36. Rapid City is having its annual citywide celebration. The city wants to rent a bumper-car ride. The pieces used to make the floor are 4 foot-by-5 foot rectangles. The ride covers a rectangular space that is 40 feet by 120 feet. a. How many rectangular floor pieces are needed? b. The ride costs $20 per floor piece and $10 per bumper car. How much would it cost Rapid City to rent the floor and the bumper cars? (You will need to decide how many bumper cars will be appropriate.)​

The length of the rectangular garden is 28 feet.

Statement represents the mathematical solution to the given word problem.

The statement clearly explains the stated circumstance.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

The area of the rectangular garden = 448 square feet.

Also, the length of the garden is 4 feet less than the twice of the width.

Let the width of garden is x feet

Then length of garden = 2x - 4

The area of rectangular garden = 448

x (2x - 4) = 448

x (x - 2) = 224

x = 16

The width of the garden is 16 feet.

The length of the garden = 2x - 4 = 2(16) - 4 = 32 - 4 = 28 feet

The required length of the garden is 28 feet.

The mathematical model to the given word problem is statement.

Statement clarify the given condition clearly.

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Answer:

  A  All real numbers

Step-by-step explanation:

You want to know the domain of a function graphed as a continuous line with negative slope.

The domain is the horizontal extent of the function, all of the values for which the function is defined.

The graph shows the function is defined not only for all integers (..., -1, 0, 1, ...), but also for all the values between.

The domain is all real numbers.

Answer: y= 3x -5

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

Remove parentheses

collect like terms

move constants to the right

calculate

divide both sides

Answer:

384cm^2

Step-by-step explanation:

8x8x6 = 384

Answer:

  a)  y = 16/x²

  b)  x = 4/5

Step-by-step explanation:

You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.

The wording "inversely proportional to the square" means the form of the equation is ...

  y = k/x² . . . . . . where k is the constant of proportionality

The value of k can be found from the given (x, y) pair.

  k = x²y = (1)²(16) = 16

The equation is ...

  y = 16/x²

Solving for x gives ...

  x = √(16/y)

Then the value of x for y = 25 is ...

  x = √(16/25)

  x = 4/5

45%

You made a higher percentage of shots.

36/80*100 = 45%

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The scale factor of the transformation is 2.25

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

Point H'(4.5, 6.75) is the result of dilating point H(2, 3)

This means that

The scale factor of the transformation = H'/H

Substitute the known values in the above equation, so, we have the following representation

Scale factor = (4.5, 6.75)/(2. 3)

Evaluate

Scale factor = 2.25

Hence, the scale factor is 2.25

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The two line segments after the reflection over the x-axis are vertical lines, and the same will be true for the third segment.

The rule for a reflection over the x-axis is given as follows:

(x,y) -> (x,-y).

Meaning that the x-axis remains constant, while the coordinates of the y-axis are changed.

The vertices of the original triangle will be attributed as follows:

A(1,1), B(4,1) and C(1,5).

Hence the vertices of the reflected triangle will be given as follows:

A'(1,-1), B'(4,-1) and C(1,-5).

Thus the lines are given as follows:

Hence there are three vertical lines.

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Answer:

To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.

For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.

Substituting these values into the first equation, we get:

5 = 2(1) + 1

5 = 2 + 1

5 = 3

This statement is not true, so (1, 5) is not a solution of this system.

On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.

I hope this helps! Let me know if you have any more questions.

Step-by-step explanation:

The possible coordinates of point A such that the distance to point B is 10 units are:

(-5, -4) and (-5, 8)

We know that the distance between two points (a, b) and (c, d) is:

distance = √( (a - c)² + (b - d)²)

In this case, we know that:

B = (3, 2)

A = (-5, y)

And the distance is 10 units, then we can write:

10 = √( (3 + 5)² + (2 - y)²)

10² = 8² + (2 - y)²

100 - 64 =  (2 - y)²

36 =  (2 - y)²

±√36 = 2 - y

±6 = 2 - y

y = 2 ± 6

The two solutions are:

y = 2 + 6 = 8

y = 2 - 6 = -4

Then the possible coordinates are (-5, -4) and (-5, 8).

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Answer: 6

Step-by-step explanation:

Answer:

the 4rd one

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] x - 5= [tex]\frac{1}{2}[/tex] x + 2x - 10

multiply through by 4 ( the LCM of 4 and 2 ) to clear the fractions

3x - 20 = 2x + 8x - 40

3x - 20 = 10x - 40 ( subtract 10x from both sides )

- 7x - 20 = - 40 ( add 20 to both sides )

- 7x = - 20 ( divide both sides by - 7 )

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

Answer:

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

Step-by-step explanation:

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

[tex]\frac{1}{2}x+2x-10=\frac{3}{4}x-5[/tex]

Simplify the left side of the equation by combing [tex]\frac{1}{2}[/tex] and [tex]x[/tex].

[tex]\frac{x}{2}+2x-10=\frac{3}{4}x-5[/tex]

To write [tex]2x[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].

[tex]\frac{x}{2}+2x*\frac{2}{2} -10=\frac{3}{4}x-5[/tex]

Simplify terms by combining [tex]2x[/tex] and [tex]\frac{2}{2}[/tex]. Combine the numerators over the common denominator.

[tex]\frac{x+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Raise x to the power of 1.

[tex]\frac{x^1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x^1[/tex].

[tex]\frac{x*1+2x*2}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x+2x*2[/tex].

[tex]\frac{x*1+x(2*2)}{2} -10=\frac{3}{4}x-5[/tex]

Factor [tex]x[/tex] out of [tex]x*1+x(2*2)[/tex]

[tex]\frac{x(1+2*2)}{2} -10=\frac{3}{4}x-5[/tex]

Multiply 2 by 2.

[tex]\frac{x(1+4)}{2} -10=\frac{3}{4}x-5[/tex]

Add 1 and 4.

[tex]\frac{5x}{2} -10=\frac{3}{4}x-5[/tex]

Combine [tex]\frac{3}{4}[/tex] and [tex]x[/tex].

[tex]\frac{5x}{2} -10=\frac{3x}{4}-5[/tex]

Move all terms containing [tex]x[/tex] to the left side of the equation.

[tex]\frac{7x}{4}-10=-5[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the equation.

[tex]\frac{7x}{4}=5[/tex]

Multiply both sides of the equation by [tex]\frac{4}{7}[/tex]

[tex]\frac{7x}{4}*\frac{4}{7} =5*\frac{4}{7}[/tex]

Simplify both sides of the equation.

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

The height of the tree that produce a shadow of length 27.25 m is 10.18 m.

Height is the vertical distance between two points.

To calculate the height of the try, we use the formula of similar angle.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the height of the tree is 10.18 m.

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Answer: x=8,r=30

Step-by-step explanation:

Answer:

y = 1/9x + 5

Hope this helps!

Step-by-step explanation:

y = mx + b

m = slope

y = [tex]\frac{1}{9} x[/tex] + b

( x, y ) = ( 0, 5 )

(5) = [tex]\frac{1}{9} (0)[/tex] + b

5 = 0 + b

5 = b or b = 5

Putting it all together gets you y = [tex]\frac{1}{9} x[/tex] + 5

Answer:

The slope of the perpendicular line is -2.

Step-by-step explanation:

A perpendicular line has a slope that is the negative inverse of the slope of the reference line.  The reference line in this problem is 3x-6y=144.

Let's rearrange this equation to standard slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the valuue of y when x=0).

3x-6y=144

-6y=144-3x

-6y=-3x + 144

 y = (3/6)x + (144/-6)

 y = (1/2)x - 24

This line has a slope of (1/2) and a y-intercept of -24.  A line perpendicular to this will have a slope that is the negative inverse of (1/2).  This would be -2.  The new line will take form:

 y = -2x + b

We are not given b, and there is not enough information to calculate one, so let's assume a value of -24, so that it intersects the original line at (0, -24).  See the attached graph.

1) The point of intersection is (1, 2) and (-1, 0).

2) The point of intersection is (4, 18).

3) The solutions are 0 and -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = x²(x + 1) and g(x) = x + 1

The point of intersection.

f(x) = g(x)

x²(x + 1) = (x + 1)

x² = 1

x = √1

x = ±1

x = 1, f(x) = 2.

(1, 2)

x = -1, f(x) = 0

(-1, 0)

x = 1, g(x) = 2

(1, 2)

x = -1, g(x) = 0

(-1, 0)

This means,

The point of intersection is (1, 2) and (-1, 0).

Now,

f(x) = (x + 5)(x - 2) and g(x) = (2x + 1)(x - 2).

The point of intersection:

f(x) = g(x)

(x + 5)(x - 2) = (2x + 1)(x - 2).

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

x = 4, f(4) = 9 x 2 = 18

x = 4, g(4) = 9 x 2 = 18

(4, 18)

The point of intersection is (4, 18).

Now,

(x - 3) (x + 5) = -15

The solutions to this equation.

x² + 5x - 3x - 15 = -15

x² + 2x - 15 + 15 = 0

x² + 2x = 0

x(x + 2) = 0

x = 0 and x + 2 = 0

x = 0 and x = -2

The solutions are 0 and -2.

Thus,

1) The point of intersection is (1, 2) and (-1, 0).

2) The point of intersection is (4, 18).

3) The solutions are 0 and -2.

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The value of the equation 3d/ac x 2ad/30 is ( d² / 5c )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = 3d/ac x 2ad/30   be equation (1)

On simplifying the equation , we get

A = 3d/ac x 2ad/30  

A = 6ad² / 30ac

On further simplification of the equation , we get

The value of A = 1/5 ( ad² / ac )

The value of A = 1/5 ( d²/c )

Therefore , the value of A is  ( d² / 5c ) or A = 1/5 ( d²/c )

Hence , The value of the equation 3d/ac x 2ad/30 is ( d² / 5c ) or

A = 1/5 ( d²/c )

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The equivalent expression is 1.5^24/0.7^18

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

one and five tenths raised to the fourth power divided by seven tenths raised to the third power, all raised to the sixth power

Rewrite properly

So, we have

(1.5^4/0.7^3)^6

Open the brackets

So, we have the following representation

(1.5^4/0.7^3)^6 = 1.5^(4 * 6)/0.7^(3*6)

Evaluate the products

(1.5^4/0.7^3)^6 = 1.5^24/0.7^18

Hence, the solution is 1.5^24/0.7^18

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The image after a dilation by a scale factor of 4 centered at the origin is (-132,-352).

Scale factor is a mathematical term that refers to the ratio of two corresponding sides of similar shapes. It is used to compare the size of objects or figures by determining the size of a model in relation to its actual size. For example, if two shapes are similar, then their scale factor will be the same. This is useful in engineering and architecture when building scaled models of structures and machines. Scale factors can also be used to determine the proportions and measurements of an object in relation to similar objects.

This is because a dilation by a scale factor of 4 is the same as multiplying the original coordinates by 4. So, if the original coordinates were (-3,-8), then the new coordinates would be (-12,-32). Then, the coordinates are shifted by the center (the origin), so the new coordinates are (-132,-352).

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The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to  54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                         = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

              = 58 × 0.94

              = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                    = √ 58 × 0.94 × 0.06

                                    = √3.2712

                                    = 1.808

Variance 'σ²' =  np( 1 - p )

                     = 58 × 0.94 × 0.06

                     = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

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Answer:

Step-by-step explanation:

directly proportional means same

x=y

512=128

64=y

512/64=8

128/8=16

when x=64 then the value of y=16

Answer:

C

Step-by-step explanation:

given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

to find k use the condition when x = 512, y = 128

128 = 512k ( divide both sides by 512 )

[tex]\frac{128}{512}[/tex] = k , that is k = 0.25

y = 0.25x ← equation of proportion

when x = 64 , then

y = 0.25 × 64 = 16

Answer: 20

Step-by-step explanation: There are 2 ways to solve this problem. This is one way, it is a shortcut. So if you didn't know, 25% of 100 (the whole thing) is 1/4, so if you divide 80 by 1/4, you should get 20. The 2nd way is to set up a proportion, so it would be 25 over 100 = ? over 80. Now, you would cross multiply the 25 and 80 to get 2000. Then you take the 2000 and divide it by 100 to get 20. I hoped this explanation helped you.

Answer:

20

Step-by-step explanation:

Write 25% as 25/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

25/100 of 80 = 25/100 × 80

Therefore, the answer is 20

If you are using a calculator, simply enter 25÷100×80 which will give you 20 as the answer.

Answer:

Seagle =10

Dolphin =2.5

Penguin-flat =0

Shark = -2.5

Clownfish= -7.5

Octpus= -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between each animal and the sea level is already shown in the image.

- for the seagull the vertical line with measurements of 0,5, 10 if you measure how high the seagull it would be 10 cm, how do I measure it? go from 0 to the height of the dolphin and you'll find the answer.

- for the dolphin, look at the vertical line with measurements of 0,5, and 10  how do I measure it? go from 0 to the height of the dolphin and you'll find the answer which would be 2cm.

you keep doing the same thing to the other animals the meters are shown on the image you have to measure from 0 and go up or down depending on where the animal is.

Answer: 18/8 = 9/4

Step-by-step explanation:

6 can be write as 6/1

6/1 timed 3/8 = 18/8

Simplify by 2 = 9/4

Answer:

Richard = 23

Teo= 5

Step-by-step explanation:

R + T = 28

R = 2T + 13

(2T+13)+T = 28

3T + 13 = 28

3T = 28 - 13

3T = 15

T = 15/3

T = 5

(Checking your answer)

R + 5 = 28

R = 28 - 5

R = 23

R = 2(5) + 13 = 10 + 13 = 23

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Answer:

20

Step-by-step explanation:

6*(60/15) = 1.5 (milles)

9*(60/40) = 13.5 (milles)

1.5 + 13.5 = 15 (milles)

15 / (45/60) = 20 (milles per hour)

The speed of Amy is 8.6 mph.

Speed is defined as the rate of change of distance with time. It has the dimension of distance by time. Thus, the SI unit of speed is given as the combination of the basic unit of distance and the basic unit of Time. Thus, the SI unit of speed is metre per second.

Given that, Jessica runs for 15 minutes at an average speed of 6 miles per hour. She then runs for 40 minutes at an average speed of 9 miles per hour. It takes Amy 45 minutes to run the same total distance that Jessica runs.

Calculating the distance covered by Jessica,

15 minutes = 0.25 hours

Speed = distance / time

Distance = speed × time

Distance = 0.25 × 6 = 1.5 mile

And,

40 minutes = 2/3 hours

Distance = 2/3 × 9 = 6 miles

Total distance covered by Jessica = 1.5+6 = 6.5 miles

Since, Amy covers the same distance in 45 minutes,

Therefore, 45 minutes = 3/4 hours

Speed = 6.5/0.75 = 8.6 mph

Hence, The speed of Amy is 8.6 mph.

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