How many 7 digit telephone numbers can be formed from the digits 0,1,2,...,9, where each telephone number begins with digit 2?

The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

What is area of square ?

Area of square can be defined as the square of given side.

Given ,

Let's assume that the side length of the original square is 's'. The perimeter of the original square is then 4s and its area is s².

The perimeter of the dilated square will be 4 times longer than the original square, so it will be 4 * 4s = 16s.

The area of the dilated square will be 4 times greater than the original square, so it will be 4^2 * s² = 16s².

Here s is 12

so ,

16s = 16 * 12 = 192

16s*s = 16 * 12 * 12 = 2304

Therefore, The perimeter and area of the original square are 4s and s², respectively, and the perimeter and area of the dilated square are 192 and 2304, respectively.

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Answer:

a= 12, b=4, Choices B and F

Step-by-step explanation:

2/2=1

8/2=4

12/2=6

Answer:

20

Step-by-step explanation:

[tex]\sqrt[3]{64xy^{3}}[/tex] = [tex]\sqrt[3]{64}[/tex] × [tex]\sqrt[3]{x}[/tex] × [tex]\sqrt[3]{y^{3}}[/tex]

a = coefficient

  = [tex]\sqrt[3]{64}[/tex]

∴a = 4

[tex]x^{b}[/tex] = [tex]x^{-2}[/tex]×[tex]\sqrt[3]{x}[/tex]

   = [tex]x^{-2}[/tex]×[tex]x^{\frac{1}{3}}[/tex]

   = [tex]x^{-2+\frac{1}{3}}[/tex]

   = [tex]x^{\frac{-6}{3} + \frac{1}{3}}[/tex]

   = [tex]x^{\frac{-6+1}{3}}[/tex]

[tex]x^{b}[/tex] = [tex]x^{-\frac{5}{3}}[/tex]

∴b = [tex]-\frac{5}{3}[/tex]

[tex]y^{c}[/tex] = [tex]y^{-4}[/tex]×[tex]\sqrt[3]{y^{3}}[/tex]

   = [tex]y^{-4}[/tex]× [tex](y^{3})^{\frac{1}{3}}[/tex]

   = [tex]y^{-4}[/tex] × [tex]y[/tex]

   = [tex]y^{-4 + 1}[/tex]

[tex]y^{c}[/tex] = [tex]y^{-3}[/tex]

∴c = [tex]-3[/tex]

∴Product of a, b and c = [tex](4)[/tex]×[tex](-\frac{5}{3})[/tex]×[tex](-3)[/tex]

                                      = 20

Step-by-step explanation:

We can start by using an equation to represent the given information. Let's call the number p, and the number k, then:

k = (1/5)p + 6

So, "six more than one-fifth of a number p is equal to a number k" can be represented mathematically as k = (1/5)p + 6. To find the value of p, we can solve for p:

p = 5k - 30

So, p is equal to 5 times the value of k minus 30.

The intervals of each behavior of the function are given as follows:

a) Increasing: (-∞, -1).

b) Decreasing: (-1, 1).

c) Constant: (1, 3).

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable .

here, we have,

to classify the function as increasing, decreasing or constant:

The function is increasing when the graph moves right and up.

The function is decreasing when the graph moves right and down.

The function is constant when the graph of the function is an horizontal line.

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With percentage=76% of foreign coins of total 150 coins, Other coins collected were 36.

What is the percentage?

In mathematics, a percentage is a statistic or ratio that may be expressed as a fraction of 100. To find the percentage of a number, divide it by its total and multiply by 100. Hence, the percentage represents one part of a hundred. The phrase % stands for one hundred percent. It is represented by the symbol "%".

Here are some instances of percentages:

Now,

Given that total coins=150

Foreign coins=76% of total

then other coins are 24% of total

so other coins=150*24/100

=72/2

=36

Hence,

          Other coins collected were 36.

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Answer: 266

Step-by-step explanation:

I = prt

p= 1900

r=.07

t=2

1900x.07x2=266

Answer:

Alex spends more time 2/5 of 100 is 40%

Answer:

C.Only Maryanne's equation has the same solution as the original equation.

The solution is : 39 is the solution to Mr. Smith's equation.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

the equation is:

(16-2w)^2 + (3y÷3z)

Let w=5 y=9 and z=3

(16-2*5)^2 + (3*9÷3*3)

PEMDAS says parentheses first

Multiply and divide in the parentheses

(16-10)^2 + (27÷9)

Then add and subtract in the parentheses

(6)^2 + (3)

Now the exponent

=36 +3

=39

Hence, The solution is : 39 is the solution to Mr. Smith's equation.

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complete question:

What is the solution to Mr. Smith's equation?

The requried hours spent babysitting and tutoring are 5 and 8 hours respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the hours spent babysitting and tutoring be x and y respectively,
According to the quesiton,

Mark gets paid $6 per hour for babysitting and $15 an hour for tutoring. He makes $150 in one week.
6x + 15y = 150 - - - -(1)

John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114.
10x + 8y = 114 - - - - -(2)

Solving above equations 1 and 2 by elimination method we get x = 5 and y = 8

Thus, the requried hours spent for babysitting and tutoring are 5 and 8 hours respectively.

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Answer:

x = 80

Step-by-step explanation:

supplementary angles sum to 180°

sum the 2 angles and equate to 180

x + 40 + x - 20 = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2 * π * r, where r is the radius of the circle. We can find the radius of the circle by rearranging the formula to r = C / (2 * π).

Substituting the given values into the formula, we get:

r = 21.98 inches / (2 * 3.14) = 21.98 inches / 6.28 = 3.50 inches

The diameter of the circle is equal to twice the radius, so we can find the diameter by multiplying the radius by 2:

d = 2 * r = 2 * 3.50 inches = 7.00 inches.

To find the diameter of a circle with a given circumference, you can use the following steps:

Define the formula for the circumference of a circle: The circumference of a circle is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Substitute the given circumference into the formula: If the circumference of the circle is 21.98 inches, we can substitute that into the formula to get 21.98 = 2πr.

Solve for the radius: To solve for the radius, we can divide both sides of the equation by 2π: 21.98 / 2π = r. Using 3.14 for π, this gives us 21.98 / (2 * 3.14) = r, which can be simplified to r = 2.01 inches.

Calculate the diameter: The diameter of a circle is twice the radius, so the diameter can be calculated as 2 * r = 2 * 2.01 = 4.02 inches.

So, the diameter of the circle with a circumference of 21.98 inches is 4.02 inches.

Answer:

$3.25 per hotdog

Step-by-step explanation:

This question can be written as a system of equations:

x = price of hotdogs

y = price of drinks

First family:

4x + 4y = 18

Second family

5x + 3y = 20

Multiply each equation so that one of the variables can cancel out:

-3(4x + 4y = 18)

4(5x + 3y = 20)

First equation:

-12x - 12y = -54

Second equation

20x + 12y = 80

Add the equations together

-12x - 12y = -54

20x + 12y = 80

8x = 26

Divide

x = $3.25

Insert the x into one of the original equations to find y:

4(3.25) + 4y = 18

13 + 4y = 18

4y = 5

y = $1.25

In right triangle ABC, the value of x is equal to 0.06.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Since the angle formed by side A is a right triangle, we have the following complementary angles;

C + B = 90

sin(C) = cos(B)

x + 0.26 = 3x + 0.14

3x - x = 0.26 - 0.14

2x = 0.12

x = 0.12/2

x = 0.06

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There will be about 95 counselors there with the help of expression 2375/50.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total campers = 2375

and for each cabin there are 2 counselors and 50 campers

then no. of cabins = 2375/50

No. of counselors= 2*no. of cabins

=2*2375/50

=95

Hence,

            There will be about 95 counselors there with the help of expression 2375/50.

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In the cyclic quadrilateral the value of R and S are

< S = 87 degrees

< R = 216 degrees

In a cyclic quadrilateral, the opposite angles are supplementary hence

< S + < Q = 180

in the problem we have that < Q = 93

< S + 93 = 180

< S = 180 - 93

< S = 87 degrees

Angle R is adjacent angle to angles 126 and 90 hence we have that

< R = 126 + 90

< R = 216 degrees

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note a variable is a alphabet can be assigned to any value, while a constant is a fixed number or value.

Answers:

variable = t

constant = -7

Step-by-step explanation:

So we know that a variable is a letter while a constant is a number

in here -7 is the constant (the number) and t is the variable (the letter)

Therefore, the variable is t and the constant is -7.

Answer:

To approximate the area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2], we can use the right rectangle method, where the heights of the rectangles are given by the value of the function at the right endpoint of each subinterval. If we divide the interval [0, 2] into 4 equal subintervals of width 0.5, the right endpoint of each subinterval would be 0.5, 1, 1.5, 2.

The height of the first rectangle would be f(0.5) = 0.5^2 + 4 = 4.25, the height of the second rectangle would be f(1) = 1^2 + 4 = 5, the height of the third rectangle would be f(1.5) = 1.5^2 + 4 = 6.25, and the height of the fourth rectangle would be f(2) = 2^2 + 4 = 8.

The sum of the areas of the rectangles is equal to (0.5) × (4.25 + 5 + 6.25 + 8) = (0.5) × 24 = 12.

So, the approximate area between the x-axis and the graph of f(x) = x^2 + 4 over the interval [0, 2] is 12.

Some way to solve binary operations are listed below

By definition, binary operations involve performing arithmetic operations on two operands in a specific way.

An example of a binary expression is a + b

Where a and b are the operands & + is the operator

Some common binary operations and how to solve them are highlited below

Other operations are

Multiplication (*), Division (/) and Modulus

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Answer:

choice B

Step-by-step explanation:

plug in a few test values of x to prove it.  The other choice would be a cube root function of x.

Lowell's verbal representation of the equation y = x - 25 is "y is equal to x minus 25".

This verbal representation accurately describes the equation. In the equation, y is the dependent variable and x is the independent variable. The equation says that y is equal to x minus 25, which means that for every value of x, there is a corresponding value of y that is x minus 25.

So, Lowell has completed the task correctly.

Answer:

So, the answer is (b) 320 feet.

Step-by-step explanation:

Let's call the length and width of the first playground "x".

The perimeter of the first playground is 160 feet, so 2 times the length plus 2 times the width is equal to 160:

2x + 2x = 160

Simplifying:

4x = 160

Dividing both sides by 4:

x = 40

So the length and width of the first playground are both 40 feet.

The second playground is twice as long and twice as wide as the first playground, so the length and width of the second playground would be 2 * 40 = 80 feet.

The perimeter of the second playground would then be 2 * 80 + 2 * 80 = 320 feet.

So, the answer is (b) 320 feet.

The values of x for which z is greater than y are 7.

In mathematics, an equation is a statement that two mathematical expressions are equal. The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

Equations can be represented in different forms, such as algebraic equations, differential equations, integral equations, and partial differential equations. Algebraic equations are the most common type of equations, and they involve algebraic operations such as addition, subtraction, multiplication, and division.

Equations can be classified according to their degree, which is the highest power of the variable in the equation. Linear equations are those with a degree of one, and they can be represented by a straight line on a graph. Quadratic equations have a degree of two, and they can be represented by a parabolic curve. Higher degree equations are generally more complex, and they may not have a simple geometric representation.

For x = -4, y = 4(-4) - 3 = -19 and z = -18, so y is greater.

For x = 2, y = 4(2) - 3 = 5 and z = 6, so z is greater.

For values of x where z is greater than y, we need to compare the values of z and y for each x value in the table.

At x = 3, y = 4(3) - 3 = 9 and z = 9, so they are equal.

At x = 7, y = 4(7) - 3 = 25 and z = 27, so z is greater.

At x = 10, y = 4(10) - 3 = 37 and z = 35, so z is not greater than y.

Therefore, the values of x for which z is greater than y are 7.

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The graph of the function is added as an attachment

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

h(x) = (1/3)ˣ - 4

The above function is an exponential function shifted down from the origin by 4 units

An exponential function of this form is represented as

h(x) = a(b)ˣ + c

Where

Initial value = a

Rate = b

Shift = c

Using the above as a guide, we have the following:

a = 1

b = 1/3

c = -4

Next, we plot the graph

See attachment for the graph of the function

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Answer:

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

Given inequality:

Consider x ≠ 0 and multiply all terms by x, 4 and 3:

The x-intercepts are:

This quadratic function has a positive leading coefficient and two zeros, and hence is positive when:

The matching choice is C.

The x-components  and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.

In mathematics, an axis is a reference line used to locate points in space. It is often used to define a coordinate system, which is a system for representing points and geometric shapes in space using numbers or coordinates.

To find the x- and y-components of the vector [tex]\mathbf{\hat v}[/tex] = (3.0 cm/s, −x-direction), we need to determine the direction of the vector. The notation "-x-direction" means that the vector points in the opposite direction of the positive x-axis. Therefore, the angle between the vector and the negative x-axis is 180 degrees.

The magnitude (or length) of the vector is given by the first component, which is 3.0 cm/s.

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 3.0 cm/s x cos(180°) = -3.0 cm/s

The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 3.0 cm/s x sin(180°) = 0 cm/s

Therefore, the x-components  and y-components of the vector [tex]\mathbf{\hat v}[/tex] are -3.0 cm/s and 0 cm/s, respectively.

Expressed as an ordered pair, the components are (-3.0 cm/s, 0 cm/s).

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The new triangle with vertices A'(0, 6), B'(12, -6), and C'(6, -6) would be larger than the original triangle by a factor of 120%.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

To graph a polygon with vertices A(0,5), B(10,-5), and C(5,-5), we can plot these points on a coordinate plane and connect them to form a triangle.

Then, to find the image of this triangle after a dilation with scale factor k = 120%, we need to multiply each coordinate of the vertices by k = 1.2.

For vertex A, the new coordinates would be (0 × 1.2, 5 × 1.2) = (0, 6).

For vertex B, the new coordinates would be (10 × 1.2, -5 × 1.2) = (12, -6).

For vertex C, the new coordinates would be (5 × 1.2, -5 × 1.2) = (6, -6).

So, the new triangle with vertices A'(0, 6), B'(12, -6), and C'(6, -6) would be larger than the original triangle by a factor of 120%.

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