Let the supply and demand equations for a certain commodity be the following.
demand: p=√√9-0.1q
supply: p=√0.1q+1 -2
a. Find the equilibrium demand.
b. Find the equilibrium price (in dollars).

Answer:

Step-by-step explanation:

given: x-y = 4

x=4+y

given: -10x + y = -58

plug in for x

-10(4 + y) + y = -58

-40 - 10y + y = -58

-9y = -18

y = -18 / -9

y = 2

now plug in 2 for y in the first equation

x-2=4

x=6

There is the solution  x=6, y=2  :)

Answer:

they are complementary angles and as thry both are the realeation between angle a and b

The relationship between angles A and B is that, they are complementary. option B

For angle ACB, the angle is at C = 90 degrees

For angle CBA, the angle is at B = 31 degrees

For angle BAC, the angle is at A = 59 degrees

Note that complementary angles are angles that sum up to 90 degrees

Angle at A = 31 degrees

Angle at B = 59 degrees

Sum of angles A and B = 31 + 59 = 90 degrees

Thus, the relationship between angles A and B is that, they are complementary. option B

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Yes, there are plenty of resources available for people who want to relearn math, computer science/programming, and science.

Here are some recommendations for books and online courses that you can use to get started:

Math:

Computer Science/Programming:

Science:

Therefore, In addition to these resources, there are many online courses and tutorials available on websites like Coursera, edX, and Khan Academy. These resources offer a variety of courses ranging from beginner to advanced levels, so you can choose one that fits your needs and skill level.

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Th given statement "The second quartile for a set of data will have the same value as the 50th percentile only when the data are symmetric." is True because the condition is true only when data is symmetric.

The second quartile, also known as the median, represents the value that separates the lower 50% of the data from the upper 50% of the data. Similarly, the 50th percentile represents the value below which 50% of the data falls.

If the data are symmetric, it means that the distribution of the data is evenly balanced around the median value. In other words, if the data are folded in half at the median, the two halves will be roughly mirror images of each other.

In such a case, the median and the 50th percentile will have the same value since they both represent the value that separates the lower 50% of the data from the upper 50% of the data.

However, if the data are not symmetric, the median and the 50th percentile will generally have different values. In this case, the median may not provide a complete representation of the center of the distribution.

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Answer:

\(\huge\boxed{\sf y = 4x - 5}\)

Step-by-step explanation:

Given that,

Slope = m = 4

Y-intercept = b = -5

Put the above values.

y = 4x + (-5)

\(\rule[225]{225}{2}\)

The z-score for x = 61.6 is 2.45.

This means that this data point is 2.45 standard deviations above the sample mean.

'

The z-score is a measure of how many standard deviations a data point is from the mean. It is calculated using the formula:

z = (x - μ) / σ

Where x is the data point, μ is the sample mean, and σ is the sample standard deviation.

In this case, x = 61.6, μ = 52.3, and σ = 3.8. Plugging these values into the formula gives:

z = (61.6 - 52.3) / 3.8

z = 9.3 / 3.8

z = 2.447

Rounding to two decimal places gives a z-score of 2.45.

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Answer:

6

Step-by-step explanation:

add a one as the denominator for the 4 then flip the 2/3 to 3/2 and change the division to multiplication

Think of

KEEP=4

SWITCH=division

FLIP=fraction

The correct answer is B. t-distribution.

In the testing of hypothesis about the population mean when the population standard deviation is unknown, the critical values are determined using the t-distribution.

When the population standard deviation is unknown, we use the t-distribution to account for the uncertainty in estimating the population standard deviation from the sample data.

The t-distribution is similar to the standard normal (z) distribution but has thicker tails, which allows for more variability in the data.

The critical values, also known as the cutoff values, are the boundary values that determine the rejection region for the hypothesis test. These values are obtained from the t-distribution table or using statistical software.

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The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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The three types of consulting services that audit firms are now prohibited from providing to clients that are public companies are:

1. Bookkeeping services: Audit firms are prohibited from providing bookkeeping services to their audit clients. Bookkeeping involves the recording, organizing, and maintaining of financial transactions.

By prohibiting audit firms from providing bookkeeping services, it helps to ensure independence and objectivity in the audit process. This separation reduces the risk of potential conflicts of interest that could compromise the integrity of the audit.

2. Legal services: Audit firms are also prohibited from providing legal services to their audit clients. Legal services include activities such as drafting legal documents, providing legal advice, and representing clients in legal proceedings.

The prohibition on providing legal services aims to maintain independence and prevent any potential conflicts of interest that could arise if the audit firm were to also provide legal advice or services to the audited company.

3. Financial information systems design and implementation: Audit firms are further prohibited from designing and implementing financial information systems for their audit clients.

This involves the development and implementation of computerized systems that record and process financial data. The prohibition on providing financial information systems design and implementation services helps to avoid any potential bias or lack of objectivity in the audit process,

as the audit firm should remain independent and not be involved in the design and implementation of the systems they are auditing.

By prohibiting audit firms from providing these consulting services, it helps to ensure that the audit process is conducted objectively and independently, without any conflicts of interest.

This enhances the credibility and reliability of financial statements and promotes transparency and trust in the financial markets.

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What is a pseudoinverse?

This is denoted by x+ and is defined as follows:

x+ = {0, if x = 0; x*-/(||x||^2), otherwise.

Here, x* denotes the conjugate transpose of x, and ||x||^2 represents the squared magnitude of x. Essentially, we are finding a vector that when multiplied with x gives us the identity matrix (or as close to it as possible). This vector is the pseudoinverse, and it is computed using the formula above.

So in summary, the pseudoinverse of the null vector is the transposed null vector, while the pseudoinverse of a non-null vector is the conjugate transposed vector divided by its squared magnitude.

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Answer:

6 m

Step-by-step explanation:

a = \(s^{2}\)

36 = \(6^{2}\)

Each side is 6 m.

Helping in the name of Jesus.

Answer:

6 meters (In the Name of Jesus, I am helping others, Amen).

Step-by-step explanation:

If a square has an area of 36 m², then the length of each side can be found by taking the square root of the area since the area of a square is equal to the length of one side squared.

So, we can find the length of each side of the square as follows:

Side length = √(Area)

Side length = √(36 m²)

Side length = 6 m

Therefore, the length of each side of the square is 6 meters.

The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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Answer:

Step-by-step explanation:

Let the other end point be (a,b)

Then the midpoint p(0,-1) is between the two end points (-1,0) and (a,b)

So

(0,-1) = ( (-1+a)/2 , (0+b)/2)

So we have

0 = (-1 +a) /2

0 = -1 + a

a =1

and

-1 = (0+b)/2

-2 = 0+b

b = -2

So the other end point is ( 1, -2)

Answer: D) 40 minutes

Step-by-step explanation:

Answers A, B, & C are incorrect because if he only had 60 minutes and he had 2 parts, with the first part being 20 minutes, then you have to solve the second part. To do that you have to subtract the first part (20 minutes) from the 60 minutes, to get 40, so he had 40 minutes left to complete part 2.

Answer:

Ryan has 40 min left for part 2.

Step-by-step explanation:

Now we have to,

→ find the time left to complete part 2.

Forming the equation,

→ m + 20 = 60

Then required value of m will be,

→ m + 20 = 60

→ m = 60 - 20

→ [ m = 40 ]

Hence, he has 40 minutes left.

Answer:

price of tv = 3000

discount =1560

discount % = 1560/3000 * 100% = 52%

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

Formula =discount ×100÷original price

1560×100÷3000=52%

Answer:

10/18

Step-by-step explanation:

11/18 - 10/18 = 1/18

Answer:

Step-by-step explanation:

It takes 1/2 hours to drive from A-ville to B-town. It takes three-fifths of the time it takes to drive from A-ville to B-town to drive from B-town to C City.

To drive from B-town to C City, it will take:

1/2 * 3/5

= 3/10 hours

Answer:

3/10

Step-by-step explanation:

A to B: 1/2 hours

B to C: 3/5 of A to B

3/5 x 1/2

= 3/10

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The first trigonometric expression cot x and sin x in terms of the second expression is one over tan x and one over cosec x.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Write the first trigonometric expression in terms of the second expression.

The cotangent can be written as

\(\cot x= \dfrac{1}{\tan x}\)

And the sine can be written as

\(\sin x = \dfrac{1}{\csc x}\)

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The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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The particular solution to the system of differential equations X’ = [ 2 3 ][ 2 1 ] which satisfies the initial conditions : Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

To obtain the particular solution using the eigenvalue method, we first need to get the eigenvalues and eigenvectors of the coefficient matrix [2 3; 2 1].The characteristic equation is given by:

det([2 3; 2 1] - λ[I]) = 0

where λ is the eigenvalue and I is the identity matrix.Solving for λ, we get:

(2-λ)(1-λ) - 6 = 0

λ^2 - 3λ - 4 = 0

(λ-4)(λ+1) = 0

So, the eigenvalues are λ1 = 4 and λ2 = -1. To get the eigenvector corresponding to λ1, we need to solve the equation:

([2 3; 2 1] - 4[I])v1 = 0

where v1 is the eigenvector.Substituting the values, we get:

[-2 3; 2 -3][x1; x2] = [0; 0]

Solving the system of equations, we get:

-2x1 + 3x2 = 0

2x1 - 3x2 = 0

x1 = 3x2/2

So, the eigenvector corresponding to λ1 = 4 is [3/2; 1]. Similarly, to get the eigenvector corresponding to λ2, we need to solve the equation:

([2 3; 2 1] + 1[I])v2 = 0

where v2 is the eigenvector.Substituting the values, we get:

[3 3; 2 2][x1; x2] = [0; 0]

Solving the system of equations, we get:

3x1 + 3x2 = 0

2x1 + 2x2 = 0

x1 = -x2

So, the eigenvector corresponding to λ2 = -1 is [1; -1]. Now, we can write the general solution to the differential equation as:

X(t) = c1e^(4t)[3/2; 1] + c2e^(-t)[1; -1]

To get the particular solution that satisfies the initial conditions x(0) = [1; 2], we can substitute the values of t = 0 and x(0) into the general solution and solve for the constants c1 and c2.x(0) = c1*[3/2; 1] + c2*[1; -1]

[1; 2] = [3c1/2 + c2; c1 - c2]

Solving the system of equations, we get:

c1 = 2

c2 = -1/2

So, the particular solution is:

Xp = 2e^(4t)[3/2; 1] - (1/2)e^(-t)[1; -1]

Therefore, Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

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a. if someone is infected with Whodat-21, there is a 98% chance that the test will correctly identify them as positive. 2. the probability that a randomly selected Who tests positive for Whodat-21 is approximately 0.0655. 3. the probability that a randomly selected Who is infected with Whodat-21 if they test positive for the virus is approximately 0.2734 (or 27.34%).

(1) The probability that a randomly selected Who tests positive for Whodat-21, assuming that they are in fact infected with the virus, is 0.98.

To calculate this probability, we need to consider the sensitivity of the test, which is the proportion of truly infected individuals who test positive. In this case, the sensitivity is given as 98%. Therefore, if someone is infected with Whodat-21, there is a 98% chance that the test will correctly identify them as positive.

(2) The probability that a randomly selected Who tests positive for Whodat-21 is 0.0655 (or approximately 6.55%).

To calculate this probability, we need to consider both the sensitivity and specificity of the test. The specificity is the proportion of truly uninfected individuals who test negative. In this case, the specificity is given as 93%. Therefore, if someone is not infected with Whodat-21, there is a 93% chance that the test will correctly identify them as negative.

Now, we can calculate the probability of testing positive, considering both infected and uninfected individuals:

P(Positive) = P(Positive | Infected) * P(Infected) + P(Positive | Not Infected) * P(Not Infected)

= 0.98 * 0.025 + (1 - 0.93) * (1 - 0.025)

≈ 0.0655

Therefore, the probability that a randomly selected Who tests positive for Whodat-21 is approximately 0.0655.

(3) The probability that a randomly selected Who is infected with Whodat-21 if they test positive for the virus is 0.2734 (or approximately 27.34%).

To calculate this probability, we need to use Bayes' theorem, which relates conditional probabilities. Let's denote I as the event of being infected and P as the event of testing positive.

P(I | P) = (P(P | I) * P(I)) / P(P)

We know P(P | I) = 0.98 (sensitivity), P(I) = 0.025 (prevalence), and P(P) = 0.0655 (probability of testing positive).

Substituting these values into the formula, we have:

P(I | P) = (0.98 * 0.025) / 0.0655

≈ 0.2734

Therefore, the probability that a randomly selected Who is infected with Whodat-21 if they test positive for the virus is approximately 0.2734 (or 27.34%).

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