the height if a triangle is 8 cm shorth than its base. if the are of the trinagle is 24cm^2 find the height of the triangle

Using the trigonometry ratio, at angle 50.81° should the arm be set.

We have to determine the angle x should the arm be set.

A crane has a 200-foot arm whose lower end is 5 feet off the ground.

The arm has to reach the top of the dome 80 feet high.

The length of crane arm = 200ft

The height of building = 160ft

The initial height of the crane = 5ft

As a result, the height of the building in relation to the crane can be expressed as;

h = 160ft - 5ft

h = 155ft

The angle x the crane makes with the horizontal can be expressed mathematically as;

sin x = opposite/hypothesis

sin x = 155ft/200ft

sin x = 0.775

Taking [tex]\sin^{-1}[/tex] on both side, we get

x = [tex]\sin^{-1}[/tex](0.775)

Using the calculator

x = 50.81°

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If children aged 12years,9 years and 4 years shareR500 in the same ratio as their ages​. They each got R240, R180,R80.

Total number of years = 12 years + 9 years + 4 years

Total number of years  = 25 years

Now let find the amount they each got

12 years

Shares  = 12/25×500

Shares = R240

9 years

Shares = 9/25×500

Shares = 180

4 years

Shares =4/25×500

Shares = 80

Therefore they each got R240, R180,R80.

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The complete question is:

Children aged 12 years,9 years and 4 years share R500 in the same ratio as their ages .How much do they each get?

The graph has (c) infinitely many solutions

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

The graph

On the graph, we have two equations represented by

y = x + 2

-3x + 3y = 6

On the graph, we can see that the equations have the same line

This means that there are lots of solutions in the system i.e. infinite many solutions

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In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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Answer:

0.1

Step-by-step explanation:

1.distribute the 6 to 1 and 10

2.now its 6+60m

3. divide 60 on both sides

4. 60/60 cancels out.

5.  6/60 =0.1

The probability that the first item is not the first to be delivered will be 1/3.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The probability that one of the other two items arrives first will be given as,

p = 1/3 + 1/3

p = 2/3

The probability that the first item is not the first to be delivered will be given as,

q = 1 - p

q = 1 - 2/3

q = 1/3

The probability that the first item is not the first to be delivered will be 1/3.

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Answer:

42

Step-by-step explanation:

Let's call the number of coupons sent to existing members as "x".

We know that:

They provided 5 times as many potential members than existing members, meaning that they sent 5*x coupons to potential members.

The total number of coupons sent is 252

So we can write an equation:

x + 5x = 252

6x = 252

x = 252/6

x = 42

Therefore, they sent 42 coupons to existing members.

Answer: 42

Step-by-step explanation:

5x + x = 252

6x = 252

x = 42

existing members = 1x

1 x 42

= 42

There are 5040 ways to place 8 rooks on an 8 x 8 chessboard.

A permutation is a systematic grouping of objects or numbers. Combinations allow you to select objects or numbers from a group of items without having to worry about the order in which they were collected. Contrary to permutations, when selecting components from a collection using the combination method, the order of selection is unimportant.

There are 8! ways to place 8 rooks on an 8 x 8 chessboard such that no two rooks are in the same row or column.

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

   = 5040

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The complete statement is Δ MTS ≅ Δ RTS

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given : Two triangles MTS and RTS

now in the triangles MTS and RTS

we have OM=RT , MN=SR , ON=ST

And therefore By SSS property of two triangles we can deduce that the two triangles are congruent.

Hence, The complete statement is Δ MTS ≅ Δ RTS

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A counter example to the statement that the difference of two positive numbers is always positive is 4 - 7.

Any exception to a generalization is a counterexample. A counterexample refutes the generalization in logic, and it does so firmly in the disciplines of math and philosophy.

A formal proof is necessary to establish the veracity of a mathematical assertion. Finding just one instance where a mathematical assertion is incorrect suffices to disprove it, though. An example like this is referred to as a counterexample because it contradicts or goes against the conclusion of the statement.

Here, a counter example to the statement that the difference of two positive numbers is always positive is:

= 4 - 7.

= -3

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The height of the CN tower found using the trigonometric function to the nearest metre is 555m.

What are the different trigonometric functions?

Trigonometric functions are used to determine the relationship between

angles and sides of a triangle.

The basic functions are sine, cosine and tangent.

sine = perpendicular/hypotenuse

cosine = base/hypotenuse

tangent = perpendicular/base

From the figure, we can see the right-angled triangles made by both the model and real CN towers.

Since the shadow is cast at the same time of the day, we can say that the angles θ and Φ formed are the same angles.

So from the figure,

tan θ = tan Φ

  0.9/0.2 = h/ 123.3

h = 554.85 m

Therefore the height of the CN Tower to the nearest metre is 555m.

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Answer:1/10 hope im right  :)

Step-by-step explanation:

Answer: 1/10

Answer step by step:

1) 3x - 4/5 = - 1/2

2) 3x = -1/2 + 4/5 (move -4/5 to the right side of the equation and inverse the negative sign)

3) 3x = 0.3 (add the values)

4) 3x / 3 = 0.3 / 3 (divide both side with 3 to get rid of the constant value)

5) x = 0.1

6) x = 1/10 (the 1 in 0.1 is in the tenth place so we convert it to 1/10)

John will walk 1,333.33 meters home from school.

Percentage is a mathematical concept used to express a number as a fraction of 100. It is generally used to compare one number to another, in terms of its relative size. For example, if 30 out of 100 people have voted for a certain candidate, then the percentage of those who voted for that candidate is 30%.

Percentage can also be used to express a change in a value over time.

For instance, if the price of a product has increased from $10 to $15, then the percentage increase in the price is 50%.

Percentage can also be used to compare different groups of data. For instance, if an organization has ten male employees and five female employees, then the percentage of male employees is 66.67%.

Percentage is an important concept in the field of mathematics and is used to calculate the percentage of a whole or part of a whole.

To find the total distance John will walk home from school, you need to multiply 200 meters, which is the distance he has already walked, by 100%, which is the total amount of the journey home from school, and then divide that answer by 15%, which is the percentage of the journey he has already walked.

200 x 100/15 = 1,333.33

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To earn at least $640 in revenue, the ticket prices should be $8 or $2

An equation is an expression that shows the relationship between two or more variables and numbers.

Revenue = number of tickets sold * price per ticket  R(p) = -40p^2 +400p-640

p² -10p +16

Factorizing the function to have

(p²-8p)-(2p+16)

p(p-8)-2(p-8)

p-2 = 0 or p-2=0

This implies that

p=8 or p=2

p = $8 or p = $2

To earn at least $640 in revenue, the ticket prices should be $8 or $2.

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Answer: I will help you, but not write because it depends on the topic

Introduction: Begin by grabbing your audience's attention with an interesting fact, story, or statistic. Then, introduce the main topic of your speech and provide some background information on it.

Body: Divide the body of your speech into several main points, each of which will address a different aspect of the topic. Use evidence, examples, and anecdotes to support your points and make them more persuasive.

Counterargument: Address any potential objections or counterarguments to your main points. This will demonstrate that you have considered multiple perspectives and will make your argument more convincing.

Conclusion: Sum up your main points and reiterate the importance of the topic. End with a strong call to action or a memorable quote.

Practice: Practice delivering your speech in front of a mirror or with friends/family to become more comfortable with the material and delivery.

Here's an example of an introduction for an Original Oratory speech on the topic of the benefits of solar energy:

"Imagine a world where our energy needs are met by a clean, renewable source that never runs out. That world is not just a dream – it's a reality that we can create by embracing solar energy. Today, I want to talk to you about the many benefits of solar energy and why it's time for us to take a closer look at this powerful technology. From reducing our dependence on fossil fuels to creating jobs and driving economic growth, solar energy has the power to change our world for the better. So, let's explore the reasons why solar energy is the energy of the future."

Veena has a dream of running her own hair empire one day. She started cutting hair as a child and has since transformed everyone's hair. Her mother loves her long, black, wavy hair and has requested that she keep it that way. Veena is already well on her way to making her dream come true.

A summary is a shortened version of the key ideas in an article, book, speech, or other type of literature. It is a concise repetition of the key ideas, conclusions, and/or facts contained in the original text. Summaries are frequently used to provide a fast summary of the essential points in a larger book, making it simpler to absorb the main concepts in less time.

Veena has a dream of running her own hair empire one day. She first started cutting hair as a child, working on her dolls. In middle school, her brother agreed to a haircut on a dare and before long she was transforming everyone's hair around her. The only person's hair she hasn't cut is her own, because her mother loves her long, black, wavy hair and has requested that she keep it that way. Everyone knows that Veena wants to have her own hair salon someday and she is already well on her way to making that dream come true.

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Answer: On a coordinate plane, the quadrants are defined as follows:

Quadrant I: x-coordinate is positive, y-coordinate is positive

Quadrant II: x-coordinate is negative, y-coordinate is positive

Quadrant III: x-coordinate is negative, y-coordinate is negative

Quadrant IV: x-coordinate is positive, y-coordinate is negative

Based on this information, the following statements are true:

A is in Quadrant I, because its coordinates are (2, 3) and both x and y are positive.

D is in Quadrant III, because its coordinates are (negative 3, negative 3) and both x and y are negative.

F is on the x-axis, because its y-coordinate is 0.

G is on the y-axis, because its x-coordinate is 0.

The other statements are not true:

B is not on the x-axis, because its y-coordinate is not 0.

C is not in Quadrant I, because its x-coordinate is negative.

E is not on the x-axis, because its y-coordinate is not 0.

Step-by-step explanation:

The average rate of rain displayed in the graph is 2.5 inches per day.

1. The C.R.O.C is 2.5.

2. The equation that can be used to find y, is y = 2.5x.

3. Yes, this is a proportional relationship.

4. Yes there is a C.O.P of 2.5.

5. The unit rate is 2.5 inch rain in 1 day.

6. The amount of rain that would fall in 15 days is 37.5 inches.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

In the graph the x-axis represents the number of days.

In the graph the y-axis represents the rain in inches.

The first point is (2,5) which tells that in 2 days the rain fell 5 inches.

So, the average rain will be 5/2 = 2.5 inches.

CROC stands for constant rate of change. The formula for constant rate of change is -

= (y2 - y1)/(x2 - x1)

= (10 - 5)/(4 - 2)

= 5/2

= 2.5

Therefore, the constant rate of change is 2.5

The first point in the graph is (2,5), the x-intercept being 2 and y-intercept being 5. The CROC is obtained as 2.5.

So the equation for y can be given as -

y = 2.5 x

A proportional relationship between two variables x and y  is when one variable is always some constant value multiplied by the other.

So, yes the relationship between the x and y value in this graph is proportional.

The “constant of proportionality” is the name given to this constant. All proportional relationships can be represented by the equation y =kx  , where k  is the proportionality constant.

Since, the equation is y = 2.5x.

Therefore, the constant of proportionality is 2.5.

The unit rate is 2.5 inches of rain in one day.

The amount of rate that would fall in 15 days is -

y = 2.5 x

y = 2.5 (15)

y = 37.5

Therefore, the amount of rain will be 37.5 inches.

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The mass of television is 6t, the mass of computer is 4t and the mass of stereo is 12t.

We have to determine the mass of each type of parts.

A transport truck transports television, computer, and stereo components

1. The mass of the truck and the parts is 28t.

2. The mass of the empty truck is 6t.

3. The mass of the computer parts is 2t less than the mass of television parts.

4. The mass of stereo parts double the mass of television parts.

truck = 6t

part = stereo + television + computer

computer = television - 2t

stereo = television × 2

truck + parts = 28t

part = 28t - 6t

part = 22t

part = computer + television + stereo

part = television - 2t + television + television × 2

part = 4 × television - 2t

22t = 4 × television - 2t

4 × television = 24t

television = 6t

computer = 6t -2t = 4t

stereo = 6t × 2 = 12t

television = 6t

computer =4t

stereo = 12t

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The graph of the linear function y = -2x is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 1, y decays by 2, hence the slope m is given as follows:

m = -2.

When x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence the function is:

y = -2x.

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The value of y is multiplied by 6 when x is divided by 6

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

y = 3/x

Also, from the question we understand that

x is divied by 6

This means that the new equation is

y = 3/(x/6)

Evaluate

y = 6 * 3/x

This means that the new value of y is  multiplied by 6

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The statement "the maximum likelihood estimator is an unbiased estimator of " is False.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

It depends on the specific probability density function (pdf) of the distribution. An estimator is unbiased if its expected value is equal to the true value of the parameter being estimated. For a given pdf, the maximum likelihood estimator (MLE) may or may not be an unbiased estimator of the true parameter value.

The MLE is the value of the parameter that maximizes the likelihood function, which is the probability of the observed sample under the assumed pdf. In general, the MLE is a consistent estimator, meaning that as the sample size increases, the MLE will converge to the true parameter value with probability 1. However, it may not always be unbiased.

The statement "the maximum likelihood estimator is an unbiased estimator of " is False.

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You started a project on 9/29/2019. The project ended on 08/01/2022. So 1037 working days you have for the entire project.

Project Start Date - 09/29/2019

Project End Date - 08/01/2022

Ignore the end date

No. of days spent for project in 2019 = 94

September - 2, October - 31, November - 30 & December - 31

No. of days spent for project in 2020 = 366

No. of days spent for project in 2021 = 365

No. of days spent for project in 2022 = 212

January - 31, February - 28, March - 31, April - 30, May - 31, June - 30 & July - 31

Total number of days spent for the project are 1037 days.

2019 - 94

2020 - 366

2021 - 365

2022 - 212

The Project took 1037 working days for its completion from 09/29/2019 to 08/01/2022.

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Answer: 8

Step-by-step explanation:

First you multiply -4(-1) a negative times a negative is a positive so that is positive 4 then you simply add 4 which equals 8

Answer: I think true

Step-by-step explanation: guess

The point(s)) where the fire road intersects the outer boundary of the service area is found using the equation of circle which is (0,20) and (-12,-16).

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

The equation of the circle is given as - x² + y² = 400 .... (1)

The equation of the fire road is given as - y - 3x = 20 .... (2)

Write the equation of fire road in slope-intercept form - y = mx + b

y = 3x + 20

Substitute the value of y in equation (1) -

x² + y² = 400

x² + (3x + 20)² = 400

Follow the (a + b)² rule, (a + b)² = a² + 2ab + b²

x² + (3x + 20)² = 400

x² + 9x² + 120x + 400 = 400

10x² + 120x + 0 = 0

x² + 12x = 0

x(x+12) = 0

x = 0, x = -12

Substituting the values of x in equation (2).

First calculate for x = 0.

y - 3x = 20

y - 3(0) = 20

y = 20

Now, calculate for x = -12.

y - 3x = 20

y - 3(-12) = 20

y + 36 = 20

y = 20 - 36

y = -16

Therefore, the points of intersection are (0,20) and (-12,-16).

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The solution of the equation 3(2x - 7) = 3 is x = 4. The equation has only one solution.

An equation is a mathematical expression that shows that two mathematical expressions are equal. Equation shows the relationships between variables, numbers and constant.

Therefore, let's solve the equation 3(2x - 7) = 3 as follows

3(2x - 7) = 3

Open the parenthesis

3(2x - 7) = 3

6x - 21 = 3

add  21 to both sides of the equation

6x - 21 = 3

6x - 21 + 21 = 3 + 21

6x = 24

divide both sides of the equation by 6

6x / 6 = 24 / 6

x = 4

Therefore, the equation has one solution which is x = 4.

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The required probability and percentage for the employee to commute from home to office is :

a. probability for less than 20 minutes is 0.09852.

b. percentile for 37 minutes is 64%

c. percentage of the commute between 25 and 45 minutes is 70.49%.

Normally distributed data for the employers to commute from home to office :

Mean 'μ' = 29 minutes

Standard deviation 'σ' = 7 minutes

let 'X' represents the time taken by employee to commute.

a. Employee take less than 20 minutes to commute

Probability of taking time less than 20 minutes is:

P ( X < 20 )

= P [ ( X -μ )/ σ < ( 20 - 29)/7 ]

= P( Z < -9/7)

= P( Z < -1.29 )

= 0.09852

b. Employee take 37 minutes then percentile is :

P ( X =37 )

= P [ ( X -μ )/ σ = ( 37 - 29)/7 ]

= P( Z = 8/7)

= P( Z = 1.14)

= 0.64

= 64%

c. P ( 25 < X < 45 )

=P ( 25 -29 /7 < X -μ /σ < 45 -29 /7 )

=P ( -4/7 < Z < 16/7 )

= P( -0.571 < Z < 2.29 )

= P ( Z <2.29 ) - [1 - P( Z < 0.571 ) ]

= 0.9889 - ( 1 - 0.7160 )

= 0.7049

= 70.49%

Therefore, when the employee commute from home to office :

a. Probability of commuting less than 20 minutes is 0.09852.

b. Percentile of taking 37 minutes is 64%

c. Percentage between 25 and 45 minutes is 70.49%.

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The function represents exponential growth and the y-intercept is 4

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

f(x) = 4(3)^x

An exponential function is represented a

f(x) = ab^x

Where

y-intercept = a

rate = b

This means that

y-intercept = 4

b = 3

Since the value of b is greater than 1, then the function is a growth function

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The statement that is true about the rental company’s charges is A. The deposit fee is $ 25 and the rental fee per day is $ 45.

The total cost function is given as C = 45d + 25. This means that the slope is 45 and the y - intercept is 25.

This also means that the rental per day is $ 45 because the slope is the amount that the total cost changes by per day which must be the daily rental cost.

The $ 25 would be the cost that a person pays as a down payment when they rent the car because this amount does not change.

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Options for this question include:

A. The deposit fee is $ 25 and the rental fee per day is $ 45.

B. The deposit fee is $ 45 and the rental fee per day is $ 25.

C. The car can be rented for $ 45 and then given back to the company at $ 25