Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library?

This is about transformation of objects.

Scale factor back to original size = 1/7

What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;

7x and 7y.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

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We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.

To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.

Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.

Answer: The rate of decay is 93.3%.

Step-by-step explanation:

Since we have given that

The exponential function is given by

[tex]n(x)=7(0.067)^x[/tex]

As we know the general equation of exponential function that is given by

[tex]n(x)=a(1-b)^x[/tex]

Here, a denotes the initial value

1-b denotes the rate of decay.

So, On comparing both the equations, we get that

[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]

Hence, the rate of decay is 93.3%.

To find the number of batches of pasta, convert the amount of flour per batch to an improper fraction, create an equation based on the total flour used, and solve for the number of batches, which is 16.

To solve for b, the number of batches of pasta the chef makes during the week using a total of 86 pounds of flour:

First, convert the amounts of each flour from mixed numbers to improper fractions:

1 5/8 pounds = 13/8 pounds

Now add the two amounts together to get the total flour used per batch:

(15/4) + (13/8) = 30/8 + 13/8 = 43/8 pounds per batch

The equation to solve for b is:

(43/8) * b = 86

To find b:

b = 86 / (43/8)

Multiply both sides by the reciprocal of 43/8:

b = 86 * (8/43)

b = (86 * 8) / 43

Calculate the value of b:

b = 688 / 43

b = 16

The value of equation ax + b is 3.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To find the value of ax + b, we need to isolate that expression on one side of the equation.

Starting with:

9ax + 9b - 6 = 21

We can add 6 to both sides:

9ax + 9b = 27

Then, we can factor out 9 from the left-hand side:

9(ax + b) = 27

Dividing both sides by 9, we get:

ax + b = 3

Therefore,

The value of equation ax + b is 3.

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Answer:

The 3 is the numerator, To read the number is "three-fourths"

Step-by-step explanation:

I hope this helps!

The answer is  y=14 and x= 10

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here:  One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.

Then we have 5x+13y=232

                         12x+7y=218

Solving these two equations here we get y=14 and x= 10

Hence, The answer is  y=14 and x= 10

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The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.

The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.

First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.

Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.

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Answer:  The perimeter of the hexagon is 18 cm.

Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.

The diagonals g and h divides the hexagon into two two equilateral triangles and one square .

Also, length of diagonal g = 3 cm.

We are to find the perimeter of hexagon.

We know that all the sides of a square are equal, so we have

length of b = length of h = length of e = length of g = 3 cm.  

Since the two triangles are equilateral, so all their sides will be equal.

That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.

We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.

Therefore, the perimeter of hexagon is given by

P = a + b + c + d + e + f  = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.

Thus, the perimeter of the hexagon is 18 cm.

Answer:

Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].

Step-by-step explanation:

Given  : f(x) = y = 100 - x²

To find : Find inverse.

Solution : We have given that :

f(x) = y = 100 - x²

Step1) : Replace every x with a y and replace every y with an x .

x = 100 - y².

Step 2): Solve for y

On subtracting 100 from both sides

x - 100 = -y²

On multiplying both side by -1

100 -x = y²

Taking square root both sides and switching sides

y = ± [tex]\sqrt{100-x}[/tex].

Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Answer:

A on edge

Step-by-step explanation: