Data on the fuel consumption y of a car at various speeds x is given. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least‑squares regression line is ^ y = 55. 3286 − 0. 02286 x

The solution of the equation is x = -1 and y = -3.

And the intersection point is (-1, -3).

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 system of equations:

y = x-2      ...... equation 1

y = −3x−6  ...... equation 2

To solve the system of equations:

Substitute the value of y from the equation 1 to equation 2,

we get,

x - 2 = -3x - 6

x + 3x = -6 + 2

4x = -4

x = -1

Then y = -1 -2 = -3.

By graphically:

1). Draw the linear equation on the graph.

2). And the intersection point of the lines is a solution of the equation.

3). The solution is x = -1 and y = -3.

The complete graph is given in the attached image.

Therefore, the solution is x = -1 and y = -3.

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After a work out, the simplest form of e:g is 3:10.

Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.

To work out the simplest form of e:g as required in the question,

e/ f = 2/ 5

2f = 5e ........... 1

f/g = 3/ 4

3g = 4f ........... 2

From equation 1,

f = 5e/2

substitute the value of f in equation 2

3g = 4(5e/2)

3g = 10e

Therefore, e:g is given as;

3/ 10 = e/ g

3:10 = e: g

Thus in its simplest form, e:g = 3:10

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According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.

let's try to learn what is multiplicative inverse.

1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

One is obtained when a number is multiplied by its own multiplicative inverse.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.

Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.

Given question is incomplete complete question here:

What is the multiplicative inverse of 7/5?

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According to question, we can say that there are 128 quarters in the machine.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

N  = the  number of dollars  2N  the  number of  quaters.....so  we  have

25(2N)  + 1N   =   96

1.50N  =  96

so, by fraction we have -

N  =  96  / 1,50   =  64   dollars

2(64)   =    128  quarters

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Therefore , the solution of the given problem of equation comes out to bem² + p² =z².

The Latin word equ has the meaning of equivalent. Many of the English language's changeable terms, including adequate, temperate, and equality, contain Latin roots in their base words. The Latin root word equ enters our lexicon rather easily because both sides of an equation are, by essence, "equal" to one another.

Here,

Given : a triangle of m,p,z of length of right triangle :

By using Pythagoras theorem :

The relationship comes out to be :

=> m² + p² =z²

Thus , relationship between m , p and z is m² + p² =z² as per Pythagoras theorem.

Therefore , the solution of the given problem of equation comes out to be m² + p² =z².

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Answer:

it is a rational number already

Step-by-step explanation:

Answer:

the one that is not equivalent to the others would be 116-34

Step-by-step explanation:

because its 116 and the others dont have anything to do with 116 :)

Answer: The statement that is not equivalent should be D. |16-34

Answer: The probability of a random student to have either ginger or blonde hair is 19/28.

Step-by-step explanation: Before anything is done, let's look and see what information the problem gives us and what we need to find out. We know that there's a 5/14 chance for a student to be ginger, and a 9/28 chance for them to be blonde. We need to find out the combined chance, as we want to know what the chances are for a student to have either hair color.

In order to do this, all we need to find is the sum of both fractions. Because the fractions have different denominators, we need to change one of them to match the other. 14 multiplied by 2 is equal to 28.

If we multiply both the numerator and denominator of 5/14 by 2, we get 10/28. Now, all we have to do is add that to 9/28. When we do that, we get 19/28.

19/28 cannot be simplified, so it is our final answer. Hope this helps!

Answer: The scale of a map is a ratio that represents the relationship between distances on the map and distances in the real world. For example, a scale of 1:20 000 means that 1 unit on the map represents 20 000 units in the real world.

In this case, we are given that the area of the forest on the first map is 50 cm² and the area of the forest on the second map is 8 cm². We can use the scale of the first map to find the scale of the second map.

Since the area of the forest on the first map is 50 cm² and the scale is 1:20 000, the area of the forest in the real world is 50 cm² * 20 000 = 1 000 000 cm².

Similarly, since the area of the forest on the second map is 8 cm², the area of the forest in the real world is 8 cm² * x, where x is the scale of the second map.

Setting these two expressions equal to each other, we get:

1 000 000 cm² = 8 cm² * x

Dividing both sides of the equation by 8 cm², we get:

x = 125 000

Therefore, the scale of the second map is 1:125 000.

Step-by-step explanation:

Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.

What is circumference of a circle?

The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.

Circumference of circle(C) = 2πR

where,

R represents the radius of the circle

π is a constant with an approximate value of 3.14

Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.

This means that C= 103.62

So, using the concept of circumference of a circle,

C= 2πR

103.62= 2*3.14*R

So, R= 103.62/6.28

R=16.5mm

Hence, the length of the minute hand is 16.5mm.

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Answer:

The Average Speed is 48mph

Step-by-step explanation:

I've done this problem before, I wish A+'s upon all that read this answer. take care man!

The time it takes for Jesse to complete his trip from New York to Boston is 5 hours.

To calculate the time it takes for Jesse's trip from New York to Boston, we need to use the formula: time = distance / speed.

Given that Jesse traveled from Boston to his grandpa Isaac in New York at an average speed of 35 mph, and the trip took him 6 hours, we can determine the distance using the formula: distance = speed × time.

Distance = 35 mph × 6 hours = 210 miles.

Now, for the return trip from New York to Boston, Jesse and Isaac travel at an average speed of 42 mph. To find the time it takes, we divide the distance by the speed:

Time = 210 miles / 42 mph = 5 hours.

Therefore, Jesse's trip from New York to Boston takes 5 hours time.

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Answer: 640

Step-by-step explanation:

1. To help identify what place value to round write out the numbers with their place

the hundreds value in this question is 600

the tens value in this question is 40

and the ones value is 8

Since the questions asks to round to the nearest 10, you would look at the number after 4 and see if it is equal or greater than 5, if so, you would round it up to the next number, which would be 5 and write it like 640.

On solving the provided question, we can say that - here in graph Between the lowest number, which is 0, and the highest value, which is 5, there is a range. The range is therefore -9=y=5.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

There is a range between the minimum value, which is 0, and the greatest value, which is 5. Thus, the range is -9=y=5.

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The missing information, considering the volume of the cone and the cylinder, is given as follows:

The volume of a cylinder of radius r and height h is given as follows:

Vcy = πr²h.

The volume of a cone is one third that of the cylinder, hence:

Vco = πr²h/3.

At the second row, the volume of the cylinder is three times that of the cone, hence:

40π x 3 = 120π.

Considering the volume of the cylinder and the radius, the height is obtained as follows:

πr²h = 120π

9h = 120

h = 120/9

h = 13.3.

For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:

πr² = 36π

r = 6. (as the base is circular).

Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.

The volume of the cylinder is three times that of the radius, hence:

3 x 48π = 144π

Meaning that the height is then calculated as follows:

πr²h = 144π

36h = 144

h = 144/36

h = 4.

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This is a triangle whose three angles are in the ratio 1:2:3 and respectively measure 30° ( π/6), 60° ( π/3), and 90° ( π/2) and the sides are in the ratio 1:√3: 2.

These triangles are also known as special right triangles, such as 30-60-90 triangles, and 45°-45°-90° triangles. Among all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, √2/2 and the greatest ratio of the altitude from the hypotenuse to the sum of the legs, √2/4.

The 30°-60°-90° triangle is the right triangle whose angles are in an arithmetic progression. The proof of this fact is simple and follows the fact that if α, α + δ, α + 2δ are the angles in the progression then the sum of the angles 3α + 3δ = 180°. By dividing by 3, the angle α + δ must be 60°. The right angle is 90°, and the remaining angle is 30°.

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Answer: Tom can come up with 13 different wacky personalities for Mr Potato Head.

Step-by-step explanation:

Tom can come up with 3 different hairstyles for Mr Potato Head, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips. He also has 2 pairs of shoes to choose from. If Mr Potato Head can be bald, Tom can also choose to not include a hairstyle.

In total, Tom can come up with 3+2+1+2+2+2+1=13 different combinations of features for Mr Potato Head. Since each combination represents a different personality, Tom can come up with 13 different wacky personalities for Mr Potato Head.

Answer:

y = 2x + 1

Step-by-step explanation:

[tex]\frac{5-3}{-3-1}[/tex] = [tex]\frac{2}{-4}[/tex] = [tex]\frac{1}{-2}[/tex]

Perpendicular slopes are the opposite reciprocals .  So the slope of the line will be 2

slope (m) = 2

y = 3  You could use either point given.  I chose (1,3)

x = 1    From the point given (1,3)

y = mx + b  substitute in what you know and solve for b

3 = (2)(1) + b

3 = 2 + b   Subtract 2 from both sides

1 = b

The y-intercept is 1.

y = mx + b

y = 2x + 1

The point (1, -2) is not a solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, the correct option is NO, the solution is (2.5, -2.6)

A system of equations are two (or more) equations that have common variables.

The system of equation is presented as follows;

20·x + 20·y = -2

2·x + 5·y = -8

The specified possible solution of the equation is; (1, -2)

Making y the subject of each of the equations, and plugging in the value of x = 1, for the first equation, we get;

20·x + 20·y = -2

20·y = -2 - 20·x

y = (-2 - 20·x)/20

Therefore; y = (-2 - 20 × 1)/20 = -1.1

When x = 1, y = -1.1, therefore, the point (1, -2), is not a solution to the first equation, 20·x + 20·y = -2

Evaluating the second equation, we get;

2·x + 5·y = -8

5·y = -8 - 2·x

y = (-8 - 2·x)/5

Plugging in x = 1, we get;

y = (-8 - 2 × 1)/5 = -2

When x = 1, y = -2, therefore, the point (1, -2), is a point on the graph of the second equation, 2·x + 5·y = -8, but it is not a solution to the system of equation

The solution to the system of equation, 20·x + 20·y = -2, 2·x + 5·y = -8, can by found by equating both expressions for y as follows;

y = (-2 - 20·x)/20 and y = (-8 - 2·x)/5

Therefore; (-2 - 20·x)/20 = (-8 - 2·x)/5

-10 - 100·x = -160 - 40·x

60·x = 150

x = 150 ÷ 60 = 2.5

x = 2.5

y = (-2 - 20 × 2.5)/20 = -2.6

y = -2.6

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When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Solving the given trinomial 3x² - x - 10.

=>3x² - 6x+5x - 10

=>3x(x-2)+5(x-2)

=>(3x+5)(x-2)

The two factors of the given trinomial 3x² - x - 10 is (3x+5) and (x-2), but according to the given options, the correct answer is option C - 3x+5.

Thus, When the trinomial 3x² - x - 10  is factored completely, one of its factors is 3x+5.

Complete question: 3x² - x - 10

When this trinomial is factored completely, one of its factors is

A) x + 2

B) x - 5

C) 3x + 5

D) 3x - 2

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The two companies will be equal in cost when 21.428 miles are driven.

How do you calculate the cost of rent?

The weekly rental amount is divided by 7 to determine the daily rental rate, then multiplied by 365 (days per year) to determine the yearly rate, and finally divided by 12 to determine the monthly rental amount. For example, a property is advertised as $200 per week, ($200 divided by 7) is $28.57 for the daily rate.

We can set up an equation to represent the cost of renting a car from each company in terms of the number of miles driven, and then solve for the number of miles at which the cost is the same for both companies.

Let x be the number of miles driven.

The cost of renting from Sunshine Rental Company is given by:

Cost1 = 17 + 0.5x

The cost of renting from Rent Me company is given by:

Cost2 = 20 + 0.36x

We can set the two equations equal to each other, and solve for x:

17 + 0.5x = 20 + 0.36x

0.14x = 3

x = 21.428 miles

Hence, the two companies will be equal in cost when 21.428 miles are driven.

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We require median, interquartile range, outliers, minimum and maximum value.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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We require median, interquartile range, outliers, and minimum and maximum values.

What are statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data.

From the upper box plot representing the top 12 men's long jumpers at the U.S. Qualifying meet, we can gather the following pieces of information:

The median (middle value) of the data is around 7.6 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.4 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.3 meters and 8.0 meters, respectively, as indicated by the lower and upper ends of the whiskers.

From the lower box plot representing the distances achieved in the men's long jump at the 2012 Olympic games, we can gather the following pieces of information:

The median (middle value) of the data is around 8.0 meters, as indicated by the line in the center of the box.

The interquartile range (IQR), which is the range between the first and third quartiles, is approximately 0.5 meters, as indicated by the height of the box.

There are some outliers or values that fall outside the range of the box, which is represented by the dots or asterisks outside the box.

The minimum and maximum values for the data are around 7.5 meters and 8.4 meters, respectively, as indicated by the lower and upper ends of the whiskers.

The main difference between the two box plots is the median value, which is 0.4 meters apart and the IQR for the Olympic games is slightly bigger than the Qualifying meet.

Hence, we require median, interquartile range, outliers, and minimum and maximum values.

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Answer:

Serena paid $194.99 for a game system and then bought two equally-priced games. She spent a total of $284.97.

Step-by-step explanation:

Answer:

This law simply states that with addition and multiplication of numbers, you can change the grouping of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT associative.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are:

20.

In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.

A number line is useful because it acts as a visual math aid. It can support teachers and parents as they teach children how to count and write numbers. It's also a tool that can help build understanding behind adding, subtracting, multiplying, and dividing numbers.

Let's assume that Gina is standing on first number while Dana on the last. Hence the total number of people in the line are: n= 23.Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are: (n-2) = 20.

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Reflection and rotation will not alter the perimeter of the quadrilateral

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformations has basically classifications

Non rigid transformation are the transformation where the dimension or size of the object will be different going from preimage to the image, example is dilation

In rigid transformation, the dimensions of the object is maintained or not altered through out the transformation process. instance of rigid transformations are

Because the transformation used are all rigid transformations then all the sides will remain same and the perimeter conserved

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There are 60 different ways of choosing a meal for this wedding.

There were five distinct main courses available for selection.

There are a total of 15 possible main dish and salad combinations when ordering these 5 distinct main meals together with any one of the 3 available salads.

A total of 60 distinct main dishes, salads, and dessert combinations are conceivable by ordering one of the four potential deserts for each of the 15 various main meals and salad combinations.

60 distinct main dishes might be purchased since.

There are 60 different ways of choosing a meal for this wedding

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On solving the provided question, we can say that - on doing the fraction we have  [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here we have,

0.1 = 1/10

0.01 = 1/100

0.0001 = 1/10000

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The expanded form in terms of the sums of powers to tens of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

As per the given data the given decimal number is 237.45.

Here we have to determine the expanded form in terms of the sums of powers to tens.

Expanded Form: In its extended sense, A number is divided up into its place values, then expanded to represent the value of each digit.

Then N can be written in expanded in for terms of 10 is

[tex]$$\Rightarrow N=a \times 10^2+b \times 10^1 + c \times 10^0+d \times 10^{-1}+e \times 10^{-2}$$[/tex]

Let the given number 237.45 is denoted by N.

N = 237.45

First, write the expanded form of a number before the decimal place.

Then using [tex]$\circledast$[/tex], we have

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times \frac{1}{10}+5 \times \frac{1}{10^2} \\[/tex]

[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2} \\[/tex]

237.45 = [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]

Therefore the expanded form of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex].

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Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens

A. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}$[/tex]

B. [tex]$237 \times 100+45 \times 1 / 1000$[/tex]

C. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0-4 \times 10^1-5 \times 10^2$[/tex]

D. 200+30+7+0.4+0.05