A train passes through a 360 m long tunnel completely in 24 seconds. It passes through another tunnel 216 m long completely in 16 seconds at the same average speed. Find the length of the train.​

5761.4 feet is the height of the mountain prior to construction

Given: 1.1h – 622.5 = 5,675

This is an algebraic equation, we need to solve for h

1.1h – 622.5 = 5675

collect like terms:

1.1h =  5675 + 622.5

Add like terms:

1.1h = 6337.5

Divide both sides by 1.1:

h = 6337.5/1.1

h = 5761.4 feet

Therefore,  the height of the mountain prior to construction is 5761.4 feet

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The equation in slope-intercept form of line k is y = - x + 5.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of a line in slope- intercept form is

y = mx + c

where,

   m is the slope and c the y- intercept.

We have,

y = x - 3

∴  It is in the slope intercept form.

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular} = -\frac{1}{m} = -\frac{1}{1} = -1[/tex] ,

The partial equation of line j is,

y = - x + c

By substituting (2, 0) into the partial equation we get, c

0 = - 2 + c

c = 0 + 2 = 2

∴ c = 2

The equation of line j is y = - x + 2.

Similarly,

The slopes of parallel lines are the same.

The partial equation of line k is,

∴ y = - x + c

By substituting (- 1, 6) into the partial equation we get, c

6 = 1 + c

c = 6 - 1 = 5

∴ c = 5

The equation of line k is y = - x + 5.

Therefore, the equation in slope-intercept form of line k is y = - x + 5.

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The percent of times the machine will dispense less than 7.75 oz. is 69.15%.

In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.

A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an​ 8-oz cup.

If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally​ ditributed.

Mean = 7.5 ,

Standard Deviation = 0.5

P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)

P(z< 7.5) = P(z<(7.75-7.5)/0.5)

P(z< 7.5) = P(z<0.25/0.5)

P(z< 7.5) = P(z< 0.5)

P(z< 7.5) = 0.6915

P(z< 7.5) = 69.15%

Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.

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The picture for the condition is attached below.

What is factors of number?

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.

Let, the factors of 72 are

72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.

When we divide 72 by 6 we get 12.

⇒ [tex]\frac{72}{6} = 12[/tex]

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Answer:

5h+35y=390$

20h+20y=360$

Step-by-step explanation:

there are many answers possible.

The following are just examples:

5h+35y=390$

20h+20y=360$

By writing both variables in the same side of the linear equation, we will get the standard form:

2y + (-1)*x = 4

A linear equation between two variables x and y written in standard form is:

a*x + b*y = c

Where the coefficients a, b, and c, are all real numbers.

In this case, we have the linear equation:

2 + (1/2)*x = y

If we multiply both sides by 2, we get:

2*(2 + (1/2)*x) = 2*y

4 + x = 2y

Now we subtract x in both sides to get:

4 + x - x = 2y - x

4 = 2y - x

This is the linear equation in standard form:

2y + (-1)*x = 4

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Answer:

Answer is x = 9                                                                

The greatest amount of sap collected from any one tree is ?

times as great as the least amount of sap collected from

any one tree. = 2 times

The inequality that would represent the possible values for the number of hours babysitting and landscaping is b + l ≤ 14.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, Alexander can work a maximum of 14 hours altogether between both jobs in a given week. This will be illustrated as:

b + l ≤ 14

b = babysitting

l = landscaping

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The values of ∠PQR = 45° and ∠POR = 90°.

The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.

Given that

O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°

We have to determine the values of ∠PQR and ∠POR

Sol. OP = OQ

⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]

Similarly, ∠OQR = 20°

∠PQR = 25° + 20°

∠PQR = 45°

Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].

⇒∠POR = 2 × 45°

∠POR = 90°.

Therefore the values of ∠PQR = 45° and ∠POR = 90°.

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Answer:

[tex]\left(m+2\right)\left(n^2+2n+m+1\right)[/tex]

Step-by-step explanation:

Hoooo boy.

This is a long one.

But let's do it!!!!

Apply exponent rule: [tex]\:a^{b+c}=a^ba^c[/tex]

The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

          = -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

                  3 = 10 + c

                  c = 3 - 10

                     = -7

Hence, equation of line is y = -5x - 7.

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It will take 1.5 minutes for printer to print 12 papers.

Given,

Time taken to print 40 papers=5 minutes

then,

Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes

then to find time taken to print 12 papers, multiply 12

Time taken to print 12 paper,

[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]

Thus, it will take 1.5 minutes for printer to print 12 papers.

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Answer:

-4

Step-by-step explanation:

m= y2-y1/x2-x1

m= 11-3/0-2

m= 8/-2

m= -4

Answer: The slope is -4

Step-by-step explanation: The general formula for calculating the slope is  [tex]\frac{y2-y1}{x2-x1}[/tex].

x1 = 2, y1 = 3, x2 = 0, y2 = 11

So we have [tex]\frac{11-3}{0-2}[/tex] = [tex]\frac{8}{-2}[/tex] = -4.

Answer:

8

Step-by-step explanation:

Price : %

  [tex]x[/tex]    :  100

 6.4  :  80     (Got 80 by 100 - 20)

Cross multiply

100*6.4 = 80[tex]x[/tex]

640 = 80[tex]x[/tex]

640/80 = [tex]x[/tex]

[tex]x[/tex] = 8

Answer:

9

Step-by-step explanation:

(2(-3)+3)^2

(-6+3)^2

(-3)^2

since the power of 2 is even it will be a positive result (if its a odd number like 3 it will be a negative result)

3^2

=9

The equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7), has no solution

An equation can have no solution, infinitely many solutions or one solution

The equation is; 3·x - 13 = 7·(x + 2) - 4·(x - 7)

Expanding the left and right expressions of the equation, gives;

3·x - 13 = 7·x + 7×2 - 4·x + 4 × 7

Collecting like terms gives;

3·x - 13 = 7·x + 14 - 4·x + 28 = 7·x - 4·x + 14 + 28

3·x - 13 = 7·x - 4·x + 14 + 28 = 3·x + 42

3·x - 13 = 3·x + 42

3·x - 13 + 13 = 3·x + 42 + 13 = 3·x + 55

3·x + 0 = 3·x + 55

3·x = 3·x + 55

3·x - 3·x = 55

3·x - 3·x = 0 = 55 (No solution for x)

Therefore, the value of x in the equation, 3·x - 13 = 7·(x + 2) - 4·(x - 7) has no solution as the left and right expressions are not the same

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The sine function is  y = 5 sin ([tex]16\pi x[/tex] ) + 3.

The function y =[tex]sin x[/tex] defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently.

It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.

In its most general form, the sine wave can be described using the function y=[tex]a sin (bx)[/tex]

Given:

Amplitude = 3

midline= 5

As, we know

General sine function:  a sin b[tex](x- c)[/tex] + d

and, amplitude = absolute value of a

b = 2π / period

c = phase shift (horizontal shift)

d = vertical shift  (i/e., midline is  y = d)

So,

a = 5, d = 3, and b = 2π / (1/8) = 16π, c = 0

Substituting the above value in Sine function we get

Thus, y = 5 sin ([tex]16\pi x[/tex]) + 3

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The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

Given equation: 2x³ + 12x² = 0

Solving this equation by factoring as follows:

2x³ + 12x² = 0

= 2x²(x+6) = 0

So, x + 6 = 0 or 2x² = 0

x = -6 or x = 0

Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.

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Answer:

22ft

Step-by-step explanation:

2+2+5+4+4+2+2= 22

The 65 represents the speed.

97.5 miles covered in 1.5 hours.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given: d= 65t

We know the Formula of Speed- distance

speed= Distance / time

and, distance = speed x time

So, comparing it with given equation

distance =d , time= t and speed= 65

Now, t=1.5 hours

Distance = 1.5 x 65 = 97.5 miles

and, d= 26 miles

t= 26 / 65

t= 0.4

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The true statement about the graph is

It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.

The range refers to all possible value in the out put of a graph.

The out put is the y coordinate and the possible values here is within the interval

0 ≤ y ≤ 5

The domain refers to all possible value in the input of a graph.

The input is the x coordinate and the possible values here is within the interval

-6 ≤ x ≤ 0

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All the steps given are take to ensure fairness when collecting data.

What is data analysts?

A data analyst examines data to find significant customer insights and potential uses for the information. They also advise the company's management and other stakeholders of this information.

You need excellent quantitative and analytical skills to succeed as a data analyst.

To answer problems logically, you must be able to pay attention to detail. Additionally, you must be able to articulate your conclusions clearly to people who will base choices on them.

Therefore, all the steps given are take to ensure fairness when collecting data.

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The height is either 10 cm,12 cm,14 cm.

Given:

The base of the parallelogram has a length of 10 cm.

Here area is not given so the height may be anything.

suppose h = 10

area = base * height

= 10 * 10

= 100 cm^2

if h = 12

area = 10 * 12

= 120 cm^2

if h = 14

area = 10 * 14

= 140 cm^2

Therefore the height is either 10 cm,12 cm,14 cm.

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Answer: My answer is 4. You may want another answer.

Step-by-step explanation:

visual studying

If she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable. A linear equation has the form y = mx + b in the slope-intercept format

It is given that, for each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length.

If x is the length in inches, of the necklace. The equation to find how many beads Li has" will be,

y=32+7x

Thus, if she uses 32 spacers, plus 7 beads per inch of necklace length. The equation to find how many beads Li has" will be,y=32+7x.

The question is incomplete. The complete question is"Li is making beaded necklaces. For each necklace, she uses 32 spacers, plus 7 beads per inch of necklace length. Where is x the length in inches, of the necklace? Write an equation to find how many beads Li has"

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Answer:

Step-by-step explanation:

Step-by-step explanation:

you can see that answer directly at x = 0. because y is then exactly the missing "?".

and that is 4.

so,

? = 4

Answer:

x = 2.875

Step-by-step explanation:

1 1/3 (9 - 6x) = -11

        12 - 8x = -11

            - 8x = -23

                x = 2.875