The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.

b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles

Range provides a precise measurement of variability for both sets of data because it compares the greatest and lowest values in a dataset.

It is a helpful measure of variability for comparing the constancy of temperature between Desert Landing and Flower Town because it is unaffected by skewness or symmetry.

The graphic representation of data points arranged into user-specified ranges is called a histogram.

The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organizing them into logical ranges or bins.

A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighboring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics.

In a bar graph, the frequency is represented by the length of each bar, which are ranked from longest to shortest. To illustrate the relationship between two sets of data, scatter plots plot observations as points.

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A function g that determine the point's x-coordinate in terms t.

g(t) = r .cos (2.t).

Now, According to the question:

The input variable and output variable are also called the domain and the range. The domain of a function is the set of all values that will work in the function, which are the inputs. The range of a function is the set of all possible outputs produced by the function. In the example above, the 3 would be part of the range and the 8 would be part of the domain.

Input data

A point started at the location (-4, 0)

and, moves CCW along a circle centered at (0, 0)

angular speed = 2 rad/s

Procedure

The value of x is equal to the cosine of the swept angle time radius.

We can calculate the swept angle as 2×t

g(t) = r .cos (2.t).

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The given question is incomplete.

For the complete question, To see the attachment.

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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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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The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The area of the circle is 9π. Then the radius of the circle is given as,

A = π

πr² = π

r² = 1

The center of the circle is at (-7, -15). Then the equation of the circle is given as,

(x + 7)² + (y + 15)² = 1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

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The measure of {x} equals to 8 and ∠WYZ is 32°.

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given is the figure as shown in the image.

It is given that ∠XYZ = 106°. We can write -

∠XYZ = ∠XYW + ∠WYZ

106 = 70 + 5x - 4

5x + 66 = 106

5x = 40

x = 8

∠WYZ = 5x - 8 = 5 x 8 - 8 = 32°.

Therefore, the measure of {x} equals to 8 and ∠WYZ is 32°.

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The number of cards were sold for mother's day is 900 cards.

To calculate a total number using a percentage, first identify the percentage and the total number. Then divide the percentage by 100 to convert it to a decimal fraction. Finally, multiply the total number by the decimal fraction to calculate the total number.

For example, if the percentage is 10% and the total number is 200, first divide 10% by 100 to get 0.1. Then multiply 0.1 by 200 to get 20. The total number is 20.

In another example, if the percentage is 25% and the total number is 500, divide 25% by 100 to get 0.25. Then multiply 0.25 by 500 to get 125. The total number is 125.

It is important to remember that percentages are based on a whole, which is usually 100. Therefore, to use percentages to calculate a total number, it is necessary to first convert the percentage to a decimal fraction by dividing it by 100. Then, multiply the total number by the decimal fraction to calculate the total number.

36 cards is 4% of the total cards sold for Mother's Day.

Total number of cards = 36 / 4%

Total number of cards = 36 x 100/4

Total number of cards = 900 cards.

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Answer:

1/7

Step-by-step explanation:

5/7 was already traveled so that leaves 2/7.

Thye traveled 1/2 of 2/7 so we multiply them.

1/2 x 2/7 = 2/14

We can simplify this by dividing both sides by 2.

1/7 is the final answer.

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 function to find the amount in dollars spent on monthly activities can be represented as: A(x) = (x - 500) * 1/4

Let x be the total monthly budget in dollars and A(x) be the function of x that determines the amount in dollars spent on monthly activities.

To find the value of A(x), we follow the steps:

First, we subtract the fixed monthly transportation cost of $500 from the total budget.

The remaining budget is then divided by 4 to find the amount spent on monthly activities.

Therefore, the function A(x) can be written as: A(x)= (x-500)/4

Thus, the function (x - 500) * 1/4 can be used to find the amount in dollars spent on monthly activities.

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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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As per the unitary method, the charge for each job in order to break even at the end of the third job is $3,000

In math the term unitary method is known as a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have given that John is starting a roofing business. He will need to buy a truck and some supplies to get his business going.

And here we we have also known as the truck costs $13000 used.

The value of truck is 13000 and material for all 3 jobs is 3000

Here we have also know that each job takes 5 days for a total of 15 days

workers get paid 125 dollars a day.

As we all know that each worker gets 125 a day.

Then here we have also know that each job requires 5 days so he pays each worker 625 per job.

Then he has them work on 3 jobs, and then he pays each worker 1875 for all 3 jobs.

Where here he has 2 workers so he pays out 3750 in total to the workers for all 3 jobs.

Then the total cost is calculated as,

=> $13,000 for the truck

=> $3,000 for the material

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Using the leg rule, the value of x in the right triangle is: 42.

The leg rule gives the relationship between the lengths of the segments formed on the hypotenuse of a right triangle by its altitude.

The leg rule is given as:

Hypotenuse/leg = leg/part.

In the image given, we have:

Hypotenuse = x + 8

Leg = 20

Part = 8

Plug in the values:

x + 8 / 20 = 20 / 8

8(x + 8) = (20)(20)

8x + 64 = 400

8x = 400 - 64

8x = 336

x = 336/8

x = 42

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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)

The approximate solution of the system of equations is given as follows:

(4, 26).

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

For the point of intersection in this problem, we obtain the coordinates as follows:

This means that the correct option is given by the third option.

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The mean of the copper measured is 45.747. when the mass of copper is 45.750.

Average Absolute Deviation:

The average deviation is a statistic that measures the absolute difference of each measurement from the mean value and then gets its average.

It also includes both the mean absolute deviation and the median absolute deviation and also defines the data set as the average of the absolute deviations from a central point.

This is given by the formula:

Average Deviation=∑ni=1|x−¯x|

where:

x is the observed value

¯x is the mean value

n is the number of observations

Computing for the mean of balance 1:

¯x=45.747+45.745+45.748/3

¯x=45.747

Computing for the mean of balance 2:

¯x=45.76+45.77+45.74/3

¯x=45.79

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The value of n=36 months.

It is given that the population is predicted to increase by 0.5%. To know the value after the increment, 215 has to be multiplied by (1 + 0.005) or 1.005.

In the equation P  =  215(1.005)t/3, the value of t/3 has to be equal to 1 for a 0.5% increase.

The population increases by 0.5 % every n month.

Initial Population = 215

Final Population:

=215+215*0.5/100

=215.1.074

=216.074

Substituting the value of, Initial and final Population

[tex]216.075=215*(1.005)^\frac{t}{3} \\\\(1.005)^\frac{t}{3} =\frac{216.075}{215}\\ \\(1.005)^\frac{t}{3}(1.005)^1\\\\\\frac{t}{3} =1[/tex]

t=3 years=>36 months.

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The solution of the system is x = 60 and y = 28.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

An algebraic equation,

[tex]a^{x} a^{y} = a^{88}[/tex]

When the base value is the same, we can add the exponents.

x + y = 88

And x - y = 32

Now, we have the system of equations,

Adding both the equations,

2x = 120

x = 60

And y = 28.

Therefore, the values are x = 60 and y = 28.

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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 relationship between r and s represents by the equation r = 1/6 s. So the option D is correct.

We have to determine which equation represents the relationship between r and s.

When we analysis the table we see that

r(1) = 1 × 1/6 = 1/6

r(2) = 2 × 1/6 = 1/3

r(3) = 3 × 1/6 = 1/2

r(4) = 4 × 1/6 = 2/3

r(5) = 5 × 1/6 = 5/6

r(6) = 6 × 1/6 = 1

So we can say that

r = s × 1/6

So, r = 1/6 s

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The complete question is:

The table shows the relationship between r and s, where s is the independent variable.

s          1          2          3          4          5          6

r          1/6       1/3       1/2       2/3       5/6        1

Which equation represents the relationship between r and s?

A. 1/6 r

B. s - 5/6

C. r - 5/6

D. r = 1/6 s

Answer: the quotient is 957.07 x 10^4 which is equivalent to 957,070

Step-by-step explanation:

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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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?

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

The number of hours Jackson worked washing cars last week is 8 hours

The number of hours Jackson worked landscaping cars last week is 6 hours

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

Jackson worked a total of 14 hours

x + y = 14

Jackson earned a total of $152

$10 per hour washing cars and $12 per hour landscaping

10x + 12y = 152

The simultaneous equation

x + y = 14

10x + 12y = 152

using calculator to solve the equation  we have that

x = 8 and y = 6

hence hours of washing cars is 8 hours while hour s of landscaping is 6 hours

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Answer

see attached

Step-by-step explanation:

x-2y = 8 means x = 8+2y.  so when y =0, x = 8; when y=1, x =10. draw a line with these 2 points.

Same with x - 2y = 4 ==> x = 4+2y.  so when y=0, x = 4, when y=1, x=6, draw a line with these 2 points.

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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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."

At 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.

Given is that two pools are being filled with water. To start, the first pool contains 1600 liters of water and the second pool contains 1186 liters of water. Water is being added to the first pool at a rate of 20.25 liters per minute. Water is being added to the second pool at a rate of 31.75 liters per minute.

We can write the equation for the first pool as -

y{A} = 1600 + 20.25x

Similarly, for the second pool is -

y{B} = 1186 + 31.75x

For the same amount of water -

y{A} = y{B}

1600 + 20.25x = 1186 + 31.75x

1600 - 1186 = 31.75x - 20.25x

x = 36

Amount of water in each pool will be -

y = 1600 + 20.25 x 36

y = 2329 liters

Therefore, at 36 minutes, the amount of water in both pools will be same. In amount, it will be 2329 liters.

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