r" items from "n" things.

Given, 7 appetizers, 10 entrees, and 4 desserts

To select a three-course meal, we will choose 1 item from each course.

i.e. 1 appetizer from 7 appetizers

AND

1 enter from 10 entrees

AND

1 dessert from 4 desserts

So, For appetizers, selections = [tex]^{7} C_{1}[/tex]

For entrees, selections = [tex]^{10} C_{1}[/tex]

For desserts, selections = [tex]^{4} C_{1}[/tex]

Total possibilities =  [tex]^{7} C_{1}[/tex] * [tex]^{10} C_{1}[/tex]* [tex]^{4} C_{1}[/tex] = 7*10*4 = 280

Hence, there are 280 ways to select a three-course meal.

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Homogeneity and additivity are the two conditions for a system to be linear.

A system is called Linear if it has two mathematical properties, homogeneity and additivity. If you can show that system has both properties, then you have proven that the system is linear.

Homogeneity means that a change in the input signal's amplitude results in a corresponding change in the output signal's amplitude.

Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same.

Additivity means signals added at the input produce signals that are added at the output.

The  value of a magnitude corresponding to a whole object is equal to the sum of the values of the magnitudes corresponding to its parts for any division of the object into parts.

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Answer:

No point,One Point.Reflex Angle Formed .

The number of times getting an even number on the top of dice if dice is rolled 600 times is 300.

We know that probability is defined as the division of number of favorable outcomes to the total number of outcomes.

Here, favorable outcomes are even number from 6 possible numbers and those are =2,4,6

So, favorable outcomes are={2,4,6)

So, count of favorable outcomes is 3

Total number of outcomes are ={1,2,3,4,5,6}

So, count of total number of outcomes are =6

Therefore, probability of getting an even number on top of dice is =number of favorable outcomes/total number of outcomes

=>P(E) = 3/6

=>P(E)=1/2

Now, dice is rolled 600 times and probability of getting even number is 1/2,so total number of times even number comes on topo of dice is =(1/2)×600=300.

Hence, even number appearance is 300.

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184,219,440 ways.

What is contestant?

A participant in a contest or competition is known as a contestant. A contestant is someone who challenges election results.

There are 570 contestants, and any one of them can win the first prize.

One of the remaining 569 people can receive the second prize.

Third may be assigned to any of the remaining 568.

We can accomplish this in 570*569*568 ways

= 184,219,440 ways.

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Answer:

t = 2

Step-by-step explanation:

First, we have to simplify the equation by multiplying 3 and -2 by everything in the corresponding parenthesis:

3(t+4) simplifies = 3t + 12

-2(2t+3) simplifies = -4t - 6

So:

3t + 12 - 4t - 6 = 4

Now we can combine like terms:

-t +6 = 4

Then we subtract 6 on both sides:

-t = -2

Then we divide by -1 in order to get rid of the negative:

t = 2, final answer.