Elliott is standing 32 feet from the base of a tree. The angle of elevation measured from a point on the ground to the tops of the tree is 61 degrees. How tall is the tree? Round your answer to the nearest foot. Sketch a picture and show all of your work in the workspace for full credit.

By answering the above question, we may state that As a result, the equation antenna's height is roughly 25 metres.

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.  

draw a diagram of the situation

                B

                |

                | h

                |

   A------------C---------

   |          θ2|        θ1

   |            |

   |            | 16 m

   |            |

   D            E

We need to calculate the height h of point B above point A. To begin, we may use the tangent function to get the heights of points C and E:

[tex]hC = 16 * tan(θ1)\\hE = 16 * tan(θ2)\\DE = hE - hC\\hB = hC + DE * tan(θ2)\\h = hB + 1.5\\θ1 = 41\\θ2 = 49\\DE = 16 * (tan(θ2) - tan(θ1)) ≈ 9.7587 m\\hC = 16 * tan(θ1) ≈ 12.2272 m\\hB = hC + DE * tan(θ2) ≈ 23.7333 m\\h ≈ hB + 1.5 ≈ 25.2333 m\\[/tex]

As a result, the antenna's height is roughly 25 metres.

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Optiοn C represents a prοpοrtiοnal relatiοnship . The values οf all the given values are prοpοrtiοnal tο each οther i.e, 1/3.

A prοpοrtiοnal relatiοnship is a mathematical relatiοnship between twο variables where the ratiο οf the twο variables is cοnstant. In οther wοrds, if we have twο variables x and y, they are said tο have a prοpοrtiοnal relatiοnship if the ratiο οf x tο y is always the same, regardless οf the values οf x and y.

This can be expressed mathematically as:

x/y = k

where k is a cοnstant called the prοpοrtiοnality cοnstant. This means that as x increases, y will increase prοpοrtiοnally, and as x decreases, y will decrease prοpοrtiοnally.

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The functions are evaluated to give;

a. f(5) = 149/25

b. f(-5) = 149/25

c. f(-x) = 6x² - 1/x²

Functions are defined as equation , laws or expressions showing the relationship between variables.

These variables are known as;

From the information given, we have that;

f(x)=6x^2-1/x^2

Now, to determine the functions, f(5), f(-5) and f(-x), we need to substitute the value inside the bracket as the value of x in each of the functions,

We have;

f(5) = 6(5)²- 1/(5)²

expand the bracket and subtract

f(5) = 149/25

For f(-5) = 6(-5)² - 1/(-5)²

f(-5) = 149/25

For f(-x) = 6(-x)² - 1/(-x)²

f(-x) = 6x² - 1/x²

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The expression is undefined when x = 9. the expression will be undefined when x-9 = 0.

To find the values of x for which the expression is undefined, we need to look for values of x that would make the denominator of the expression equal to zero. In this case, the denominator is x-9. Therefore, the expression will be undefined when x-9 = 0. Solving for x, we get x = 9.

When x is equal to 9, the denominator becomes zero, which would make the expression undefined as dividing by zero is undefined in mathematics. For all other values of x, the expression is defined and can be evaluated.

We can verify this by substituting x = 9 in the expression and observing that it becomes (9² - 36)/(9-9), which is (81-36)/0, and division by zero is undefined.

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Complete Question:

For which values of x is the expression undefined?

[tex]x^2-36/x-9[/tex]

a. The area of the family room is 162 ft².

b. 24 tiles will be needed to cover the floor.

c. Mr. Dieter will have to buy 2 boxes to tile the family room.

The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are thought to be sufficiently described by the four basic operations, also referred to as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.

a. There are two different shapes of which one is rectangle and other is triangle.

So,

⇒ Area of rectangle = length x width

⇒ Area of rectangle = 16 x 8

⇒ Area of rectangle = 128 ft²

Also,

⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x base x height

⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x 4 x 3

⇒ Area of first triangle = 6 ft²

Similarly,

⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x base x height

⇒ Area of first triangle = [tex]\frac{1}{2}[/tex] x 8 x 7

⇒ Area of first triangle = 28 ft²

On adding the three areas, we get

⇒ Area of family room = 128 + 6 + 28

⇒ Area of family room = 162 ft²

b. We will convert the area into inches.

We know that 1 feet = 12 inches.

So, using the multiplication, we get

162 feet = 162 * 12 in²

162 feet = 1944 in²

Now,

⇒ Area of tile = 9 * 9

⇒ Area of tile = 81 in²

So,

⇒ Number of tiles = [tex]\frac{1944}{81}[/tex]

⇒ Number of tiles = 24

c. Since, tiles are sold in boxes of 12 so, using the division operation, we get

⇒ Number of boxes needed = [tex]\frac{24}{12}[/tex]

⇒ Number of boxes needed = 2

Hence, the required solution has been obtained.

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Answer:

Total amount = R41 337.50

Step-by-step explanation:

The value of the deposit is 15% of the total purchase price:

Deposit = 15/100 x R35 000

Deposit = R5 250

To calculate the balance that Claire will have to pay off, we need to subtract the deposit from the total purchase price:

Balance = Total purchase price - Deposit

Balance = R35 000 - R5 250

Balance = R29 750

To calculate the interest that Claire will have to pay on the balance, we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the balance

Rate is the annual interest rate (13%)

Time is the duration of the loan in years (3)

So, the interest that Claire will have to pay is:

Interest = R29 750 x 0.13 x 3

Interest = R11 587.50

Therefore, the total amount that Claire will have to pay back over the 3-year period is:

Total amount = Balance + Interest

Total amount = R29 750 + R11 587.50

Total amount = R41 337.50

Note that this assumes that the interest is calculated annually and added to the balance at the end of each year. In reality, the interest may be calculated differently depending on the terms of the hire purchase agreement.

C is Correct

C. Variety is the characteristic of big data that is referred to in the following statement: "Data also comes in all types, forms and granularity, both structured and unstructured."What is big data?Big data is a term used to describe vast, intricate data sets that cannot be processed or analyzed using conventional data processing tools. It is a term used to describe large amounts of structured, unstructured, and semi-structured data that cannot be processed using conventional processing methods. It is characterized by volume, speed, and complexity, and it necessitates new technologies, procedures, and strategies to manage, store, and analyze it.There are four essential characteristics of big data: volume, velocity, variety, and veracity, referred to as the four Vs. The different characteristics of big data are:Variety: Big data comes in all types, forms, and granularity, both structured and unstructured. It may include everything from text, images, and video to social media and IoT data. It can be a challenge to store, manage, and analyze data of such variety. Therefore, organizations must use tools and techniques that can handle all kinds of data.Velocity: The pace at which data is created and generated is referred to as velocity. In real-time, big data is collected and handled. The quicker you can process the data, the more valuable it becomes. Stream processing, complex event processing (CEP), and real-time analytics tools are examples of technologies that can handle high-velocity data.Volume: Big data is characterized by a large volume of data. Every day, we produce a tremendous amount of data that needs to be stored, processed, and analyzed. The huge data sets can make data analysis and management challenging.Veracity: The precision, relevance, and dependability of the data are referred to as veracity. Before processing and analyzing, big data must be checked for errors and inconsistencies. Quality checks and data cleansing procedures should be implemented to maintain data accuracy and reliability.

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The correct option is the relation is not a function.

A function is defined as a relation in which each input has exactly one output. A relation is any set of ordered pairs. According to the given chart:|Year|Sacramento River|Feather River| 2008|271,999|0| 2009|123,739|0| 2010|174,948|16,857| 2011|158,956|22,129| 2012|163,603|19,799| As we can see in the table, the Sacramento river has different number of salmon at a given year.

For example, in the year 2008, there are 271,999 salmon in the Sacramento river, in the year 2009, there are 123,739 salmon in the Sacramento river. The same with the Feather river. There is a year when there are zero salmon and there are years with different number of salmon.

Therefore, this relation is not a function. Hence, the correct option is the relation is not a function.

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Answer:

(5w + 9)(5w - 9)

Step-by-step explanation:

hmmm, dunno man.

(5w + 9)(5w - 9)

My end of the year balance is $2,142.45.

If the amount that is deposited is compounded bi-annually, it means that both the amount deposited and the interest earned, increases in value twice in a year. This is because bi-annually means twice in a year. An amount that is compounded grows at an exponential rate at each compounding date.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

2000 x (1 + 0.035)^(2 x 1)

2000 x (1.035)^2 = $2,142.45

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Answer:

x = 3.1 Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

3.1 rounded to the nearest tenth

Step-by-step explanation:

Using Sine Rule;

Sin A / a = Sin B / b = Sin C / c

Which is also as Sin M / m = Sin N / n = Sin P / p

Working with M and N;

Sin 15 / x = Sin 90 / 12

Sin 15 / x = 1 / 12 (cross multiply)

Making x the subject of the formula

x = 12 * Sin 15 = 3.10 = 3.1 rounded to the nearest tenth

Answer:          1

Step-by-step explanation:

i cant

Answer= [tex]50cm^{2}[/tex]

With a sample of 9 tables, the probability that diners would spend fewer than 100 minutes at their table during dinner is [tex]0.8413[/tex], or around [tex]84.13[/tex] percent.

The ratio of beneficial results to all beneficial results in the population is a common way to define probability.

Probability has many uses in both analysis and gaming. Probability is used in sectors of real life and business where making predictions is important. The utilisation of probabilistic principles was necessary for forecasting market prices and cricket team performance.

With the values from the problem substituted, we obtain,

[tex]z = (100 - 97) / (18/\sqrt{9} ) = 1[/tex]

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score less than [tex]1[/tex] is [tex]0.8413[/tex].

Therefore tables is [tex]0.8413[/tex] or approximately [tex]84.13[/tex]%.

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The terminal point P(x,y)=(-23) can be located on the coordinate plane at the point (-23, -23).

The terminal point P(x,y)=(-23) can be visualized on a coordinate plane. To calculate the x- and y-coordinates of this point, we must first understand the definition of a terminal point. A terminal point is a point that marks the end of a line.

In this case, the terminal point P is the end of a line with coordinates (x, y) = (-23).

To calculate the x-coordinate of this point, we can simply look at the first number in the coordinate pair. In this case, the x-coordinate of P is -23.

To calculate the y-coordinate of this point, we must look at the second number in the coordinate pair. In this case, the y-coordinate of P is also -23.

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The estimate of 445 pints in ounces is 7120 ounces

The given measurement from the question can be represented as

Measure = 445 pints

By the standard metrics of conversion, we have

1 pint = 16 ounces

Using the above conversion rules as a guide, we have the following:

Measure = 445 * 16 ounces

Evaluate the product

So, we have the following representation

Measure =  7120 ounces

The above represents the required estimate

Hence, the estimate is 7120 ounces

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The expression for time will be, Time = 5/r + 10/w.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, symbols, and operators that represent a value or a computation.

Expressions can be simple or complex, and they can contain variables, constants, and functions. They can be evaluated to produce a single value, or they can be simplified or transformed using mathematical rules and operations.

Now,

Let's assume that Juan ran at a speed of "r" miles per minute, and let's also convert the 10 minutes of walking to miles per minute by dividing by the walking speed "w".

Then, the total time Juan spent exercising can be expressed as:

Time = Time Running + Time Walking

Time Running = Distance / Speed = 5 / r

Time Walking = 10 / w

Therefore,

             the expression for the total amount of time Juan spent exercising is:

Time = 5/r + 10/w

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The value of x in this isosceles triangle is equal to: D. 50.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

In isosceles triangle ABC, side DE intersects its congruent sides and is parallel to side AB. Therefore, there are two sides that are congruent (equal) and as such we have;

(54 - 2x)° = (3x + 4)°

3x - 2x = 54 - 4

x = 50

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Answer:

y = -3x

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = -3,

y = -3x + c

Substituting (0,0) into the above equation:

0 = 0 + c

Hence,

y = -3x

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Therefore , the solution of the given problem of equation comes out to be it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces b + 7, in contrast to another algorithm, which can evaluate data from y + 7, divides 12 through two components, and produces y + 7.

Here,

The formula Hayden created is:

=> 470/h = 3008

We must separate h on one side of the equation in order to solve for it. By increasing both parts of the equation by h, we can achieve this:

=> 470 = 3008h

Then, to get h on its own, split the two sides of the equation by 3008:

=> h = 470/3008

By dividing the numerator and denominator by their 2 largest common factor, we can simplify this fraction:

=> h = 235/1504

Therefore, it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

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Answer:

20)  y = 3/4x + 3 1/2

21)  Parallel: y = 3/4 x - 2 3/4

Perpendicular: y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

20)

y = mx + b

y = __x + ___  We need to find the slope that the y-intercept. We are given the slope 3/4.  We will you the x and y values from the point (2,5) to find the y intercept. Use 5 for y and 2 for x

y = mx + b

5 = 2(3/4) + b

5 = 3/2 + b  Subtract 3/2 from both sides

5 - 3/2 = 3/2 -3/2 +b

[tex]\frac{10}{2}[/tex] - [tex]\frac{3}{2}[/tex] = b

[tex]\frac{7}{2}[/tex] or 3 [tex]\frac{1}{2}[/tex]

y = 3/4x + 3 1/2

21)

Parallel slopes are equal so the slope will be 3/4.  Now we will use the x and y values from the point (5,1) to find the y-intercept.  We will use 1for y and 5 for x

y = mx + b

1 = 5(3/4) +b

1 = 15/4 + b  Subtract 15/4 from both sides.

[tex]\frac{4}{4}[/tex] - [tex]\frac{15}{4}[/tex] = [tex]\frac{15}{4}[/tex] - [tex]\frac{15}{4}[/tex] + b

[tex]\frac{-11}{4}[/tex] or - 2 [tex]\frac{3}{4}[/tex]

y = 3/4 x - 2 3/4

Perpendicular slopes or the opposite reciprocals.  So the slope of the reciprocal equations would be [tex]\frac{-4}{3}[/tex]. We would still use the x and y values from the point (5,1)

1 = -4/3(5) + b

1 = [tex]\frac{-20}{3}[/tex] + b  Add 20/3 to both sides

[tex]\frac{3}{3}[/tex] + [tex]\frac{20}{3}[/tex] = [tex]\frac{-20}{3}[/tex] + [tex]\frac{20}3}[/tex] + b

[tex]\frac{23}{3}[/tex] or 7 2/3

y = [tex]\frac{-4}{3 }[/tex] x + 7 [tex]\frac{2}{3}[/tex]

Helping in the name of Jesus.

Answer: To calculate the sales growth, we need to find the difference between the current year's revenue and the last year's revenue, divide it by the last year's revenue, and then multiply by 100 to convert it to a percentage.

Sales Growth = ((Sales Revenue Current Year - Sales Revenue Last Year) / Sales Revenue Last Year) x 100%

Sales Growth = (($150,000 - $125,000) / $125,000) x 100%

Sales Growth = ($25,000 / $125,000) x 100%

Sales Growth = 0.20 x 100%

Sales Growth = 20%

Therefore, the sales growth is 20%.

Brainliest  is appreciated. (:

Step-by-step explanation:

Answer: 5.9%

Hope this helps!

The estimated area of the sidewalk that is getting wet is 706.5 square feet

The area of the sidewalk that is getting wet can be estimated by using the formula for the area of a circle: A = πr2, where "r" is the radius of the circle, which in this case is 15 feet. (A = π(152) = 706.5).

Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. This quantity has importance in almost all circle-related formulas. The area and circumference of a circle are also measured in terms of radius.

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The populations from which the samples are selected must not be equal variances, which is not consistent with assumptions for the independent-measures ANOVA.

Therefore, option A is the correct answer.

Independent-measures ANOVA Assumptions for the independent-measures ANOVA are listed below.

The one which is not consistent with the independent-measures ANOVA is described below:

The populations from which the samples are selected must have equal variances.

The populations from which samples are selected must be normal, especially as sample sizes decrease.

The observations within each sample must be independent.

The populations from which samples are selected must be normal, especially as sample sizes increase.

ANOVA is a statistical method that compares three or more groups' means to determine whether the differences are significant.

Independent Measures ANOVA (also known as One-Way ANOVA) compares the means of three or more unrelated groups to determine whether there are any significant differences.

When dealing with Independent Measures ANOVA, the following assumptions must be met:

Assumptions for the Independent-Measures ANOVA:

Independence: Observations in each group should be independent from one another.

Normally Distributed Populations:

Each group's scores should come from a normally distributed population.

Homogeneity of Variance: Each group's variance should be similar.

Mean Equality: Each group's means should be equal.

The above-mentioned assumptions are consistent with independent-measures ANOVA.

However, the populations from which the samples are selected must not be equal variances, which is not consistent with assumptions for the independent-measures ANOVA.

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P(x) is a continuous function on [0, 2]. We can conclude that the given function has a root on [0, 2].

The Intermediate Value Theorem is a mathematical theorem that states that a continuous function between two points takes on every value between the two points. The proof of this theorem is easy to understand and uses the definition of a continuous function. The theorem is used to establish the existence of roots or zeroes of functions.The statement is given by the Intermediate Value Theorem that “if f(x) is a continuous function on the interval [a,b], then for any value k that lies between f(a) and f(b) inclusive, there must be at least one value c on the interval [a,b] such that f(c)=k”.Use the Intermediate Value Theorem to show that P(x) = x5 + 4x3 − 10x − 6 has a root on [0, 2]Given, the function P(x) = x5 + 4x3 − 10x − 6Step 1: Verify if the function is continuous on [0, 2].The function P(x) is a polynomial function, and all the polynomial functions are continuous functions.

Therefore, P(x) is a continuous function on [0, 2].Step 2: Check the signs of the function at the endpoints f(0) and f(2).Let’s check f(0) and f(2)f(0) = P(0) = 0^5 + 4(0)^3 – 10(0) – 6= -6f(2) = P(2) = 2^5 + 4(2)^3 – 10(2) – 6= 50Step 3: Check if the value 0 lies between f(0) and f(2) inclusive.f(0) < 0 < f(2)Since 0 lies between f(0) and f(2), according to the Intermediate Value Theorem, there must be at least one value c on the interval [0,2] such that f(c)=0Hence, we can conclude that the given function has a root on [0, 2] Therefore, we can conclude that the given function has a root on [0, 2].

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Answer: well f(x) equeals a funtction

your x is a given so all you have to do is plug in the given (X) to the equation given f(x)=x/2

Step-by-step explanation:

example for the first slot:

F(x)=-4

      ——

         2

Answer:

Below

Step-by-step explanation:

Here is how to do the first one....the others are similar

f(x) = x/2       when x = -4,     f(-4) = -4/2 = -2    (just put the number in for 'x')

                 when x = - 2 ,   f(-2) =  -2/2 = -1

              when x = 0 ,     0 /2 = 0

           when x = 1 ,        1/2 = 1/2

        when x = 6 ,         6/ 2 = 3

So the answers across the bottom for the first one are

    -2     -1     0    1/2     3

I think you can do the rest.....just put the number value in for 'x' in the equation....

Joe charges more per acre than Chris. Joe charges $20 per acre and Chris charges $30 per acre.
 

Starting a lawn mowing business can be a profitable and rewarding venture if you have the right tools, skills, and strategies in place.Research your local area to determine the demand for lawn mowing services, the competition, and the going rate for services. This will help you determine whether starting a lawn mowing business is a viable option in your area.Create a business plan that outlines your goals, target market, services, pricing, and marketing strategies. This will help you stay organized and focused as you launch and grow your business.Check with your local government to find out what licenses and permits you need to start a lawn mowing business in your area.Therefore,from the given information Joe charges more per acre.

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From the given question, the value of the height of the cone is given by 57.3 centimeters to the nearest 1 decimal place: Option B

We should note that a cone is a three-dimensional geometric figure with a flat and curved surface pointed towards the top.  It is formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex)

The volume of the cone is given by the formula

Volume = 1/3πr²h

Where Volume = 1500 centimeters cube, radius = 5 cm, π = 22/7

1500 = 1/3*22/7*5*5*h

1500 = (22*5*5*h)/3*7

Simplifying the expression further we have

1500 = 550h/21

1500(21) = 550h

31500 = 550h

Making h the subject of the relation we have

h = 31500/550

h= 57.272727...

h= 57.3 to one decimal place

Therefore the height of the cone is 57.3 cm

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