Michael bought a guitar that was on sale for 15% off the regular price of $200. The total cost included 8% sales tax. What was the total cost?

Answer:

35

Step-by-step explanation:

Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.

Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.

Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.

The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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Answer. I think is A

Step-by-step explanation:

I believe it would be x = -5.

Hope this helps!

The expression x -2 y-4 3 sqrt 64xy³ can be written in the form axby as follows:

ax -2by-4c 3 sqrt 64xy³

Coefficient in mathematics is a numerical value that is used to represent the magnitude of a given quantity in an equation. It is normally the numerical factor associated with the variables in an equation that represent a certain amount of change in the equation. For example, the coefficient of x in the equation y = 5x + 7 is 5, which indicates that x is multiplied by 5 in the equation.

In this expression, a, b, and c refer to the coefficients of the x, y, and the cube of y respectively. Thus, a is equal to 1, b is equal to -2, and c is equal to -4. Therefore, the product of a, b and c is equal to 8.

To break down the expression further, the coefficient of x is a, which is equal to 1. The coefficient of y is -2b, which is equal to -2. The coefficient of the cube of y is -4c, which is equal to -4. Finally, the coefficient of the square root of 64xy³ is 3, which is equal to 3.

Thus, when written in the form axby, the expression x -2 y-4 3 sqrt 64xy³ is equal to 1 -2 -4 3 sqrt 64xy³. The product of a, b, and c in this expression is equal to 8.

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Answer:

\(\boxed{x=13.89\:km}\)

Step-by-step explanation:

Pythagorean theorem

\(x^2=(12^2)+(7^2)\)

\(x^2=144+49\)

\(x^2=193\)

\(x=\sqrt{193}\)

\(\boxed{x=13.89\:km}\)

The commitment scheme for committing a single bit 0 or 1 is a bad commitment scheme.

Consider the following commitment scheme for committing a single bit 0 or 1: for 0, pick a random even element a (mod p) and commit a² (mod p). For 1, pick a random odd element and similarly commit its square. Let p be a big prime. To show that this is a bad commitment scheme, let's look at an example.

Suppose that p = 7 and the sender wants to send the value 1. Therefore, he chooses an odd number, say a = 3, and computes a² = 9 mod 7 = 2. Now he sends 2 to the receiver. The receiver has two possible options for guessing the number sent: 1 or 0. Let's assume that he guesses the number 0 and then he can choose any even number, say a = 2.

Now he computes a² = 4 mod 7. As 4 is the residue of an even number, it's impossible to distinguish between the values sent by the sender. Therefore, this is a bad commitment scheme.

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This is not a good commitment scheme.

A good commitment scheme should satisfy two properties: hiding and binding. Hiding means that the committed value should be computationally infeasible to determine without the commitment opening. Binding means that once the commitment is opened, it should be computationally infeasible to change the committed value.

In the given commitment scheme, the committed value is the square of a randomly chosen even or odd element modulo p. However, this scheme is not secure because it does not satisfy the hiding property.

To see why the hiding property is not satisfied, consider the case when the committed value is 0. Since we commit the square of a randomly chosen even element, any square root of the committed value modulo p will reveal the committed value. In this case, finding the square root of a modulo p, where a is even, is straightforward and does not require excessive computation. Therefore, an attacker can easily determine the committed value without knowing the opening.

This lack of hiding makes the commitment scheme insecure because an adversary can guess the committed value by calculating the square root. Thus, an attacker can break the hiding property of the commitment scheme, rendering it ineffective for secure communications.

In summary, the given commitment scheme is not a good one as it fails to satisfy the hiding property. It is important to use a commitment scheme that provides both hiding and binding properties to ensure the security and integrity of the committed values.

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Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer:

hello:

Step-by-step explanation:

If f(x) = -8x - 6 and g(x) = x+8 ,  (f • g) (- 7)= f(g(-7))

but g(-7)=-7+8=1

(f • g) (- 7)= f(1) =-8(1)-6 =-14

Answer:

Solving an Inverse Variation Problem

-Write the variation equation: y = k/x or k = xy.

-Substitute in for the given values and find the value of k.

-Rewrite the variation equation: y = k/x with the known value of k.

-Substitute the remaining values and find the unknown.

Step-by-step explanation:

yeah

Answer:

4/5

Step-by-step explanation:

Since we know that the first ratio that we have is 16:20, all you have to do is simplify by dividing and you get 4/5.

There you go.

Answer:

Surface area of a cone = πrs + πr2

Volume of a cone = 1/3πr2h.

The slant of a right circle cone can be figured out using the Pythagorean Theorem if you have the height and the radius.

Answers for volume problems should always be in cubic units.

Step-by-step explanation:

The ratio of the error is; 0.3333

The Percent error of the given problem is;  33.33%

We are given;

Amount spent by John on shopping = $75

Amount expected to spend = $100

Since this is what was given then it means we will have the following;

The approximate value to be spent = 100 dollars

Exact Value  spent = 75 dollars

Therefore, the error made is;

Error = Approximate value - Exact value  

Error = 100 - 75

Error =  25 dollars

Thus, the error when it is absolute is;

Absolute Error = ±25 dollars

Now, the ratio will be;

Ratio(e) = Error/exact value spent

e = 25/75 = 0.3333

Percent Error = error * 100%

Percent error = 0.3333 * 100%

Percent error =  33.33%

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Factor theorem is most commonly used for factoring a polynomial or integer and searching the roots of the polynomial. It is a particular case of a polynomial remainder theorem.

As defined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.

Here we can prove the factor theorem, according to which we can.

factories the polynomial.

Consider a polynomial f(x) which is divided by (x-b), then f(c)=0.

Using remainder theorem,

f(x)= (x-b) q(x)+f(b)

Where f(x) is the target polynomial and q(x) are the quotient polynomial.

because f(b) = 0, So,

f(x)= (x-b) q(x)+f(b)

f(x) = (x-b) q(x)+0

f(x) = (x-b) q(x)

So, (x-b) is a factor of the polynomial f(x).

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Answer:

C

Step-by-step explanation:

a point (x, y) reflected over y-axis becomes ( -x, y)

(2, -4) becomes (-2, -4)

The point (-5.2, -27) satisfies the equation of the line. Then the point belongs to the line.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The equation is given below.

y = 5x - 1

If the point satisfies the equation, then the point belongs to that equation.

Substitute x = - 5.2 and y = - 27, then we have

- 27 = 5 · (-5.2) - 1

- 27 = - 26 - 1

- 27 = - 27

Thus, the point (-5.2, -27) satisfies the equation of the line. Then the point belongs to the line.

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Build-borrow-or-buy.

The build-borrow-or-buy framework is a conceptual model used by strategists to help them decide whether to build capabilities internally, borrow them through partnerships and alliances, or buy them through mergers and acquisitions. The framework helps organizations identify the most efficient and effective way to acquire the resources, capabilities, and competencies they need to achieve their strategic goals. It is a useful tool for decision-making when considering growth strategies, and can help managers evaluate the costs, risks, and benefits of each option.

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(a) build-borrow-or-buy. This framework helps strategists decide whether to pursue internal development, enter into an alliance, or acquire new resources, capabilities, and competencies.

the build-borrow-or-buy framework suggests that companies have three options when it comes to acquiring new resources and capabilities. First, they can build or develop these resources and capabilities internally through investments in research and development or employee training. Second, they can borrow or enter into strategic alliances with other companies to gain access to new resources and capabilities. Finally, they can buy or acquire companies that already possess the desired resources and capabilities.

the build-borrow-or-buy framework provides a structured approach for companies to evaluate their options when it comes to acquiring new resources and capabilities. By considering the pros and cons of each option, companies can make more informed decisions that align with their strategic goals and objectives.


The build-borrow-or-buy framework is a conceptual model that helps strategists decide whether to seek internal development (build), enter into an alliance (borrow), or acquire new resources, capabilities, and competencies (buy). This model assists organizations in evaluating their options for growth and resource allocation based on their strategic goals and objectives.

the build-borrow-or-buy framework is a valuable tool for strategists when choosing between internal development, alliances, or acquisitions to achieve their organization's growth and resource needs.

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A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.

a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.

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The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

The probability that Melinda will be able to make an integer between 10 and 20 (inclusive) with the two numbers she rolls can be calculated by determining the number of favorable outcomes and dividing it by the total number of possible outcomes.

To find the number of favorable outcomes, we need to identify the combinations of two numbers that will result in a two-digit number between 10 and 20. We can list these combinations as follows:

11, 12, 13, 14, 15, 16

Notice that we only have six favorable outcomes.

Now, let's determine the total number of possible outcomes when rolling two six-sided dice. Each die has six possible outcomes (1, 2, 3, 4, 5, 6), so the total number of outcomes is 6 multiplied by 6, which equals 36.

To calculate the probability, we divide the number of favorable outcomes (6) by the total number of possible outcomes (36):

Probability = Favorable outcomes / Total outcomes
Probability = 6 / 36
Probability = 1 / 6

Therefore, the probability that Melinda will be able to make an integer between 10 and 20 (inclusive) is 1/6.

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Step-by-step explanation:

1)x is less than 7

2)x is greater than and equal to -4

The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

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Answer:

17 pt

Step-by-step explanation:

Cause 8 quarts= 16 pt and i added 1 pint to it so its 17 pints

Remember 1 quart = 1 pint

Have a good day!

The requried, to find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To find the angle by which AB turns clockwise about point B to coincide with BC, we need to first identify points A, B, and C on a diagram. Once we have done that, we can draw a line from B to C, and then compare the direction of AB to the direction of BC. The angle between these two lines will be the angle by which AB turns clockwise to coincide with BC.

Similarly, to find the angle by which AB turns counterclockwise to coincide with BE, we need to identify points A, B, C, and E on a diagram. Once we have done that, we can draw a line from B to E, and then compare the direction of AB to the direction of BE. The angle between these two lines will be the angle by which AB turns counterclockwise to coincide with BE.

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Shortest length of ramp that can be built to reach a ledge .83 meters from the ground is 8.333 meters, according to the ADA standards.

What is Shortest length?

Shortest length is the shortest distance measured from one end to the other.

According to the ADA standard, the maximum slope for a wheelchair-accessible ramp is one unit vertically for every twelve horizontal units. To find the length of the ramp needed to reach a height of .83 meters, we can use the formula:

rise / slope = run

Where:

rise = the vertical distance to be covered (in this case, .83 meters)

slope = the maximum allowed slope (1:12, or 1/12)

So we can plug in the values we know:

.83 meters / (1/12) = run

To find the length of the ramp, we need to multiply the run by the slope:

run * slope = ramp length

Therefore, the length of the ramp is:

run * (1/12) = (run/12) meters = (10/12) = 8.333 meters.

So, the shortest length of ramp that can be built to reach a ledge .83 meters from the ground is 8.333 meters, according to the ADA standards.

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The total duration of the puberty process can be different for each girl who is about to enter it, as the length of time for the different stages of puberty can vary from person to person.  Hence, if a girl is about to enter puberty, the total process will take a variable length of time for different girls.

The total process of puberty for a girl can take a variable length of time, but typically it takes around 2 to 5 years to complete. The onset of puberty usually occurs between the ages of 8 and 13, with most girls starting around age 11.

The process of puberty includes physical changes such as breast development, the growth of pubic and underarm hair, and the onset of menstruation.

The duration of puberty can also depend on factors such as genetics, nutrition, and overall health. Some girls may experience a shorter or longer duration of puberty than others. However, in general, the process of puberty for a girl usually takes around 2 to 5 years to complete.

Therefore, the correct answer is "a variable length of time for different girls", but typically takes around 2 to 5 years to complete.

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Answer:

feel like its C

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we are to find f(x) + g(x) that we means that we are to add the functions together by combining like terms, if any, and put it all together into one function. Adding them looks like this:

\(-3x+7+2x^2-8\) and combining like terms gives us

\(2x^2-3x-1\)

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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Answer:

9

Step-by-step explanation:

2^28(3^-2/2^3)^4 x 1/(3^-5 x 2^8 x 6^0)^2

2^28(3^-2/2^3)^4 x 1/(3^-5 x 2^8 x 1)^2

2^28(3^-2/2^3)^4 x 243^2/256^2

2^28 x 1/2^12 x 3^8 x 243^2/256^2

243^2 x 1 x 2^28/256^2 x 3^8 x 2^12

2^28 x 243^2/2^12 x 3^8 x 256^2

2^16 x 243^2/3^8 x 256^2

2^16 x 3^10/2^16 x 3^8

=3^2

=9