The measure of angle STV is 80

The measure of angle STW is 45

The measure of angle WTV is x

Find the value of x

There are campers y = 650(676/650)^x.

The number of campers, y, x years after the camp opens, can be modeled using an exponential equation with the form y = a(b)x. Let's use x = 0 for the first year the camp was open (last year), and x = 1 for this year.

Then, we have:

y = a(b)^0 = 650 (when x = 0)

y = a(b)^1 = 676 (when x = 1)

These two points can be used to find the values of a and b.

We will first use the first equation to find a:

a = 650

Next, we'll use the second equation to solve for b:

676 = 650(b)^1

676/650 = (b)^1

b = 676/650

To describe the number of campers, an exponential equation of the type y = a(b)^x is needed.

y = 650(676/650)^x

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Answer:

Weight

Ant Team

Gorilla Team

Item

(in kilograms)

Empire State Building

no

no

Mount Everest

no

yes

Mount McKinley

no

no

Washington Monument

yes

yes

The inverse of the the matrix A is  |1/8 0 0 |

                                                          |0 1/8 0 |

                                                          |0 0 1/8|

To find the inverse of the matrix by using Cayley-Hamilton Theorem, we need to find the characteristic polynomial of the matrix first.

The characteristic polynomial of the matrix A is given by:

|λ-1 0 0 |

|0 λ-1 -1 | = (λ - 1)^2 (λ - 2)

|0 -2 λ-4|

Next, we need to evaluate the inverse of A using the Cayley-Hamilton Theorem, which states that a matrix A satisfies its own characteristic polynomial.

That is,

A^3 - 7A^2 + 14A - 8I = 0

Multiplying both sides by A^(-1), we get

A^2 - 7A + 14I - 8A^(-1) = 0

Rearranging, we get

A^(-1) = 1/8(A^2 - 7A + 14I)

Substituting the matrix A, we get

A^(-1) = 1/8

|1 0 0| |1 0 0| |14 -7 0|

|0 1 1| x (-2 1 0) + |-4 2 0|

|0 -2 4| |0 -2 4| | 0 0 8|

= 1/8

|1 0 0|

|0 1 0|

|0 0 1|

Therefore, the inverse of the matrix A is

A^(-1) =

|1/8 0 0 |

|0 1/8 0 |

|0 0 1/8|

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Comparing with  y = ? x+ ?  this equation we get the first value is 2.50 and the second value is 8

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal ('=') sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

A bike rental costs $2.50 per hour plus a fee for renting a helmet, which is required. The total cost

of renting a bike for 2 hours (h) is $13.

If it rented for 2 hours then rental costs will be $(2×2.50)= $5

Let the number of hours be x

Then the equation will be

y= 2.50x+8 --------(1)

As the total cost is $13

c= 8 [as 13- 5 =8]

Hence, comparing with  y = ? x+ ? we get the first value is 2.50 and the second value is 8.

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Therefore, The dilated triangle △K'L'M' is similar to the original triangle △KLM, but it is three times larger and centered at the origin.

To graph the image of △KLM after a dilation with a scale factor of 3 centered at the origin, we can simply multiply the coordinates of each vertex by 3.

Assuming that the coordinates of the original triangle △KLM are  [tex]K(1,1), L(3,2),[/tex] and  [tex]M(2,4),[/tex] the coordinates of the dilated triangle △K'L'M' are:

[tex]K' = (3(1), 3(1)) = (3, 3)[/tex]

[tex]L' = (3(3), 3(2)) = (9, 6)[/tex]

[tex]M' = (3(2), 3(4)) = (6, 12)[/tex]

We can plot these new vertices on a coordinate plane to get the graph of the dilated triangle △K'L'M'.

Therefore, The dilated triangle △K'L'M' is similar to the original triangle △KLM, but it is three times larger and centered at the origin.

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The calculated previous population of the city was 42,500.

Let's denote the previous population as "x".

According to the problem, the current population is 28% less than the previous population, which can be represented as:

x - 0.28x = 30,600

Simplifying and solving for x, we have:

0.72x = 30,600

Divide by 0.72

x = 30,600 / 0.72

x = 42,500

Therefore, the previous population was 42,500.

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Note that the multiplier in this scenario is 2.

To calculate the multiplier in this scenario, we need to use the formula:

Multiplier = ΔY / ΔE

where ΔY is the change in income and ΔE is the change in expenditure.

Here, we have two expenditure functions:

E¹ = 30 + 0.5Y

Eo = 20 + 0.5Y

To calculate the multiplier, we need to find the change in expenditure for a given change in income.

Let's assume that income increases by $1. In that case:

With E¹ function, expenditure increases by:

E¹(Y+1) - E¹(Y) = (30 + 0.5(Y+1)) - (30 + 0.5Y) = 0.5

With Eo function, expenditure increases by:

Eo(Y+1) - Eo(Y) = (20 + 0.5(Y+1)) - (20 + 0.5Y) = 0.5

Therefore, for a $1 increase in income, expenditure increases by $0.5 in both cases.

Now, we can calculate the multiplier:

Multiplier = ΔY / ΔE = 1 / 0.5 = 2

Therefore, the multiplier in this scenario is 2.

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8. y=3(x-1)² +2 can be written in standard form as y = 3x² - 6x + 5.  9. y=-4(x+6)²-4 can be written in standard form as y = -4x² - 48x - 148. 10. x=2(y+3)²-5 can be written in standard form as 2(y+3)² = x + 5.

A parabola is a two-dimensional geometric shape that is symmetrical around a vertical or horizontal axis. It is a type of conic section, which is formed by the intersection of a plane and a right circular cone. When the plane intersects the cone at an angle that is parallel to one of the sides, a parabola is formed.

A parabola is defined by a quadratic equation of the form y = ax² + bx + c, where "a" is a non-zero constant that determines the shape of the curve, "b" is the linear coefficient, and "c" is the constant term. The vertex of the parabola is located at the point (-b/2a, c - b²/4a), and the axis of symmetry is a vertical or horizontal line that passes through the vertex.

The shape of a parabola depends on the value of "a." If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The vertex of the parabola is the maximum or minimum point of the curve, depending on the direction of the opening. Parabolas are commonly used in physics and engineering to model the trajectory of projectiles, as well as in optics to describe the shape of mirrors and lenses.

8. y=3(x-1)² +2 can be written in standard form as y = 3x² - 6x + 5.

9. y=-4(x+6)²-4 can be written in standard form as y = -4x² - 48x - 148.

10. x=2(y+3)²-5 can be written in standard form as 2(y+3)² = x + 5, which simplifies to (y+3)² = (1/2)(x+5).

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Angle 1 and angle 3 are vertically opposite angles.

We know that :

▪︎ Vertically opposite angles are always equal.

Which means :

Angle 1 = Angle 3

Thus, the measure of angle 3 = 70°

▪︎Therefore, the correct option is (I) 70

Therefore, we can expect Greg and Meg to sell about 122 lemonades in a day, given that there is a chance the temperature will be over 90 degrees Fahrenheit. However, this is just an estimate.

To determine the expected number of lemonades Greg and Meg will sell in a day, we need to use the concept of conditional probability.

Let A be the event that the temperature is over 90 degrees Fahrenheit, and let B be the event that Greg and Meg sell lemonades in a day. We want to find P(B), the probability that they sell lemonades in a day, given that there is a chance the temperature will be over 90 degrees Fahrenheit.

We can use Bayes' theorem to express P(B) in terms of P(A) and P(B|A), the probability that they sell lemonades in a day given that the temperature is over 90 degrees Fahrenheit:

P(B) = P(A) * P(B|A) + P(not A) * P(B|not A)

where P(not A) is the probability that the temperature is not over 90 degrees Fahrenheit.

From the problem statement, we know that P(A) = the chance the temperature this week will be over 90 degrees Fahrenheit, and P(B|A) = 175, the number of lemonades they sell when the temperature is over 90 degrees Fahrenheit.

We don't have information about P(B|not A), the number of lemonades they sell when the temperature is not over 90 degrees Fahrenheit. But we can assume that it is some number less than 175, since the hotter weather tends to increase the demand for lemonade.

Assuming that P(B|not A) = 100, we can estimate P(not A) as follows:

[tex]P(not A) = 1 - P(A)[/tex]

Let's say that the chance of the temperature being over 90 degrees Fahrenheit this week is 0.3 (or 30%). Then:

[tex]P(A) = 0.3[/tex]

[tex]P(not A) = 0.7[/tex]

[tex]P(B|A) = 175[/tex]

[tex]P(B|not A) = 100 (assumption)[/tex]

Using these values in Bayes' theorem, we get:

[tex]P(B) = 0.3 * 175 + 0.7 * 100[/tex]

[tex]= 122.5[/tex]

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The period of the function f ( x ) = 4 sec ( π /2 ( x + 3 ) ) is π/2 and the horizontal shift is 3 units.

A periodic function is a function that repeats itself over an interval. In this case, the function is periodic because it is a sine or cosine function.  

The period and horizontal shift of the function

f ( x ) = 4 sec ( π /2 ( x + 3 ) ) can be found by examining the shape of the graph.

In order to determine the period, we must first identify the function's periodicity.

The horizontal shift of the function is determined by examining the graph of the function. A horizontal shift is the amount the graph is shifted to the left or right.

The period of the function f ( x ) = 4 sec ( π /2 ( x + 3 ) ) is π/2 and the horizontal shift is 3 units.

This can be seen in the graph of the function. The period can be determined by finding the distance between two points on the graph where the function repeats itself. The horizontal shift can be determined by finding the distance between the x-axis and the point where the function crosses the x-axis.

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Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

Step-by-step explanation:

first we need to find how many square metres of aluminum we need to make 1 mailbox. to find the surface area of the mailbox we seperate it into the bottom cube and the top cylindir. the bottom cubes surface area is

[tex]0.55 \times 0.3 + 0.3 \times 0.4 \times 2 + 0.55 \times 0.4 \times 2 = 0.165 + 0.24 + 0.44 = {0.845m}^{2} [/tex]

the top half cylindirs surface area is

[tex]( {0.3}^{2} \times 3.14 \div 2 \times 2) + (0.3 \times 3.14 \times 0.55 = {0.2826m}^{2} + {0.5181m}^{2} = {0.8007m}^{2} [/tex]

then add both of them together and its

[tex] {0.8007m}^{2} + {0.845m}^{2} = {1.6457m}^{2} [/tex]

then multiply that by 1927 and its

[tex]1927 \times {1.6457m}^{2} = {3171.2639m}^{2} [/tex]

round that up to 3171m squared.

Answer:

2264 m²

Step-by-step explanation:

To calculate the total amount of aluminium needed to make the mailboxes, multiply the surface area of one mailbox by the total number of mailboxes.

The surface area of one mailbox is made up of the following areas:

Calculate the areas:

[tex]\begin{aligned}\textsf{Area of the rectangular base}&=0.3 \times 0.55\\&= 0.165\; \sf m^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area of the 2 smaller rectangular sides}&=2(0.3 \times 0.4)\\&=2 \times 0.12\\&= 0.24 \; \sf m^2 \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area of the 2 larger rectangular sides}&=2(0.55 \times 0.4)\\&=2 \times 0.22\\&= 0.44 \; \sf m^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area of the 2 half circular ends}&=\pi r^2\\& = 3.14 \times 0.15^2\\&=3.14 \times 0.0225\\& = 0.07065 \; \sf m^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area of half the curved area of a cylinder}&=\pi rh\\&= 3.14 \times 0.15 \times 0.55\\&=0.471 \times0.55\\& = 0.25905 \; \sf m^2\end{aligned}[/tex]

Sum the areas to find the total surface area of one aluminium mailbox:

[tex]\begin{aligned}\textsf{Total S.A. of one mailbox}&= 0.165 + 0.24 + 0.44 + 0.07065 + 0.25905\\& = 1.1747 \; \sf m^2\end{aligned}[/tex]

Finally, to calculate the total amount of aluminium needed to make 1927 mailboxes, multiply the surface area of one mailbox by 1927:

[tex]\begin{aligned}\textsf{Aluminium needed to make 1927 mailboxes}&= \textsf{S.A. of one mailbox} \times 1927\\&=1.1747 \times 1927\\&= 2263.6469\\&= 2264 \; \sf m^2\end{aligned}[/tex]

Therefore, 2264 square meters of aluminium will be needed to make 1927 mailboxes (rounded up to the next square meter).

Answer:

the answer is

[tex] {13.5cm}^{2} [/tex]

The pattern that is formed that makes it always true is that the patterns were formed from triangles that are upside down as well as the use of Sierpiński triangle and lastly, with the use of black and white fillings.

The pattern of the Sierpiński triangle is one that comes up as a result of repeatedly removing certain triangles from an original equilateral triangle.

The Sierpiński triangle is known to be a kind of self-similar fractal equilateral triangle that is known to be made up of smaller equilateral triangles.

Note that It is a basic example of a mathematically generated pattern that can be reproduced at any magnification. It was named after Polish mathematician Wacław Sierpiński, but pre-dates his work as a decorative pattern.

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Answer:

Brand X

Step-by-step explanation:

Brand X has 4mL of vinegar for every 20mL of water:

We can put this as 4/20=1/5=20%

Brand Y has 5mL of vinegar for every 30mL of water

We can put this as 5/30=1/6=16.6%

Step-by-step explanation:

after the first year its 10000÷100*8+10000=10800. after the second year its 10800÷100*8+10800=11664. after the third year its 11664÷100*8+11664=12597.12. and after the fourth year its 12597.12÷100*8+12597.12=13,604.8896$. If you want you can round it up to 13,605$

The measure the length of BC is 9.23 cm.

Given that a triangle ABC has side AB = 7 cm, ∠A = 95°, ∠B = 36° we need to find the measure of the side BC,

Using the angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

∴ 95° + 36° + ∠C = 180°

∠C = 49°

Now, using the sine law for triangle,

AB / Sin C = BC / Sin A = AC / Sin B

∴ AB / Sin C = BC / Sin A

7 / Sin 49° = BC / Sin 95°

BC = 9.23

Hence, the measure the length of BC is 9.23 cm.

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Considering the information, the mean number of books read is approximately 3.06 books.

We need to calculate the sum of the number of books read by each student and divide it by the total number of students:

Therefore, mean, also known as the average, is a measure of central tendency that represents the sum of a set of values divided by the total number of values. In this case, we have a sample of 33 students, and we want to find the mean number of books they read. We can conclude that the mean number of books read is approximately 3.06 books.

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Answer:

≈ 63,4°

Step-by-step explanation:

Given:

A right triangle

AB = 2

BC = 1

Find: ∠C - ?

Use trigonometry:

[tex] \tan(∠c) = \frac{ab}{bc} [/tex]

[tex] \tan(∠c) = \frac{2}{1} = 2[/tex]

[tex] {tan}^{ - 1} (2) ≈63.4°[/tex]

An equation of the lines that pass through this pair of points (3,-5) and (2, -1) is equal to y = -4x + 7.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 + 5)/(2 - 3)

Slope (m) = 4/-1

Slope (m) = -4.

At data point (2, -1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = -4(x - 2)  

y + 1 = -4x + 8

y = -4x + 7

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Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.

Every day represents a trial in this binomial probability issue, and there are only two potential results:

either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.

The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.

We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:

P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹

where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:

(7 choose 6) = 7! / (6! * 1!) = 7

Plugging in the values, we get:

P(6 successes) = 7 * (1/6)⁶ * (5/6)¹

P(6 successes) ≈0.00012502

Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.

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The transformation rule used to create this image is (x, y) → (1/4x + 1, 3/8y + k)

A transformation in geometry is the process of altering a geometric shape or object's position, orientation, or size.

This transformation involves moving a shape from one place to another without altering its size, shape, or orientation. To put it another way, the entire shape is moved a specific amount in one direction

Here we have

A pre-image has coordinates B(8, 4), U(6, 10) and N(5, −2). The image has coordinates B’(2, 1), U’(1.5, 2.5) and N’(1.25, −0.5).

To find the transformation rule, identify the type of transformation that maps the pre-image coordinates to the image coordinates.

One way to do this is to find the changes in the x-coordinates and y-coordinates between the pre-image and image points.

Let's start with point B.

The x-coordinate has decreased from 8 to 2, and the y-coordinate has decreased from 4 to 1.5.

This implies that there has been horizontal compression and vertical compression.

Here the x-coordinate has been compressed by a factor of 2/8 = 1/4, and the y-coordinate has been compressed by a factor of 1.5/4 = 3/8.

So, the transformation rule for point B is:

=> B(x, y) → B'(1/4x, 3/8y)

Using the same method for points U and N, we can find the transformation rules for those points:

U(x, y) → U'(1/4x, 3/8y + 7/8)

N(x, y) → N'(1/4x + 1, 3/8y - 1/4)

So, the overall transformation rule is:

(x, y) → (1/4x + 1, 3/8y + k)

where k is a constant that depends on the particular point being transformed.  

Therefore,

The transformation rule used to create this image is

(x, y) → (1/4x + 1, 3/8y + k)

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Answer:

Step-by-step explanation:

Kaylee held 1000 shares after the split. The post-split price per share was $17.06.

Explanation:

Before the split, Kaylee held 500 shares of the stock, and each share was worth $34.12. So, her total investment was 500 x $34.12 = $17,060.

After the 2-for-1 split, each share is split into 2 shares. So, the total number of shares she holds becomes 500 x 2 = 1000.

To find the post-split price per share, we divide the pre-split price by 2.

Post-split price per share = $34.12 / 2 = $17.06.

Answer:

Step-by-step explanation:

Among the roles in the digital media production team, the creative director is in charge of overseeing the creative element.

Step-by-step explanation:

[tex]( {2x}^{3} - {6x}^{2} + x - 8) - ( {2x}^{3} + 6x - 4) = - 12x - 4[/tex]

so the second polynomial is -12x-4

The inverse of the function f(x) = 9x^2 - 12, x≥0 is q(x) = (√[x + 12])/3

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

f(x) = 9x^2 - 12, x≥0

Replace f(x) with y

So, we have

y = 9x^2 - 12

Swap x and y

x = 9y^2 - 12

So, we have

9y^2 = x + 12

Divide by 9

y^2 = (x + 12)/9

Take the square roots of both sides

y = (√[x + 12])/3

Hence, the inverse function is

q(x) = (√[x + 12])/3

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Complete question

if the domain of the function,f, is restricted to x≥0, which function is the inverse of f? the function is f(x) = 9x^2 - 12, x≥0. A. p(x)=√z-12/9 B. q(x)=√x+12/9. C. h(x)=√x-12/3. D. g(x)=√x+12/3

we must round up to a whole number, we need to purchase 4 cases of cantaloupe.

How to solve?

First, we need to calculate how many pounds of cantaloupe are needed in total:

184 guests ×0.5 pounds per guest = 92 pounds of cantaloupe

Next, we need to determine how many cantaloupes are needed. Since the average cantaloupe weighs 2 pounds, we can divide the total pounds of cantaloupe needed by the weight of one cantaloupe:

92 pounds of cantaloupe / 2 pounds per cantaloupe = 46 cantaloupes

Finally, we need to figure out how many cases of cantaloupe to purchase, given that they come 12 to a case:

46 cantaloupes / 12 cantaloupes per case = 3.83 cases

Since we must round up to a whole number, we need to purchase 4 cases of cantaloupe.

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The answer of the given question based on the Expression is , the answer is C. 81x* - 216x3 + 216x2y2 - 96xy3 + 16y*.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that represents a value or a mathematical relationship. Expressions can be as simple as a single number or variable, or as complex as a combination of several variables and operations.

To expand the expression (3x - 2y), we need to distribute the terms in the parentheses to get:

(3x - 2y) = 3x - 2y

Now, to expand the expression (3x - 2y)*, we need to multiply the expression (3x - 2y) by its conjugate, which is (3x + 2y):

(3x - 2y)*(3x + 2y) = 9x² - 6xy + 6xy - 4y²

Simplifying this expression, we get:

(3x - 2y)*(3x + 2y) = 9x² - 4y²

Therefore, the answer is C. 81x* - 216x3 + 216x2y2 - 96xy3 + 16y*.

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The expression used to determine the answer to the question is

[tex]81x^*-216x^3+216x^2y^2-96xy^3+16y^*[/tex]. option (c) is correct.

An expression in mathematics is a group of digits, variables, and mathematical operations that denotes a number or a mathematical relationship.

Expressions can range in complexity from being as simple as a single variable or number to being a complicated combination of numerous variables and actions.

By distributing the terms in the brackets, we can broaden the expression (3x - 2y) to obtain:

(3x - 2y) = 3x - 2y

We must now multiply the expression (3x - 2y)* in order to extend it

(3x - 2y) by its conjugate, which is (3x + 2y):

(3x - 2y)*(3x + 2y) = 9x² - 6xy + 6xy - 4y²

If we condense this phrase, we get:

(3x - 2y)*(3x + 2y) = 9x² - 4y²

Therefore, the answer is C. [tex]81x^*-216x^3+216x^2y^2-96xy^3+16y^*[/tex].

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