The table lists the speeds of the fastest roller coasters in North America and Asia.

Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .

Answer:

3x + 16 + 30/x - 13

Step-by-step explanation:

Answer:

  8:07:12 am

Step-by-step explanation:

The lights will change simultaneously after any multiple of the least common multiple of their cycle times.

The least common multiple of a set of numbers is the product of the highest powers of their prime factors.

  48 = 2⁴×3

  72 = 2³×3²

  108 = 2²×3³

The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...

  LCM = 2⁴×3³ = 16×27 = 432

The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.

Answer:

Situation 2 (B)

Step-by-step explanation:

I think it would be B since the power of the gear increases proportionally with the radius.

The function that represents the difference between the moving companies' rates is:

h(x) = -2x + 200.

The difference of two functions is found subtracting the like terms from the functions.

In this problem, the functions for the rates are given as follows:

Hence the difference is given by:

h(x) = 3x + 400 - (5x + 200) = 3x - 5x + 400 - 200 = -2x + 200.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The given graph doesn't represent a function, as it has two values of y for a single value of x ( that is : for x = 3 it has two solutions, -3 and -6 )

therefore it can't be considered as a function ~

Answer:

100

Step-by-step explanation:

Formulate a plan based on the conditions stated: 65/(13/20)

A fraction is divided by multiplying its reciprocal: 65x(20/13)

Remove the connecting element: 5x20

Determine the quotient or product: 100

100 tokens are bought by mark for his daughter.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Mark bought gift tokens for her daughter, Sally, to use at the state fair. Sally used 13/20 of the tokens on rides.

let "x" be the total token she have

Since, total token she used is 65

Thus,

13/20 * x = 65

x = 100

Therefore, Mark bought for his, daughter 100 Tokens.

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Step-by-step explanation:

Given,

s=5

t=8

solution,

= 3st² - s²

= 3*5*8² - 5²

= 3*5*64 - 25

= 960 - 25

= 935

The value of A such that cos A = 0.7715 is 39.5 degrees

The equation is given as:

cos A = 0.7715

Where the angle is in degrees

There are several ways to solve this equation, some of which include:

In this case, we make use of the first option; using a scientific calculator

Recall that the equation is represented as:

cos A = 0.7715

Next, we take the arccos (or anti cosine) of the above equation.

This is represented as

arccos(cos A) = arccos(0.7715)

Evaluate the expression on the left-hand side

A = arccos(0.7715)

Evaluate the expression on the left-hand side using the scientific calculator

A = 39.5112207183

Approximate the above expression

A = 39.5

Hence, the value of A such that cos A = 0.7715 is 39.5 degrees

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The definition of the given piecewise function is:

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x until 2, the function is the cube function shifted down 3 units, hence the definition is:

[tex]y = x^3  - 3, x \leq 2[/tex]

For x greater than 2, the function is the square function shifted up 6 units, hence the definition is:

[tex]y = x^2 + 6, x > 2[/tex]

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Answer:

A. (3x + 4)(x-7)

Step-by-step explanation:

3x times x = 3x^2

3x times -7 = -21x

4 times x = 4x

4 times -7 = -28

-21x + 4x = -17x

3x^2 - 17x - 28

The resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

Quadratic equation are equations that has a leading degree of 2. Most quadratic equations have 3 terms.

Given the quadratic equation x^2-19x-39 = 0

Add 39 to both sides to have:

x^2 - 19x - 39 + 39 = 0 + 39

x^2 -19x = 39

Complete the square of the resulting

x^2-19x+(19/2)^2 = 39 + (19/2)^2
(x+19/2)^2 = 39 + (19/2)^2

x + 19/2 = ±√39 + (19/2)^2

x = ±√39 + (19/2)^2 - 19/2

Hence the resulting equation on completing the square is (x+19/2)^2 = 39 + (19/2)^2

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The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

6x - 5y = -8

6x - 5y = -8

Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8

6x - 5y = -8

- 6x - 5y = -8

----------------------

0 = 0

This in other words means that the difference between both equations is 0

When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions

Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions

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Answer: The answer is D for those who don't like to read extra long expert answers (no offense to experts, just shorten answers to the direct answer pls)

Step-by-step explanation: Edge 2022

Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.

Answer: In 2 pounds there are 0.907 kilograms.

Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.

The future value formula is given by:

[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]

In which:

For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:

P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.

Hence the amount available is given by:

[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]

[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]

F = $100,336.67

The amount deposited was:

15 x 4 x $1000 = $60,000.

Hence the amount earned in interest was:

$100,336.67 - $60,000 = $40,336.67

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The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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Step-by-step explanation:

Transcribed image text: Choosing a Photo Francesca wants to give one of her photographs to a friend as a gift. Help her choose the photograph and determine the style and size of the mat she can afford 1. Describe the design and original dimensions of the photo you chose for Francesca to give as a gift. 2 points: 1 point for describing the photo and 1 point for including the dimensions) Photo description: The photo Shous Francasca and has Friend huagina. Dimensions (including units): The still Photo is a Xg meaning its width is indas and Langth is gind Finding the Total Area of the Photo and Mat 2. Francesca wants to glue her photo on top of a mat that will increase the length of each side. The mat border has a width of x, so the length of each side would increase by 2x inches. Represent the length and width of the mat with an expression. (2 points) Length: Width: 3. The area of the mat is the product of the length and width. Write an expression for area as the product of two binomials. Do not multiply.(1 point)

The answer is y = -5.5x - 52.

First, let's find the slope of the line.

m = Δy/Δx

Now, substitute the slope and one of the given points in the point slope equation.

y - y₁ = m (x - x₁)

Answer: y=-5,5x-52.

Step-by-step explanation:

                        Equation of a straight line

                               [tex]\displaystyle\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

[tex](-10;3)\ \ \ \ \ (-8;-8).\\\displaystyle\frac{x-(-10)}{-8-(-10)} =\frac{y-3}{-8-3}\\ \frac{x+10}{-8+10}=\frac{y-3}{-11} \\ \frac{x+10}{2}=\frac{y-3}{-11} \\-11*(x+10)=2*(y-3)\\-11x-110=2y-6\\2y=-11x-104\ |:2\\y=-5,5x-52.[/tex]

Answer:

By definition, angles A and 1 are corresponding angles and angles B and 1 are consecutive angles. By the corresponding angles postulate, angles A and 1 are congruent, and by the consecutive angles theorem, angles B and 1 are supplementary. By the definition of supplementary angles, measures of angle B and 1 add up to 180 degrees (m<B + m<1 = 180). By definition of congruent angles, angles A and 1 have same measurement (m<A = m<1). By substitution property of equality, measures of angles A and B add up to 180 degrees (m<A + m<B = 180). By definition of supplementary angles, angles A and B are supplementary.

by breaking it down u can write it as

15p^-4/_20p^-12 * q^-6/q^-3

15/-20=-3/4

using law of indices we have

-3/4p^-4+12 * q^-6+3

-3/4p^8q^-3

the answer is the first own

Answer:

376.8 [tex]units^{2}[/tex]

Step-by-step explanation:

There are a lot of moving parts.  We need to find the area of the bottom of the circle the center and the top circle.

The top and the bottom will be the same.

The area of a circle:

a = [tex]\pi[/tex][tex]r^{2}[/tex]

a = 3.14([tex]5^{2}[/tex])

a = 3.14(25)

a =78.5  

The center:  Think of this as a label on soup can.  If you tear the label off it would be a rectangle.  To find the area we would multiply the height of the can by the circumference of the circle.  They tell us the height is 7 and we can calculate the circumference.

C = [tex]\pi[/tex]d The d is the diameter it is 2 of the radiuses.  

C = [tex]\pi[/tex]10

C = 3.14(10)

C = 31.4

Now we multiply 31.4 and 7 together to find the area of the center of the cylinder.

(31.4)(7) = 219.8

The total area:

top 78.5

center 219.8

bottom 78.5

Total 376.8

The average median and mode price is $18. Option C is correct.

Given that certain item is available at 7 stores, three stores sell them for $20, two stores sell them for $15, one store sells them for $13, and one sells them for $16.

The mean is the average of the given numbers and is calculated by dividing the sum of the given numbers by the total number of numbers.

Firstly, we will find the median of the given items by arranging the given numbers in ascending order, we get

13,15,15,16,20,20,20

To find the median use the formula (n+1)/2, where n is the number of values in your dataset.

(7+1)/2=8/2=4

In the ascending order numbers 4th term is 16.

So, median is 16

Mode is the highest repeating term in the set or numbers.

So, here mode is 20

Now, we will calculate the average of median and mode, we get

Average=(median +mode)/2

Average=(16+20)/2

Average=18

Hence, the average (arithmetic mean) of the median price and the mode price where certain item is available at 7 stores, three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16 is $18.

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The base area of cube B is 25/9  times larger than the base area of cube A.

What is area cubic?

We know that volume of cube with each side of  units is equal to .

First of all, we will find the each side of cube A and B as:

[tex]A^{3} = 27[/tex]

[tex]\sqrt[3]{A^{3} } = \sqrt[3]{27}[/tex]

A = 3

[tex]B^{3} = 125[/tex]

[tex]\sqrt[3]{B^{3} } = \sqrt[3]{125}[/tex]

B = 5

Now, we will find base area of both cubes as:

[tex]\frac{Base area of B}{Base area of A} = \frac{B^{2} }{A^{2} }[/tex]

[tex]\frac{Base area of B}{Base area of A} = \frac{5^{2} }{3^{2} }[/tex]

[tex]\frac{Base area of B}{Base area of A} = \frac{25}{9}[/tex]

Therefore, the base area of cube B is 25/9  times larger than the base area of cube A.

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Answer: the area of the triangle is 5.

Step-by-step explanation:

[tex]A(0;0) \ \ \ \ B(1;3) \ \ \ \ C(4;2) \ \ \ \ S_{ABC}=?\\Use \ the\ formula:\\\displaystyle\\\boxed{S=\frac{1}{2}*|[(x_A-x_C)*(y_B-y_C)-(x_B-x_C)*(y_A-y_c)] |}\\x_A=0\ \ \ \ x_B=1\ \ \ \ x_C=4\ \ \ \ y_A=0\ \ \ \ \ y_B=3\ \ \ \ \ y_C=2.\\S=\frac{1}{2}*|[(0-4)*(3-2)-(1-4)*(0-2)]|\\S=\frac{1}{2}*| [(-4)*1-(-3)*(-2)]|=\\ S=\frac{1}{2}*| (-4-6)|\\S=\frac{1}{2}*|(-10)|\\S= \frac{1}{2} *10\\S=5.[/tex]

Total charges from bank A exists $15.

Total charges on Bank B spending exists $45.

Given: Bank A charges a $15 monthly fee for a checking account and debit card, with unlimited transactions.

Shade 25 transactions.

Total charges from bank A = $15 monthly

Bank B charged a $35 monthly fee for a checking account and debit card, plus $ 0.70 for each transaction.

She made 25 transactions.

Total charges on bank B = $35 + (0.40)25

Total charges on bank B = $35+10

Total charges on bank B = $45

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There is only one solution for the equation 4z + 2(z -4) = 3z + 11 because the exponent for the power of z is 1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A solution is any value of a variable that makes the specified equation true.

According to the given information:

4z + 2(z-4)= 3z+11

Solve the equation,

4z+2z-8=3z+11

6z-3z=11+8

3z =19

z=

Hence,

Number of solution that can be found for the equation 4z + 2(z-4)= 3z+11 is option(2) one

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Answer:

x^2

Step-by-step explanation:

So there's very two obvious ones we can elimination immediately, that's f(x) = x, and f(x) = |x|. The reason for this is because we can just look at the first ordered pair of (-2, 4). If it was f(x) = x, then the ordered pair would be (-2, -2), but it isn't. Very similar reasoning for f(x) = |x|, except for this function each ordered pair should have the same magnitude or absolute value. So the f(-2) should output 2, since it's the absolute value, but of course this isn't the case since it's 4.

So let's look at 2^x

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

Since the y value is 4 and not 1/4, this is not the parent function

It should be the second option (x^2), and we can double check

(-2)^2 = 4

(-1)^2 = 1

(0)^2 = 0

(1)^2 = 1

(2)^2 = 4

It outputs the same y-values as the table so this is the parent function

[tex] \sf \blue{True✅}[/tex]

Yes, it's true sometimes we don't use negative value of 'x'.

So, we conclude it's True.

The numeric value of the expression -a² - 2bc - |c| for a = -3, b = -5 and c = 2 is of 9.

The numeric value of an expression is found replacing each letter by it's attributed value.

In this problem, the expression is:

-a² - 2bc - |c|

The attributed values are:

a = -3, b = -5 and c = 2

Hence the numeric value will be given by:

-a² - 2bc - |c| = -(-3)² - 2(-5)(2) - |2| = -(9) + 20 - 2 = -9 + 18 = 9.

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Let [tex]X(s)[/tex] and [tex]Y(s)[/tex] denote the Laplace transforms of [tex]x(t)[/tex] and [tex]y(t)[/tex].

Taking the Laplace transform of both sides of both equations, we have

[tex]\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s[/tex]

[tex]\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}[/tex]

Eliminating [tex]Y(s)[/tex], we get

[tex]\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)[/tex]

Take the inverse transform of both sides to solve for [tex]x(t)[/tex].

[tex]\boxed{x(t) = \dfrac14 (1 - e^t)}[/tex]

Solve for [tex]Y(s)[/tex].

[tex](s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}[/tex]

Taking the inverse transform of both sides, we get

[tex]\boxed{y(t) = e^t - 1 + \dfrac14 t}[/tex]

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.