A salesman's commission varies directly as his sales.If the commission is $10 for $100 in sales, find the commission for $150 in sales.
a. $12 b. $20 c. $15 d. $25

The solution to the inequality is n ≤ 412.

An inequality is a statement that asserts that two values are not equal. An inequality can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The inequality can be written as:

(1/4)n - 6 ≤ 97

To solve for n, we will isolate n on one side of the inequality. First, we can add 6 to both sides:

(1/4)n ≤ 103

Then, we can multiply both sides by 4:

n ≤ 412

Therefore, the solution to the inequality is:

n ≤ 412

This means that any number less than or equal to 412 satisfies the original inequality.

For example, "x > 5" is an inequality that states that the value of x is greater than 5. The inequality "y 10" indicates that the value of y is less than or equal to 10.

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Answer: the height of the hockey puck is approximately 0.835 inches.

Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:

The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).

The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.

As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.

It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.

The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.

The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.

The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1

Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.

The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.

The employment of a calculator to compute the aforementioned expression:

The observed value of h is approximately equal to 0.835 inches.

The slope of the function f(x) = -3x^2 +11 at any value of x is given by 6x.

The definition of derivative is given by the limit as h approaches 0 of [f(a+h) - f(a)] / h,

where f(x) is a function and a is a fixed value of x.

To find the slope of the function[tex]f(x) = -3x^2 +11[/tex]  at any value of x, we need to use this definition of derivative.
So, let's plug in f(x) = -3x^2 +11 and a = x into the formula.

This gives us:
lim as h approaches 0 of [tex][-3(x+h)^2 + 11 - (-3x^2 + 11)] / h[/tex]
Simplifying this expression, we get:
lim as h approaches 0 of [tex][-3x^2 - 6hx - 3h^2 + 11 + 3x^2 - 11] / h[/tex]
Combining like terms, we get:
lim as h approaches 0 of [tex][-6hx - 3h^2] / h][/tex]
Factoring out an h from the numerator, we get:
lim as h approaches 0 of [-h(6x + 3h)] / h
Canceling out the h in the numerator and denominator, we get:
lim as h approaches 0 of 6x + 3h
Now, we can plug in h = 0 to find the slope of the function at any value of x:
6x + 3(0) = 6x.

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The result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

Rotation is a transformation in geometry that involves turning or spinning an object around a fixed point called the center of rotation. The center of rotation remains stationary while all the points of the object move along circular paths, at the same angle and distance from the center.

To rotate a point [x/y] counterclockwise by 90 degrees, we can use a 2x2 matrix of the form:

[ 0 -1 ]

[ 1 0 ]

To multiply this matrix by a point [x/y], we can use the following matrix multiplication:

[ 0 -1 ] [ x ] [ -y ]

[ 1 0 ] [ y ] = [ x ]

So, if we have a point [x/y] and we want to rotate it 90 degrees counterclockwise, we can multiply it by the matrix [ 0 -1 ; 1 0 ] to get the new point [-y/x].

To rotate a point 90 degrees counterclockwise using a matrix, we need to represent the point as a column matrix and then multiply it by the 2x2 rotation matrix.

Assuming that the point is [x, y] = [-5, 2], we can represent it as a column matrix:

| -5 |

| 2 |

To rotate the point counterclockwise by 90 degrees, we can use the following 2x2 rotation matrix:

| 0 -1 |

| 1 0 |

Multiplying the rotation matrix by the column matrix representing the point gives:

| 0 -1 | | -5 | | 2 |

| 1 0 | ×| 2 | = | -5 |

So the result of rotating the point [-5, 2] by 90 degrees counterclockwise is the point [2, -5].

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The area of this tile is 12 cm2.

Area is a two-dimensional measure of space, referring to the total surface area of a shape. It can be measured in terms of square units, such as square feet, meters, or kilometers. Area is an important concept in geometry and can be used to calculate the perimeter, circumference, and volume of a shape. Area calculations are also used in fields such as engineering, architecture, and construction.

Area is the size of a two-dimensional shape or the amount of space within a three-dimensional figure. It is a measure of how much space an object occupies.

The area of this tile can be calculated using the formula:
Area = Length x Width

In this case, the length of the tile is 6 cm and the width is 2 cm. Therefore, the area of the tile is 12 cm2.

To calculate the area, we multiplied the length and width of the tile. This formula is applicable to all rectangles, as the area of any rectangle is determined by multiplying the length and width.

It is important to note that the units used to measure the length and width must be the same in order to get an accurate area measurement. For example, if the length was measured in inches and the width in centimeters, then the area would be incorrect.

In conclusion, the area of this tile is 12 cm2.

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The function f has a relative maximum at x = -√[(2 + sqrt(2))/5], so the answer is (b) - root 5/5.

To find the relative maximum of a function, we need to find the critical points of the function, where the derivative of the function is zero or undefined.

Let's start by finding the derivative of f(x)

f'(x) = 15x⁴ - 12x² - 3

Now, we can find the critical points by solving the equation f'(x) = 0

15x⁴ - 12x² - 3 = 0

We can factor this equation by substituting y = x²

15y² - 12y - 3 = 0

Solving for y, we get

y = (2 ± √(2))/5

Substituting back x² for y, we get

x² = (2 ± √(2))/5

Taking the square root of both sides, we get

x = ± √[(2 ± √(2))/5]

Therefore, the critical points are

x = -√[(2 + √(2))/5], √[(2 - √(2))/5]

Now, we need to determine whether these critical points are relative maximum or minimum.

We can use the second derivative test to determine the nature of the critical points. The second derivative of f(x) is

f''(x) = 60x³ - 24x

Plugging in the critical points, we get

f''(-√[(2 + √(2))/5]) = -48√(2) < 0 (relative maximum)

f''(√[(2 - √(2))/5]) = 48√(2) > 0 (relative minimum)

Therefore, the relative maximum of the function f(x) is at

x = -√[(2 + √(2))/5]

So, the correct answer is (b) - root 5/5.

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Answer:

y = [tex]-\frac{19}{9} (x+3)^{2} + 5[/tex]

Step-by-step explanation:

The form of a quadratic function is y = a(x-h)^2 + k, where (h, k) is the vertex. From the givens in the problem, we know that (h, k) = (-3, 5), and another point on it will be (x, y) = (0, -14). Plug both of these into the equation to get:

-14 = a(3)^2 + 5

-19 = 9a

a = -19/9

∴ The equation is y = [tex]-\frac{19}{9} (x+3)^{2} + 5[/tex]

Answer:

PEMDAS. Division first. 68/5 is 13.6. Subtract 13.6 from 23 and the answer is 9.4. Therefore J = 9.4

Step-by-step explanation:

The minimum amount of fencing Mendel will need to enclose 2500 m² = 317 meters

Let's assume that x represents the length of and y represents the width of the rectangular garden.

Using the formula for tha area of rectangle, the area of the garden would be,

A = length × width

A = xy

Here, A = 2500 m²

so, 2500 = xy

⇒ y = 2500/x

Using the formula for the perimeter of the rectangle, the perimeter of the garden would be,

P = 2x + 2y

But  a rectangular garden is partitioned into 4 parts by constructing three additional fences parallel to one of the side.

So, the perimeter would be,

P = 2x + 5y

sides, in addition to fencing the perimeter.

P = 2x + 5(2500/x)

P = 2x + (12500/x)

Consider the derivative of P(x) with respect to x.

P'(x) = 2 - 12500/x²

To find the minimum value consider P'(x) = 0

2 - 12500/x² = 0

2 = 12500/x²

x² = 12500/2

x² = 6250

x = 79.05 m

and y =  2500/79.05

y = 31.63 m

So, the minimum amount of fencing would be,

P = 2x + 5y

P = 2(79.05) + 5( 31.63 )

P = 316.25 meters

P ≈ 317 meters

The minimum amount of fencing need to enclose 2500 m² = 316.25 meters

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the value of f(6) is -972.To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:

4, -12, 36, -108, 324, -972, ...

How to solve the question?

We can use the recursive formula given to find the value of f(6). Let's start by calculating f(2):

f(2) = -3f(1) = -3(4) = -12

Next, we can calculate f(3) using the same formula:

f(3) = -3f(2) = -3(-12) = 36

We can continue this process for f(4) and f(5):

f(4) = -3f(3) = -3(36) = -108

f(5) = -3f(4) = -3(-108) = 324

Finally, we can use the formula to find f(6):

f(6) = -3f(5) = -3(324) = -972

Therefore, the value of f(6) is -972.

To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:

4, -12, 36, -108, 324, -972, ...

Each term in the sequence is obtained by multiplying the previous term by -3. We can see that the sequence alternates between positive and negative values, with the magnitude of each term growing rapidly. By the time we reach f(6), the magnitude has grown to 972, and the negative sign indicates that the term is negative. Thus, f(6) is equal to -972.

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The Pythagorean Theorem can be utilized in any situation to establish a connection between the side lengths of the squares and the sort of triangle that results.

Let's use the notation "a, b, and c" to indicate the three squares' side lengths, where "a" stands for the shortest side, "b" for the midpoint, and "c" for the longest side.

The area of the largest square (c), which is created by the hypotenuse of the triangle, is equal to the sum of the areas of the two smaller squares when three squares' sides form an acute triangle.

The areas of the two smaller squares (a and b) formed by the two larger squares (a and b) are equal when three squares have sides that form an obtuse triangle.

If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square (c) formed by the hypotenuse of the right triangle.

In all cases, the Pythagorean Theorem can be used to determine the relationship between the side lengths of the squares and the type of triangle formed.

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Answer:

The definition of LCD is Least Common Denominator.

Step-by-step explanation:

Question 2:

LCD of 7/8 and 3/4 is 8

Question 3 :

7/8 - 3/4

7/8 - 6/8

1/8

Hope this helps :) !!

Answer:

Step-by-step explanation: First of all, the full form of LCD is "Lowest Common Denominator"

LCD is the least common denominator that can be used for all types of fractions.

For example, if we have the fractions 1/2 and 2/3, we can write:

1/2 as 2/4,3/6 or 4/8

           and

2/3 as 4/6,6/9 or 8/12

Hence, the least common denominator of 1/2 and 2/3 is 6, since it is present in the denominators of all the fractions.

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Answer:

I already did this go check the answers on the other one

Step-by-step explanation:

The area of the composite figure for this problem is given as follows:

A = 90 in².

The area of the composite figure is given by the sum of the areas of all the parts that compose the figure.

The right triangle has a side length of 5 in and an hypotenuse of 13 units, hence the missing side is given as follows:

5² + x² = 13²

25 + x² = 169

x² = 144

x = 12.

Thus the entire base is of:

12 + 4 = 16 in.

Then the figure is composed as follows:

Hence the area is given as follows:

A = 3 x 16 + 0.5 x 12 x 5 + 4 x 3

A = 90 in².

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The area swept clean by the wiper blade is approximately 239.3 square inches.

We need to find the area of the circular sector that is swept out by the blade as it rotates through an angle of 130 degrees. The radius of the circular sector is the length of the wiper arm, which is 16 inches.

The formula for the area of a circular sector is

A = (θ/360) × πr^2

Where

In this case, θ = 130 degrees and r = 16 inches, so we can plug these values into the formula to get:

A = (130/360) × 3.14 × (16)^2

Simplifying this expression, we get:

A ≈ 239.3 square inches

Therefore, the area swept clean by the wiper blade is approximately 239.3 square inches.

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Answer:g maybe

Step-by-step explanation:

Answer:

[tex] \sqrt{ \frac{4}{49 {d}^{4} } } = \frac{2}{7 {d}^{2} } [/tex]

Answer:

No

Step-by-step explanation:

If you divide 6 by 7, it is not equal to the number you get when you divide 1 by 2, therfore making them not equavalent.

~~~Harsha~~~

Answer:

No, the are not equivalent

Step-by-step explanation:

The ratios 6:7 & 1:2 are already in their simplest form, meaning we can't simple them anymore.

6:7 ≠ 1:2

Rounding to the nearest cent, the cost of the utility pole is $2,061.33 with a diameter of 1. 5 ft and a height of 45 ft.

To calculate the cost of a utility pole, we first need to find its volume, which is the product of its height and the cross-sectional area of its base. Since the pole is in the form of a right cylinder, the cross-sectional area of its base is a circle with radius equal to half the diameter, which is 0.75 ft. Therefore, the cross-sectional area is:

Area = πr^2 = π(0.75)^2 = 1.767 ft^2

The volume of the pole is then:

Volume = Area x Height = 1.767 x 45 = 79.515 ft^3

Finally, we can calculate the cost of the pole by multiplying its volume by the cost per cubic foot of wood:

Cost = Volume x Cost per cubic foot = 79.515 x $25.97 = $2,061.33

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The general form of the equation is x² + y² - 10x - 12y + 60 = 0.

The general form of the equation of a circle is given by:

x² + y² + Cx + Dy + E = 0

Where C, D and E are constant

Given the standard form of the equation of a circle as (x−5)² + (y−6)² = 1, we can rewrite it as follow:

(x−5)² + (y−6)² = 1

(x² - 10x + 25) + (y² - 12y + 36) = 1        (Expand the brackets)

x² + y² - 10x - 12y + 25 + 36 - 1 = 0

x² + y² - 10x - 12y + 60 = 0

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The response falls between 3 and 4, as a result of: 11/3 = 3.67 as Ben therefore travelled 3 to 4 miles further than his sister.

In geometry, the separation separating two points is determined by the length of the segment of a straight straight line linking them. In two- or two half space, this is referred to as the Euclidean distance. Distance is a crucial idea that is applied in numerous contexts in real life. For instance, distance is employed in transportation to gauge route length and determine trip times. Distance is a unit of measurement used in sports to indicate how far apart two things are or how long a race is. The measurement of distance to celestial objects is a common practise in many scientific disciplines, including astronomy.

given

Ben covers the following distance after walking 5/6 miles per day for 11 days:

11 days at 5/6 miles each day equal 55/6 miles.

Over the course of 11 days, his sister covered a total distance of:

11 days at 3/6 miles per day equal 33/6 miles.

We must take the distance between them out to determine how much farther Ben went than his sister:

22 miles from 55/6 miles to 33/6 miles.

By multiplying the numerator and denominator by 2, we may reduce the following fraction:

22/6 = 11/3

Ben therefore travelled 11.33 miles further than his sister.

The response falls between 3 and 4, as a result of: 11/3 = 3.67 as Ben therefore travelled 3 to 4 miles further than his sister.

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The equation 12x + 3(x - 5) = 6x + 9x - 15 has infinite many solutions

Part A:

Starting with the given equation:

12x + 3(x - 5) = 6x + 9x - 15

Simplify by distributing the 3:

12x + 3x - 15 = 6x + 9x - 15

Combine like terms on both sides:

15x - 15 = 15x - 15

Add 15 to both sides:

0 = 0

Therefore, the equation has infinite many solutions

Part B:

The property used to solve this equation is the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, we used the distributive property to simplify 3(x - 5) to 3x - 15.

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Answer:

Step-by-step explanation:

I think it’s b

The volume of the solid created by revolving a curve f(x) around the y-axis is  2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

What is the cylindrical shell?

A region enclosed by two identically sized cylinders with the same central axis is known as a cylindrical shell. We often denote the height of the cylinders by H, the inner cylinder's radius by r, and the thickness of the shell by t, resulting in a larger cylinder's radius equal to r + t.

Here,

We consider a strip of height y = f(x), and width dx; it is x units away from the axis of rotation.

Now, we rotate this strip about the y-axis; we obtain a cylindrical shell with  

radius = x

height = f(x)

thickness = dx

The volume of cylindrical shell = (circumference)×(height)×thickness

= (2πx)×(f(x))×dx

The volume of revolution = 2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

Hence, the volume of the solid created by revolving a curve f(x) around the y-axis is  2π [tex]\int\limits^a_b {xf(x)} \, dx[/tex]

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The value of the product is 6.9  × 10⁵ m

It is important to note that to determine the product of two different measurements, we need to make sure they have the same units.

Now, we have that;

6.9cm *10000000m​

First, let's convert the centimeters to meters , we have;

1m = 100cm

then, xm = 6.9cm

cross multiply the values

x = 6.9/100

Divide the values

x = 6. 9 × 10⁻²m

Then, we have;

6. 9 × 10⁻² × 10⁷m

Multiply the values and add the exponents

6. 9  × 10⁻²⁺⁷

Add the values

6.9  × 10⁵ m

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Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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