for breakfast bob has three options: cereal, eggs or fruit. he hasto choose exactly two items out of the three available.(a) describe the sample space of this experiment

Answer:

Parallel: y= -(7x/3)-20

Perpendicular: y= 3x/7 - 24/7

Step-by-step explanation:

Slope of parallel line: -7/3

So the equation is y=-7x/3+a

Solve for A:

−6=(−7/3)⋅(−6)+a

So A is -20 and the equation is y=-7x/3=20

Slope of perpendicular line: 7/3

So the equation is y=3x/7 + a

Solve for A:

-6=(3/7)*(-6)+a

Therefore, a= -24/7

So the equation is y= 3x/7 - 24/7

Answer:

Equation of the parallel line: [tex]y = -\frac{7}{3}x - 20[/tex]

Equation of the perpendicular line: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Step-by-step explanation:

To find the equation of a parallel line, we already know that the slope is the same as the original line, so let's find the equation of our original line. We are given:

-7x - 3y = 5

So, we will add 7x to both sides to leave y on a side by itself:

-3y = 7x + 5 (This is the slope-intercept form which is what we will be using)

Then, divide by -3 to isolate y, giving us:

[tex]y= -\frac{7}{3} x - \frac{5}{3}[/tex]

Since it is a parallel line, our slope is the same, giving us:

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

Now, the slope of a line is [tex]\frac{rise}{run}[/tex]. Rise is the gain in y, and run is the gain in x. So, since we want to find the y-intercept, we need x to be 0, so let's say for every 3 we gain on the x-axis, we lose 7 on the y-axis (because we need one of the two values to have a negative so that our overall fraction is negative). Now, since we have the point (-6, -6) We need to gain 6 on the x-axis. Meaning, we need to use our slope twice. This means that we will need to also multiply our -7 by 2. So we have:

(-6 + 6, -6 - 14)

Giving us:

(0, -20)

Which is our y-intercept. So our equation for the parallel line is:

[tex]y = -\frac{7}{3}x - 20[/tex]

Now, for the perpendicular line, we need to get the negative reciprocal of the slope of our original line. Our original line's slope was [tex]-\frac{7}{3}[/tex]. So, the negative reciprocal of that is [tex]\frac{3}{7}[/tex]. So, our equation is:

[tex]y = \frac{3}{7}x + b[/tex]

Now, we will find the y-intercept. Since we need to gain 6 on the x-axis, but we have a normal gain of 7, we will need to multiply both our run and rise (3 and 7 respectively) by [tex]\frac{6}{7}[/tex]. Giving us that our x coordinate is:

[tex](-6 + 7 * \frac{6}{7} , -6 + 3 * \frac{6}{7} )[/tex]

Simplifying gives us:

[tex](-6 + 6 , -6 + \frac{18}{7} )[/tex]

Adding the x coordinates gives us:

[tex](0, -6 + \frac{18}{7})[/tex]

Now, to make this simple, we will put -6 over 7. To achieve this, we will need to multiply -6 by 7, giving us -42. So, we have:

[tex](0, -\frac{42}{7} + \frac{18}{7})[/tex]

42 - 18 = 24. So, we get:

[tex](0, -\frac{24}{7})[/tex]

So, the slope of the perpendicular line is:

[tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

So, these are the two equations of the parallel and perpendicular lines respectively:

Parallel: [tex]y = -\frac{7}{3}x - 20[/tex]

Perpendicular: [tex]y = \frac{3}{7}x - \frac{24}{7}[/tex]

Hope this helped!

On solving the provided question we can say that from statistical data she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

she obtains data from 167 currently enrolled students. in this context, the variable of interest would be age

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A photo with dimension 5 x 7 in is reduced so that the width becomes 4 in. The reduced size of the length of the photo is 5.6 in.

When two shapes are identical but differ in size, they are considered to be similar shapes. A similar shape can be created by scaling all of the lengths of the original shape. This means they've been stretched or shrunk in the same proportions. This is referred to as the scale factor.

In this case, the original photo and the smaller photo are similar shapes. Hence, the proportion of the corresponding sides have to be the same.

We can find the scale factor as:

Scale factor = reduced width / initial width

                   = 4 in. / 5 in. = 0.8

The length has to be reduces at the same scale factor. Therefore,

reduce length = 0.8 x 7 in = 5.6 in.

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Triangle ΔABC is comparable to triangle ΔABC, which was formed after ABC's dilatation. The appropriate answers are The characteristics of dilations show that angles ∠B =∠ B'.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the flanks of the hook, that converge at the vertex of both the angle, which is located in the centre. Two rays may combine to form an angle in the plane in which they are positioned. Two planes colliding results in an angle as well. We refer to them as dihedral angles.

Here,

Assuming that A (0, -3), C (0, 5), and B are the triangle's vertices (6, 3)

Set point P to be (0, 0)

There is;

A' = 3/2 * (0,-3) = (0,-9/2) = (0,-4.5) (0,-4.5)

C' = 3/2 * (0,5) = (0, 15/2) = (0,7.5) (0,7.5)

B' = 3/2 * (6,6/3) = (9 , 9/2) = (9,4.5) (9,4.5)

Therefore, on a scale, the image of ABC is bigger than that of the image of A'B'C.

The proportion of the adjacent angles of ABC is given by a factor of 1.5.

since and "A'B'C" are both equal, the angle made by section BC and

BA,

AB/sin(C) = AC/sin(B)

AB/sin(C) = A'C'/A'B' = sin(B)/sin (C)

This means that

sin(B)/sin(C) = sin(B')/sin(C').

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The complete question is "A. Dilate triangle ABC using center p and scale factor 3/2.

B. What do properties of dilations tell you about B'? (please answer B)"

The required average increase in the number of students enrolled per hour are 120 students.

A function of time is anything that can be described by a mathematical equation that varies reliably over time. Over time, a moving object's position changes. The location is said to be a function of time if it fluctuates in a way that can be mathematically predicted.

The function appears to be f(x) = 4. (x - 1).

You can find out how many pupils are registered at hours 2 and 4 using that function.

At hour two, there are f students enrolled (2),

f(2) = 4^ (2 - 1) = 4

At hour four, there are f students enrolled (4),

f(4) = 4^(4 - 1) = 4^3 = 64

The average growth is therefore [64 - 4] students / [4 - 2] hours = 60

students / 2 hours = 30 pupils every hour.

The numbers are as follows if the function is f(x) = 4(x - 1) rather than f(x) = 4x - 1.

f(2) = 4^2 - 1 = 16 - 1 = 15

f(4) = 4^4 - 1 = 256 - 1 = 255

The average growth rate is (255 - 15) / (4 - 2) = 240 / 2 = 120 pupils per hour.

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Complete Question:

The number of students enrolled in a new course as a function of time can be represented by the function. f(x)=(4)^x−1 What is the average increase in the number of students enrolled per hour between hours 2 and 4?

Answer:

x = 2√2

Step-by-step explanation:

If is inversely proportional to x², then:

[tex]y \propto \dfrac{1}{x^2} \implies y=\dfrac{k}{x^2} \quad \textsf{(for some constant k)}[/tex]

Given:

Substitute the given values into the found equation and solve for k:

[tex]\implies 2=\dfrac{k}{4^2}[/tex]

[tex]\implies 2=\dfrac{k}{16}[/tex]

[tex]\implies k=32[/tex]

Therefore:

[tex]y=\dfrac{32}{x^2}[/tex]

To find the value of x when y = 4, substitute y = 4 into the found equation and solve for x:

[tex]\implies 4=\dfrac{32}{x^2}[/tex]

[tex]\implies x^2=\dfrac{32}{4}[/tex]

[tex]\implies x^2=8[/tex]

[tex]\implies x=\sqrt{8}[/tex]

[tex]\implies x=\sqrt{4 \cdot 2}[/tex]

[tex]\implies x=\sqrt{4} \sqrt{2}[/tex]

[tex]\implies x=2\sqrt{2}[/tex]

The circumference of a circle with a radius of 18 feet is 113.04 ft.

The distance around the circle's edge is referred to as the circumference. It is a basic characteristic of a circle and is incorporated into a number of geometric and trigonometric calculations.

C = 2πr, where C is the circumference, is a mathematical constant, and r is the circle's radius, is the formula for calculating a circle's circumference. An irrational number is one that contains an endless number of decimal places and cannot be stated as a ratio of integers. However, the value of is roughly 3.14 for the majority of practical purposes.

The circle's radius in the provided situation is 18 feet. We can use pi = 3.14 to determine the closest approximation for the circumference of this circle.

C = 2πr = 23.1418 = 113.04 feet.

  So ,the circumference of circle is 113.04 feet.

       Therefore, 113.04 feet is a circle's circumference with a radius of 18 feet.

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The following are true assertions concerning the polynomial function: The highest level is a 3. It is trinomial since it has three terms. One of the factors is (x-1).

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomial equations are expressions that contain many constants and variables. The conventional way to write a polynomial equation is to place the greatest degree first, followed by the constant term.

Here,

f(x)=x³-x²-3

The statements that are true about the polynomial function: The highest degree is 3. It has 3 terms so it is trinomial. It's one of the factor is (x-1).

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Complete question:

which statements are true about the polynomial function f(x)=x^3-x^2-3

The highest level is a 3.

It is trinomial since it has three terms.

One of the factors is (x-1).

f(x) divided by (x+1) has a remainder of 0

Based on the diagram presented, it can be concluded that for every 1 cup of fruit juice, 1.2 cups of iced tea and 0.6 cup of sugar are used.

The diagram shows the three ingredients required to prepare a pitcher of fruit tea and the amount of the ingredients required.

Ingredients required:

Fruit juce: 2.5 cups

Sugar: 1.5 cups

Iced tea: 3 cups

Let's use the rule of three to find the answer:

Sugar required:

2.5 cups = 1.5 cups

1 cup  = x

x= 1.5 / 2.5 = 0.6 cups

Iced tea required:

2.5 cups = 3 cups

1 cup  = x

x = 3 / 2.5 = 1.2

Note: Here you can find the missing diagram:

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The missing side is  6√13 in the given right-angled triangle.

If one of a triangle's angles is a right angle (90 degrees), the triangle is known as a right-angled triangle or just a right triangle, according to the definition of a right triangle. Triangle ABC is a right triangle that contains the base, altitude, and hypotenuse in the example image.

Base AB, altitude AC, and hypotenuse BC are shown in this equation. The largest side and the side that faces away from the right angle in a right triangle is the hypotenuse, and it is this side that is significant.

Given that A right angle triangle has sides 12cm and 18 cm

y = [tex]\sqrt{12^2 + 18^2}[/tex]

y = 6√13

Thus, the missing side y is  6√13.

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The exact value of  the cosine ( (4π)/3) ] is -0.5.

The exact value of  the cosine function [ Cos ( (4π)/3) ] is calculated by resolving the pi radian into degrees as shown below.

π radian = 180 degrees

The exact value of  the cosine ( (4π)/3) ] is calculated as

Cos ( ( 4π ) / 3 ) = cos ( 4 x 180 / 3 )

cos ( 4 x 180 / 3 )  = cos ( 4 x 60 )

cos ( 4 x 60 ) = cos ( 240 )

cos ( 240 ) = -0.5

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The AM = 6 because of Definition of Perpendicular Bisector.

The correct option is A.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

Given:

Kyle is creating a frame for a model car.

He begins by piecing two rods together,

as shown in the attached diagram.

A perpendicular bisector means,

a line intersects another line.

And divide into two same parts.

And angle between two lines is 90°.

Here, the if the one piece of one rod is 6.

Then that means, the rod is divided into 2 equal parts.

Therefore, the definition is the definition of Perpendicular Bisector

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The area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.

A chord of a circle is a straight line segment that connects any two points on the circumference of the circle.

The area of the major sector can be found by using the formula:

Area of major sector = (Angle of sector / 360) * π * r^2

Where the angle of sector is 120°, and the radius of the circle is 10cm.

So the area of the major sector = (120/360) * π * (10 cm)^2 = (1/3) * π * 100 cm^2 = 33.33 cm^2

To find the area of the minor segment, we need to find the area of the minor sector and then subtract it from the area of the triangle formed by the center of the circle, the midpoint of the chord, and the endpoint of the chord.

The area of the minor segment = area of the triangle - area of the minor sector

As the angle subtended by the chord is 120°, the minor sector will subtend an angle of (360-120) = 240°.

So the area of the minor sector = (120/360) * π * (10 cm)^2 = (2/3) * π * 100 cm^2 = 33.33 cm^2

The area of the triangle can be found by using the formula:

Area of the triangle = (1/2) * b * h

Where b is the distance between the center of the circle and the midpoint of the chord and h is the length of the altitude drawn from the center of the circle to the chord.

So the area of the minor segment = (1/2) * (10cm) * (10cm) * sin(120/2) -33.33 cm^2 = 50*sqrt(3) - 33.33 cm^2=53.27 cm^2

Therefore, the area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.

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Given line equation y=x+2

Compare above equation with slope intercept form y=mx+b

slope m=1 and y-intercept=(0,2)

Here it is line equation graph

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The student has 1024 number of possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

4*4*4*4*4 = 1024

The student has 4 number of possible answer choices for each question. This means that for each question the student has 4 possible choices.

For the 5 multiple choice questions, the student has 4 possible choices for each question. This means that the student has 4^5 = 4*4*4*4*4 = 1024 possible ways to answer the five questions.

The student has 1024 possible ways to answer the five multiple choice questions in the test, since there are 4 possible answer choices for each question.

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From the descriptive statistics, we can see that the mean score for the sample is 22.25, with a standard deviation of 2.49.

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Each walkway is around 51 yards long.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

Divide the square in half to make a right triangle. Now, use Pythagoras' theorem to solve for the hypotenuse.

a²+b²=c²

⇒ 36²+36²=c²

⇒ 1296+1296=c²

⇒ 2592=c²

∴ c =50.9116

Round to the nearest whole number, we get c = 51 yards.

Thus, each walkway is around 51 yards long.

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Simplifying the linear inequality, x has a value in the range of -2 to + 1 and can be expressed as -2 < x < 1

A mathematical statement in which the maximum power of the variable is 1 is known as a linear inequality. The equation "ax + b c" or "ax + b > c" is used to describe it, where "a," "b," and "c" are constants and "x" is the variable. The collection of all 'x' values that satisfy the inequality is the solution to a linear inequality. A straight line on a coordinate plane represents the graph of a linear inequality.

In the given problem, the linear inequality is;

1 < x + 3 < 4

To solve for x, we have to subtract 3 from all sides of the inequality

-3 + 1 < x + 3 - 3 < 4 - 3

Simplifying this;

-2 < x < 1

The solution of value of x is between -2 to + 1

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The possible solution would be 10 bags of popcorn and 3 pretzels.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 'x' represents the number of bags of popcorn purchased and 'y' represents the number of bags of pretzels purchased.

Therefore,

x + y ≥ 13 and 7x + 5y ≤ 85.

The possible solution to these inequalities is where the graph of two intersects which is at (10, 3).

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Answer: 12

Step-by-step explanation:

For the equation to have infinitely many solutions, it must be an identity.

[tex]3(5+x)+kx+8=7(2x+3)+(x+2)\\\\15+3x+kx+8=14x+21+x+2\\\\x(k+3)+23=15x+23\\\\\implies k+3=15 \implies k=12[/tex]

Step-by-step explanation:

a) 2x - 7

because "seven less than twice a number". if it says "seven less twice a number" it would be 7 - 2x.

b) x/2 + 4

c) (x - 6)y

the comma after "six" is important. without it it should be x - 6y

d) x + 2/3

If Young is replacing fencing around his rabbit pens and garden , then to replace the two rabbit pens and his garden the number of feet of fencing required is 76 ft .

The Dimensions of the Rabbit Pen is :

the length of rabbit pen is = 3.5 ft ;

the width of the rabbit pen is = 4.5 ft ;

the Dimensions of the Garden are :

the length of garden is = 12 ft ;

the width of garden is = 10 ft ;

So , Perimeter of Rabbit Pen is = [tex]2\times (Length + Width)[/tex] ;

Perimeter = [tex]2\times (3.5 + 4.5)[/tex]

= 16 ft .

Since there are 2 rabbit pens ,

So , the Perimeter of two rabbit pen is = [tex]16+16[/tex] = 32 ft ;

And , Perimeter of Garden is = [tex]2\times (12 + 10)[/tex] = 44 ft .

Total Perimeter of Pen and Garden is  = [tex]32+44[/tex] = 76 ft .

Therefore , Young would require 76 ft of fencing to replace the two rabbit pen and garden .

The given question is incomplete , the complete question is

Young is replacing the fencing around his rabbit pens and garden. The table shows the dimensions of the different areas. How many feet of fencing will he need to replace two rabbit pens and his garden?

Item             Length(ft)   Width(ft)

Rabbit Pen      3.5             4.5

Garden             12               10

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DSS help users make decisions by providing them with access to information, analytical tools, and models. ES are designed to emulate the decision-making capabilities of experts in a particular field. Finally, AI systems are designed to mimic human intelligence and behavior.

1. Transaction Processing Systems (TPS)

2. Management Information Systems (MIS)

3. Decision Support Systems (DSS)

4. Expert Systems (ES)

5. Artificial Intelligence (AI)

1. Transaction Processing Systems (TPS): These systems are designed to capture, store, update and retrieve transaction data for business operations. Examples include point-of-sale systems, accounting systems and inventory control systems.

2. Management Information Systems (MIS): These systems are designed to provide managers and decision makers with the information they need to make informed decisions. Examples include financial reporting systems, sales tracking systems, and customer service systems.

3. Decision Support Systems (DSS): These systems are designed to help users make decisions by providing them with access to information, analytical tools, and models. Examples include budgeting systems, forecasting systems, and data mining systems.

4. Expert Systems (ES): These systems are designed to emulate the decision-making capabilities of experts in a particular field. Examples include medical diagnosis systems, legal advice systems, and financial planning systems.

5. Artificial Intelligence (AI): These systems are designed to mimic human intelligence and behavior. Examples include natural language processing systems, robotics systems, and machine learning algorithms.

The five main types of systems are Transaction Processing Systems (TPS), Management Information Systems (MIS), Decision Support Systems (DSS), Expert Systems (ES), and Artificial Intelligence (AI). TPS are designed to capture, store, update and retrieve transaction data for business operations, while MIS provide managers and decision makers with the information they need to make informed decisions. DSS help users make decisions by providing them with access to information, analytical tools, and models. ES are designed to emulate the decision-making capabilities of experts in a particular field. Finally, AI systems are designed to mimic human intelligence and behavior.

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N'  =(-2, 6) will be the coordinates of vertex N' of the image.

A coordinate system is a system made up of a collection of points, lines, or surfaces, where each point is given a specific position, or coordinate.

Given that,

Triangle MNP will be dilated according to the rule  (x,y), where point P is the center of dilation.

The coordinate N = (0, 2)

The rule of dilation with scale factor k =2 and point P is the center of dilation is given by: (x,y) =>(2x-2, 2y-2)

thus, N(0,2)=N'(2(0)-2,2(2)+2) = N'(-2,6)

Therefore, N'  =(-2, 6) will be the coordinates of vertex N' of the image.

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Answer:

The dimensions of the larger triangle are 48 cm * 15 cm.

Answer: 180 degrees

Step-by-step explanation:

If there are two parallel lines such as we could see in the problem, you can basically carry some angles to the other corners if these corners show the same direction.

In this case, you can carry "a" angle to the corner which is at the top of the "b" angle. Then, you can notice that a and b angles are complementary to 180 degrees for each other. So, this is the answer.

Note: Actually, you can also realize that these two corners at the intersections of the lines should have the same angle otherwise there would be no parallelism.

Answer:

A; -6

Step-by-step explanation:

Well, the cube root of 216 is just 6, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -216 is just -6

Answer:

x = 11 , CE = 98

Step-by-step explanation:

• If 2 chords are congruent, then they are equidistant from its centre , so

CE = FC , that is

10x - 12 = 8x + 10 ( subtract 8x from both sides )

2x - 12 = 10 ( add 12 to both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Then

CE = 10x - 12 = 10(11) - 12 = 110 - 12 = 98

The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.

The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.

Bus 2 starts at 8.30, So it will be at 0 miles.

By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles

By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.

By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles

By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.

So at the 360 the, the both the buses passes each other.

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