a cabinet holds shelves that are 12 1/2 inches apart. On one shelf, Katherine stacked a CD player that is 4 5/8 in. high on top of an amplifier that is 6 3/4 in. high. How much space was left above the CD player?

A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.

A graph can show a functional relationship by showing a line or curve that consistently increases or decreases when the independent variable is changed. This will show a direct relationship between the two variables, and the pattern of the line or curve will show the functional relationship that exists.

A graph can demonstrate a functional relationship by showing a line or curve that changes with the independent variable, indicating a direct relationship between the two variables.

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4/5 and 6/10 form a proportion.

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Using the function f(x) = 500(0.67)^x :

A).f(0) = 500, f(1) = 335, f(2) = 224.45 and f(3) = 150.3815

B). 33% of bugs are eaten each day

C). 67% of the bugs remain each day

D). After day 7 will there remain fewer than 40 bugs in the farm.

The function of a function rule is defined as the process that changes the input value to output.

day 1 will have 165 bugs eaten with a percentage evaluated as;

(165 × 100)/500 = 33%

day 2 will have 110.55 bugs eaten with a percentage evaluated as;

(110.55 × 100)/335 = 33%

day 3 will have 74.0685 bugs eaten with a percentage evaluated as;

(74.0685 × 100)/224.45 = 33%

day 1 will have 335 bugs remaining with a percentage evaluated as;

(335 × 100)/500 = 67%

day 2 will have 224.45 bugs remaining with a percentage evaluated as;

(224.45 × 100)/335 = 67%

day 3 will have 150.3815 bugs remaining with a percentage evaluated as;

(150.3815 × 100)/224.45 = 67%

At day 7;

f(7) = 500(0.67)⁷

f(7) = 30.30.

Therefore, 500, 335, 224.45 and 150.3815 are the respective population the days:0, 1, 2, and 3. for the function f(x) = 500(0.67)^x

33% of bugs are eaten each day

67% of the bugs remain each day and,

After day 7 will there remain fewer than 40 bugs in the farm.

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Answer:

the highest (hcf) would be 6 , while lowest (lcm) is 5,040

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

In math, it is possible to multiply, divide, add, or subtract. The following sentence form describes an expression: (Mathematical Operator, Number or Variable, Expression) Numbers, variables, and operations make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be compared.

given

expression = x²+7x+8/x²+2x-1

x²+8/x²+7x+2x-1

5x + 1/x2 + 2x -1

5x/x²+2x-1

The expression that is equal to the provided expression, x2+7x+8, is 5x/x2+2x-1.

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Answer:

4,6,8,12

Hope it helps because im not sure if its right

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Answer:

27000 m

Step-by-step explanation:

1km = 1000 m

27km = 27 x 1000 = 27000 m

So, the answer is 27000 m

Answer:27 km in meters is 27000 m

Step-by-step explanation:

multiply the length by 1000!

The solution of the system of equations for this problem is given as follows:

(x-intercept, 0).

Via graphing, the solution of the system of equations is obtained by the point of intersection of the points.

An horizontal line can be traced through the point of intersection.

This line coincides with the x-axis, hence the y-coordinate of the solution is given as follows:

y = 0.

Due to the x-intercept method, the x-coordinate of the solution is the x-intercept.

The equations for this problem are not given, hence the solution is given in general terms.

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The total words Cecilia types over a 4 minute period is 152 words

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The slope intercept form of a linear equation is:

y = mx + b

where m is the slope and b is the y intercept.

Let y represent the total words that Cecilia types after x minutes.

Cecilia types at a speed of 38 words per minute. Hence:

y = 38x

After 4 minutes:

y = 38(4) = 152 word

The total words Cecilia types over a 4 minute period is 152 words

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The size of the cardboard piece required is 7627.0 in.

The formula for finding the size of a box is

2(L + W) + 8L + 8W = Perimeter of the cardboard piece

Where L = Length, W = Width

We need to find L and W to find the size of the cardboard piece.

7623 = 2(L + W) + 8L + 8W

7623 = 2L + 2W + 8L + 8W

7623 = 10L + 10W

7623/10 = L + W

762.3 = L + W

Let's take L = 500 and W = 262.3 (762.3 - 500 = 262.3)

Now we plug in the values of L and W in the original formula

2(500 + 262.3) + 8(500) + 8(262.3) = 7623

2(762.3) + 4000 + 2102.4 = 7623

1524.6 + 4000 + 2102.4 = 7623

7627.0 = 7623

Therefore, the size of the cardboard piece required is 7627.0 in.

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According to the notes of Maggie the price for per foot length of deck division board is -6 feet for $5.88 = $0.98,8 feet for $8.79 = $1.09 ,10 feet for $10.68 = $1.06 ,12 feet for $13.43 = $1.11 .

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Here,

The first record for deck board noted by Maggie is -

The length of the deck board = 6 feet

Price for 6 feet of deck board = $5.88

Use the division method -

Price for 1 feet of deck board = 5.88/6

Price per feet of deck board = $0.98

The second record for deck board noted by Maggie is -

The length of the deck board = 8 feet

Price for 6 feet of deck board = $8.79

Use the division method -

Price for 1 feet of deck board = 8.79/8

Price per feet of deck board = $1.09

The third record for deck board noted by Maggie is -

The length of the deck board = 10 feet

Price for 6 feet of deck board = $10.68

Use the division method -

Price for 1 feet of deck board = 10.68/10

Price per feet of deck board = $1.06

The fourth record for deck board noted by Maggie is -

The length of the deck board = 12 feet

Price for 6 feet of deck board = $13.43

Use the division method -

Price for 1 feet of deck board = 13.43/12

Price per feet of deck board = $1.11

The fifth record for deck board noted by Maggie is -

The length of the deck board = 14 feet

Price for 6 feet of deck board = $15.65

Use the division method -

Price for 1 feet of deck board = 15.65/14

Price per feet of deck board = $1.11

The sixth record for deck board noted by Maggie is -

The length of the deck board = 16 feet

Price for 6 feet of deck board = $17.88

Use the division method -

Price for 1 feet of deck board = 17.88/16

Price per feet of deck board = $1.11

The seventh record for deck board noted by Maggie is -

The length of the deck board = 18 feet

Price for 6 feet of deck board = $20.99

Use the division method -

Price for 1 feet of deck board = 20.99/18

Price per feet of deck board = $1.16

The eighth record for deck board noted by Maggie is -

The length of the deck board = 20 feet

Price for 6 feet of deck board = $24.99

Use the division method -

Price for 1 feet of deck board = 24.99/20

Price per feet of deck board = $1.24

Therefore, the value for deck board per foot length is $0.98, $1.09, $1.06, $1.11, $1.11, $1.11, $1.16, $1.24.

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Answer:

Step-by-step explanation:

10.00 amps

The solution for given linear inequality will be x>11/2.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given linear inequality is

10<2x-1

i.e. x>11/2.

The number line is in image.

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The polynomial 8X/Y has a coefficient of X of 8.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is often a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

In the above polynomial 8X/Y, the coefficient of X is 8.

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The total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

We can start by using the following equation to find the total cost of the child tickets:

Child tickets cost = Number of child tickets x Cost per child ticket

In this case, the number of child tickets is 4 children/family x 6 families = 24 children

The cost per child ticket is $4.

So, the total cost of the child tickets would be:

24 children x $4/child = $96

Similarly, we can find the total cost of the adult tickets:

Adult tickets cost = Number of adult tickets x Cost per adult ticket

In this case, the number of adult tickets is 2 adults/family x 6 families = 12 adults

The cost per adult ticket is $8.

So, the total cost of the adult tickets would be:

12 adults x $8/adult = $96

To find the total cost of the festival tickets, we can add the cost of the child tickets and the cost of the adult tickets:

Total cost = Child tickets cost + Adult tickets cost

$96 + $96 = $192

So, the total cost of the festival tickets for 6 families with 2 adults and 4 children would be $192.

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A bivariate probability distribution is a statistical distribution that describes the joint probability of two random variables. It provides the probability of each combination of values for the two variables. In simple words, it's a way to model the joint probability of two variables and the relationship between them.

A bivariate probability distribution is represented by a probability density function (pdf) or a probability mass function (pmf) depending on whether the variables are continuous or discrete. The function gives the probability of a given pair of values of the two variables. Bivariate probability distributions are useful in understanding the relationship between two variables and can be used to make predictions or draw inferences. It can be visualized using a scatter plot, a contour plot or a 3D plot. It can also be used to calculate the covariance and correlation between the two variables.

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Complete question:

Describe Bivariate Probability Distribution.

The scale factor for the dilation from the quadrilateral EFGH to form DABC is the fraction 3/5.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

Considering the coordinates (1/2, 3/4) and (3/10, 9/4) centered at the original, we will observe the the point 1/2 was increased by 3/5 to become 3/10 at the x–axis, that is;

1/2 × 3/5 = 3/10

Also, the point 3/4 was increased by 3/5 to become 9/20 at the y–axis, that is;

3/4 × 3/5 = 9/20

Therefore, 3/5 is the scale factor of the dilation for the quadrilateral EFGH to DABC.

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4 2 add y 2 root that

it's pretty easy and thanks for the high points ur welcome ur in the matrix kid

To find g(0) we need to substitute x = 0 into the function g(x) = 6x + 2.

g(0) = 6(0) + 2 = 0 + 2 = 2

So, g(0) = 2

Therefore, the value of the function g(x) when x is equal to 0 is 2.

The slope of the line passing through the points is given by the equation Slope m = 15/11

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P = P ( 7 , 10 )

Let the second point be represented as Q = Q ( 18 , 25 )

Now , the slope of the line between the points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 25 - 10 ) / ( 18 - 7 )

On simplifying the equation , we get

Slope m = 15/11

Hence , the slope of the line is m = 15/11

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Answer:

To find the final balance of an account earning interest compounded continuously, you can use the formula:

A = Pe^(rt)

where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.

Substituting in the given values:

A = 550 * e^(0.066 * 10)

Therefore, the final balance would be approximately $1064.14.

Answer:

C)  $1064.14

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=550e^{0.066 \times 10}[/tex]

[tex]\implies A=550e^{0.66}[/tex]

[tex]\implies A=550(1.93479233...)[/tex]

[tex]\implies A=1064.13578...[/tex]

Therefore, the balance of the account after 10 years would be $1064.14.

The value of the 7th term of the Geometric sequence is 6

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

r is found by dividing the second term by first term.

The nth term of a geometric sequence is S(n) = ar^(n-1).

The common ratio in the sequence = 1458/4374 = 1/3

therefore S(7) = 4374×1/3^( 7-1)

= 4374× (1/3)⁶

= 4374/729

= 6

Therefore the value of the seventh term is 6

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In given word problem the number of cards Alan has is 13 and Number of cards Calvin has is 13.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order  to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here , Let us take Number of card Alan has as A and Number of card bill has as B and Number of cards does Calvin has as C.

Now Alan has 11 less than 2 times the number of cards Bill has then,

=> A = 2B-11 ------------->1

And Calvin has 1 more than 1 times the number of cards Bill has then,

=> C =  B+1 ----------> 2

Here Alan and Calvin has same number of cards then

=> 1 = 2

=> 2B - 11 = B +1

=> 2B-B = 11+1

=> B = 12

Now put B= 12 into 1 then

=> A = 2(12)-11= 24-11 = 13

Now put B= 12 into 2 then

=> C = 12+1 = 13

Hence the number of cards Alan has is 13 and Number of cards Calvin has is 13.

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Brianna wants to reduce it by a scale factor of 1/2, the area of the new garden is 48 ft².

The territory a rectangle occupies inside its four sides or limits is known as its area. A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper.

The formula for calculate the area of a rectangle is:

area of a rectangle = length × width

Where "I" is the length and " w " is the width.

The dimensions of the garden box are:

l = 12 ft

w = 8 ft

Therefore, its area is:

A = (12 ft)(8 ft)

A = 96 ft²

Since Brianna wants to reduce it by a scale factor of 1/2, the area of the new garden is:

Area of new garden = 1/2(96 ft²)

Area of new garden = 48 ft²

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Answer:

[tex]D'(-3,-1.5), E'(0,4.5), F'(3,-3)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

For the value of f (x) = 11, the value of x is

A relation between a set of inputs having one output each is called a function.

We have to given that;

The function is,

⇒ f(x) = -5x + 1

And, f (x) = 11

Now, We have;

⇒ f(x) = -5x + 1

Substitute f (x) = 11, we get;

⇒ 11 = - 5x + 1

⇒ 5x = - 11 + 1

⇒ 5x = - 10

⇒ x = - 2

Thus, The value of x = - 2

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Answer:

  6.9

Step-by-step explanation:

You want half the side length of an equilateral triangle with an altitude of 12.

The altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:

  (2x)² = x² +12²

  3x² = 144 . . . . . . . . subtract x²

  x² = 48 . . . . . . . . divide by 3

  x = √48 = 4√3 . . . take the square root

  x ≈ 6.9

__

Additional comment

You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.

The equation of the function g(x) will be √ [ (x) -  4 )].

A line that, in analytical geometry, is an asymptote of a curve is one where, as one or both of the x or y coordinates tend to infinity, the distance between the curve and the line approaches zero.

An asymptote of a curve is a line that is tangent to the curve at a point at infinity in projective geometry and related contexts.

Given that the function F(x) is √x and is horizontally stretched by a factor of 4 to form function g(x).

The equation of the stretched function can be written as:-

f(x) = √x

g(x) = √ [ (x) -  4 )]

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The sides 10 cm, 24 cm and 26 cm can form a right-angled triangle. The Pythagorean theorem can be used to verify this.

From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angled triangle.

Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,

CA² = AB² + BC²

Now, let us check this rule for the above given sides of the triangle.

Longest side² = Sum of squares of other two sides

26² = 24² + 10²

676 = 576 + 100

Thus, the sides 10 cm, 24 cm and 26 cm can form a right-angled triangle.

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