John has $400. He gave one friend 25% and $158.67 to another friend. How much money does John have left​

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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A rock that contains equal amounts of potassium-40 and argon-40 is old as  1.25 billion years half life.

The duration it takes for a substance's radioactivity to decrease to half of what it once was is known as half-life.

The half-life of potassium-40 is about  1.25 billion, years. it undergoes beta decay and becomes argon-40. Equal amounts would be one half-life, so the sample is also 1.25 billion years old.

A property of a specific isotope is whether or not it emits radioactive material. While some isotopes are stable for all time, others are radioactive and degrade through a distinctive sort of emission. The radioactivity level falls with time as the radioactive isotope is present in decreasing amounts. The time it takes for one-half of a radioactive isotope to decay is known as its half-life, and it is both an intriguing and practical feature of radioactive decay. A particular radioactive isotope's half-life is constant; it is unaffected by environmental factors and is unrelated to the starting concentration of that isotope.

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Answer:

24

Step-by-step explanation:

GCF means greatest common factor.

Factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

Factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest common factor between both sets is 24, so the GCF of 24 and 48 is 24.

Random variables that can take on any value in some interval are called continuous random variables.

A continuous random variable is defined over a continuous range of values and can take on any value within that range. This is in contrast to discrete random variables, which can only take on a finite or countably infinite set of distinct values.

The probability distribution of a continuous random variable is described by a probability density function (PDF), which specifies the likelihood of the random variable taking on different values. The area under the PDF curve within a given interval represents the probability of the random variable falling within that interval.

Examples of continuous random variables include the height of a person, the time it takes for an event to occur, or the temperature at a specific location.

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Answer:

y= 1-x

Step-by-step explanation:

● (a^2x)/a^(x-y) = a

This means that:

● 2x-(x-y) = 1

● 2x - x +y = 1

● x + y = 1

Substract x from both sides

● x+y -x = 1-x

● y = 1-x

Rewrite Power Property of Logs is log394 ≈ 3.6721, log2.9344 ≈ 1.4755, log9718 ≈ 3.9872.

What are logarithms?

Logarithms are mathematical functions that help solve equations involving exponential expressions. They represent the inverse operation of exponentiation, meaning that logarithms tell us what exponent is needed to produce a certain number. The most commonly used logarithms are base 10 (written as log) and natural logarithms (written as ln), which have specific rules and property that allow for their use in various mathematical applications.

According to the question:

\(log3(94) = log3(2^2 * 47) = 2log3(2) + log3(47)\)

\(log2.9344 = log10(2.9344) / log10(2) \approx 1.4755\)

\(log9718 = log10(9718) \approx 3.9872\)

2log2 = 2

Using the power property of logs, we have:

log394 = 2log2 + log47

= 2 + log47

≈ 2 + 1.6721

≈ 3.6721

Thus, log394 ≈ 3.6721.

To evaluate log2.9344, we can use the change of base formula to convert it to base 10:

log2.9344 = log10(2.9344) / log10(2)

≈ 1.4755

Finally, log9718 = log10(9718) ≈ 3.9872.

Therefore, the answer is:

log394 ≈ 3.6721, log2.9344 ≈ 1.4755, log9718 ≈ 3.9872.

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m∠MAR is 68°. Answer: 38°.

What is the angle bisectors?

In geometry, an angle bisector is a line or ray that divides an angle into two equal parts. More formally, given an angle ABC, an angle bisector is a line or ray AD such that it divides the angle ABC into two equal angles: ∠ABD ≅ ∠CBD.

Since ray AT bisects ∠MAR, we know that m∠MAT + m∠RAT = m∠MAR.

Substituting the given values, we get:

(4x - 5)° + (2x + 7)° = m∠MAR

Simplifying and solving for x, we get:

6x + 2° = m∠MAR

Now, we know that the sum of the angles in a triangle is 180°. So:

m∠MAT + m∠RAT + m∠MAR = 180°

Substituting the given values and the expression we found for m∠MAR, we get:

(4x - 5)° + (2x + 7)° + (6x + 2°) = 180°

Simplifying and solving for x, we get:

x = 11°

Finally, we can substitute x = 11° into the expression we found for m∠MAR:

6x + 2° = 6(11°) + 2° = 68°

Hence, m∠MAR is 68°. Answer: 38°.

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Step-by-step explanation:

So, the variable x can not represent adults and students because they tell us that 45 are clearly students.

Answer:

14 mm squared is the area

Step-by-step explanation:

Answer:

I think the answers would be 12 and 9.

sorry if it's wrong...

Step-by-step explanation:

Answer:

(2) The statement is true.

-1 < r < 1

On a certain portion of an experiment, a statistical test result yielded a p-value of 0.18. From here we can conclude that test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant.

a field of mathematics concerned with the gathering, examination, interpretation, and presentation of large amounts of numerical data.: a set of numerical data

Statistics is the study and manipulation of data, including methods for data collection, evaluation, analysis, and interpretation. Descriptive statistics and inferential statistics are the two main subfields of statistics.

In the exercise, we obtain a value of p of 0.21; we assume that for it to have statistical significance, the value must be less than 0.05, which is constant; if this result is higher, it indicates that there is no statistically significant evidence. The test of the statistical p helps us determine the probability that a statistical value occurs in the null hypothesis.

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If you set x = 0, then Φ(0) = cos(0) = 1. If you set x = π/2 (or 90 degrees in radians), then Φ(π/2) = cos(π/2) = 0. If you set x = π (or 180 degrees in radians), then Φ(π) = cos(π) = -1.

You can plug in any real value for x, and the function will compute the corresponding cosine value.

The function Φ(x) = cos(x) is a mathematical function that takes a real number x as input and returns the cosine of that number. The cosine function, denoted as cos(x), is a trigonometric function that gives the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle with an angle x.

In this case, Φ(x) simply represents the cosine function applied to the input x. For any real number x you provide, the function will evaluate cos(x) and give you the corresponding result. The output of Φ(x) will also be a real number between -1 and 1, inclusive since the cosine function's range is bounded within that interval.

For example:

If you set x = 0, then Φ(0) = cos(0) = 1.

If you set x = π/2 (or 90 degrees in radians), then Φ(π/2) = cos(π/2) = 0.

If you set x = π (or 180 degrees in radians), then Φ(π) = cos(π) = -1.

You can plug in any real value for x, and the function will compute the corresponding cosine value.

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Answer:

C. 2x

Step-by-step explanation:

Let

B's age = x years

A's age = 2 times older than B

= 2 * x

= 2x years

A's age = 2x years

For instance, if B's age is 17 years

Then,

A's age = 2x

= 2(17)

= 34 years old

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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The real interest rate, using the approximation formula, is 0.01 or 1%. This means that after considering the expected inflation rate, the purchasing power of the money grows at a rate of 1%.

The real interest rate can be calculated using the approximation formula: real interest rate = nominal interest rate - expected inflation rate.

We have:

Nominal interest rate (i) = 0.04

Expected inflation rate (+1) = 0.03

Using the formula, we can substitute the given values:

Real interest rate = 0.04 - 0.03

Calculating the difference:

Real interest rate = 0.01

Therefore, the real interest rate, using the approximation formula, is 0.01 or 1%.

The nominal interest rate represents the rate at which money grows in a bank account or investment without considering inflation. On the other hand, the real interest rate takes into account the effects of inflation, allowing us to understand the true purchasing power of the money.

To calculate the real interest rate, we subtract the expected inflation rate from the nominal interest rate. In this case, the nominal interest rate is 0.04 (4%), and the expected inflation rate is 0.03 (3%).

Substituting the values into the formula, we get:

Real interest rate = 0.04 - 0.03

Real interest rate = 0.01 or 1%

Therefore, the real interest rate, in this scenario, is 0.01 or 1%. This means that after accounting for inflation, the purchasing power of the money grows at a rate of 1%.

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The parametric equations for the path of a particle that moves once around clockwise on the circle x^2 + (y-1)^2 = 9,
Starting at (3,1), are x(t) = 3cos(2π-t) and y(t) = 1 - 3sin(2π-t), where 0 ≤ t ≤ 2π.
Starting at (3,1), are x(t) =3cos(4π+t) and y(t) = 1 + 3sin(4π+t), where 0 ≤ t ≤ 4π.
starting at (0,4), are x(t) = 3sin(t) and y(t) = 1 + 3cos(t), where 0 ≤ t ≤ π.

To find the parametric equations for the path of a particle that moves around the circle x^2 + (y-1)^2 = 9, we can use the standard parametric equations for a circle centered at (a,b) with radius r:

x = a + r cos(t)

y = b + r sin(t)

(a) Since the particle moves once around clockwise, starting at (3,1), we need to reverse the direction of t in the standard equations, so that the particle moves clockwise instead of counterclockwise. Thus, we have x(t) = 3cos(2π-t) and y(t) = 1 - 3sin(2π-t), where 0 ≤ t ≤ 2π.

(b) Since the particle moves twice around counterclockwise, starting at (3,1), we need to increase the range of t so that it covers two full circles. We also need to adjust the direction of t so that the particle moves counterclockwise. Thus, we have x(t) = 3cos(4π+t) and y(t) = 1 + 3sin(4π+t), where 0 ≤ t ≤ 4π.

(c) Since the particle moves halfway around counterclockwise, starting at (0,4), we need to adjust the standard equations so that the particle starts at (0,4) instead of (3,1), and moves halfway around the circle in the counterclockwise direction. Thus, we have x(t) = 3sin(t) and y(t) = 1 + 3cos(t), where 0 ≤ t ≤ π.

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Answer:

30%

Step-by-step explanation:

smart highschooler brain

Answer:12 tiles will be needed.

Answer:

i thin it is 8960

Step-by-step explanation:

44800 divided by five = 8960

Answer:

D) 15

Step-by-step explanation:

\(d=\sqrt{(x_{2}-x_{1} )^2+(y_{2}-y_{1} )^2}\)

False, an industry standard is to randomly select 10% of the completed surveys for purposes of making a call-back to validate that the interview was conducted.

What are industries standards?

A collection of standards within an industry referring to how activities are typically carried out in their respective domains of production.

                  In other words, it refers to the standards that are commonly accepted by an industry's participants.

Why is this industry norm?

Industry standards are primarily intended to make products compatible with one another and to ensure that consumers can mix and match products from various brands without risk.

                             Best Industry Standards refers to benchmarks that, taking into account elements like the nature and size of the parties, are in the upper quartile in the relevant industry for the delivery of comparable services that are essentially similar to the Services or the relevant part of them.

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Answer:

Step-by-step explanation:

Given the expression 4x-1 = 4x+7, we are to simplify the expression and find the value of x. To do that the following steps must be carried out.

Step 1: collect the like terms by regrouping the expression

4x-1 = 4x+7

4x - 4x = 7+1

0x = 8

Step 2: Dividing both sides by the number next to x

0x/0 = 8/0

x = ∞

Any constant dividing zero will always return infinity as a value.

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

If 12 workers can complete a building project in 54 days, to determine this we can divide the rate of work by the number of workers by the number of days: 12 workers / 54 days = 0.2222 workers/day.

If the construction manager wants to complete the project in 36 days, he needs to increase the rate of work to complete the project in that shorter timeframe. To do this, he can add more workers or increase the productivity of the current workers.

To determine how many more workers the manager needs, we can use the formula:

(number of workers) = (rate of work) x (number of days)

By plugging in the desired rate of work and number of days, we get:

(number of workers) = (0.2222 workers/day) x (36 days) = 7.999 workers

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

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Answer:

-2x + 10

Step-by-step explanation:

When you add units you affect the y axis.

Knowing this you can translate it 14 units up by adding 14 + (-4).

The Walt Disney Company has successfully used related diversification to create value by leveraging its existing brand and intellectual properties to enter new markets and expand its product offerings.

Through related diversification, Disney has been able to extend its brand into various industries such as film, television, theme parks, consumer products, and digital media. By utilizing its well-known characters and franchises like Mickey Mouse, Disney princesses, Marvel superheroes, and Star Wars, Disney has been able to capture the attention and loyalty of consumers across different age groups and demographics.

For example, Disney's acquisition of Marvel Entertainment in 2009 allowed the company to expand its presence in the superhero genre and tap into a vast fan base. This strategic move not only brought in new revenue streams through the production and distribution of Marvel films, but also opened doors for merchandise licensing, theme park attractions, and television shows featuring Marvel characters. Disney's related diversification strategy has helped the company achieve synergies between its various business units, allowing for cross-promotion and cross-selling opportunities.

Furthermore, Disney's related diversification has also enabled it to leverage its technological capabilities and adapt to the changing media landscape. With the launch of its streaming service, Disney+, in 2019, the company capitalized on its vast library of content and created a direct-to-consumer platform to compete in the growing digital entertainment market. This move not only expanded Disney's reach to a global audience but also provided a new avenue for monetization and reduced its reliance on traditional distribution channels.

In summary, Disney's successful use of related diversification has allowed the company to create value by expanding into new markets, capitalizing on its existing brand and intellectual properties, and leveraging its technological capabilities. By strategically entering complementary industries and extending its reach to a diverse consumer base, Disney has been able to generate revenue growth, enhance its competitive position, and build a strong ecosystem of interconnected businesses.

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Answer:

800

Step-by-step explanation: I have the question before and got it right

The expression 4^3/2 is equal to 32 in exponentiation operation and  4√2 in division operation.

If the exponentiation operation (4^3) is performed before the division operation (/2), then the expression can be written as:

4^3/2 = (4^3) / 2

= (4 × 4 × 4) / 2

= 64 / 2

= 32

If the division operation (/2) is performed before the exponentiation operation (4^3), then the expression can be written as:

4^3/2 = 4^(3/2)

= 4^(1.5)

= 2 × 2 × 2^(0.5)

= 2 × 2 × √2

= 4√2

It's important to note that when dealing with expressions involving exponents, the order of operations matters and can significantly affect the resulting value.

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Use the equation formula to find the area of a circle

The radius is given on the question, replace this value on the equation and find the area.

The area of the circle is 201.06 mm^2