What is the difference between plotting (2,3) and (3,2) on coordinate plane? Explain

The solution of the function which satisfies the initial value problem is equal to  y = { (4-e^(-3x))/3, 4-3y > 0

                    { (4+e^(-3x))/3, 4-3y < 0

Function y=y(x)

Simplify the differential equation,

dy/dx = 4 -3y

Separate the variables dx and dy,

dy/dx = 4 - 3y

dy/(4-3y) = dx

Integrate both sides,

∫ dy/(4-3y) = ∫ dx

⇒(-1/3) log|4-3y| = x + C

where C is a constant of integration.

Use the initial condition y(0) = 0

(-1/3) log|4-3(0)| = 0 + C

⇒C = (-1/3) ln(4)

Substitute the value of C,

⇒(-1/3) log|4-3y| = x - (1/3) ln(4)

⇒log|4-3y| = -3x + ln(4)

⇒|4-3y| = e^(-3x + ln(4))

For an absolute value consider two cases,

Case 1: 4 - 3y > 0

4 - 3y = e^(-3x + ln(4))

y = (4-e^(-3x))/3

Case 2: 4 - 3y < 0

-4 + 3y = e^(-3x + ln(4))

y = (4+e^(-3x))/3

Therefore, the required solution of the function to the initial value problem is equal to  y ={ (4-e^(-3x))/3, 4-3y > 0

                                       { (4+e^(-3x))/3, 4-3y < 0

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The above question is incomplete, the complete question is:

Find the function y=y(x) which satisfies the initial value problem:

dy/dx = 4 -3y ,y(0)=0.

Answer:

22

Step-by-step explanation:

66 ÷3=22

3= one third

The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

Now,

Hence, The differences between two samples are more likely to be statistically significant if the samples are and the standard deviations of the samples are: large and the standard deviations of the samples are small.

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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The required equation is x × 3 = 336 - 141. The cost of the labor per hour is $65.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x be the cost of the labor per hour.

We know that

x × 3 = labor cost

141 + x × 3 = total cost

We also know that the total cost is $336

So we can write the equation:

141 + x × 3 = 336

Solving for x:

x × 3 = 336 - 141

x × 3 = 195

x = 195/3

x = 65

Therefore, the cost of the labor per hour is $65.

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Answer:

20

50+35=80

180-80= 100

100-80=20

Answer:

64 km/1 h

Step-by-step explanation:

A Mathematical model for the determination of total area under glucose tolerance and other metabolic curves is called: Tai Mathematical model.

The Team Assisted Individualization method is a learning method developed by Slavin, Leavy, Kraweit and Madden in 1982 to 1985 in the book Cooperatine Learning: Theory, Research and Practice.

The Team Assisted Individualization method is structured to solve problems in teaching programs, for example in terms of individual student learning difficulties. This model pays attention to differences in the initial knowledge of each student to achieve learning achievement.

Students individually study learning material that has been prepared by the teacher. Individual learning outcomes are brought to groups to be discussed and mutually discussed by group members and all group members are responsible for the overall answer as a shared responsibility.

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Answer:  3/5 inches

Step-by-step explanation:

l= 5w+7

A = wl

w(5w+7) = 6

5w²+7w = 6

5w²+7w -6 = 0

5w²+10w-3w-6=0

5w(w+2)-3(w+2)=0

(5w-3)(w+2)=0

5w-3=0            w+2=0

   5w=3                w=-2in

     w=3/5in

width cannot be negative, so the width is 3/5 inches.

Answer:

it is A

Step-by-step explanation:

i had the question on ed

Answer:

y greater - than - or - equal - to StartFraction 2 over 15 EndFraction

Step-by-step explanation:

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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Answer:

( 3,-3)

Step-by-step explanation:

see the coordinates....it's easy....

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

5! = 120

Step-by-step explanation:

using the definition of factorial !

n! = n(n - 1)(n - 2) .... 3 × 2 × 1 , then

5! = 5 × 4 × 3 × 2 × 1 = 20 × 12 × 1 = 120

Answer:

8%.

Step-by-step explanation:

There are 1000 millimeters in 1 meter.

So the percentage is (80/1000) * 100

= 80/10

= 8%.

Answer: D

Step-by-step explanation:

The given function is even function.

What is Mathematical function ?

Mathematical function is the representation of relation between independent variables and dependent variables.

here, the give function is given as  \(f(x) = \frac{3x^{2}}{1-x^{4}}\)

First let us find the value of f(-x) :

\(\begin{aligned}f(x)&=\frac{3x^{2}}{1-x^{4}}\\f(-x)&=\frac{3(-x)^{2}}{1-(-x)^{4}}\\&=\frac{3x^{2}}{1-x^{4}}\\f(-x)&=f(x)\end{aligned}\)

Thus it is clear that upon taking negative value of x it is equals to f(x) function. It should be noted that the for the function to be odd function the value of f(-x) must be equals to negation of f(x) that is f(-x) = - f(x).

Therefore, The given function is even function.

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Answer:

-3.75

Step-by-step explanation:

False. The range of a linear transformation is a subset of the codomain, not the domain.

The domain is the set of inputs to the transformation, while the codomain is the set of possible outputs. The range is the set of actual outputs produced by the transformation. The statement "The range of a linear transformation must be a subset of the domain" is false. The range of a linear transformation is a subset of the codomain, not the domain. The domain is the set of input vectors, while the codomain contains the possible output vectors after applying the linear transformation.

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Answer:

inductive

Step-by-step explanation:

Option(C),  the approximate standard deviation of X is 7.59. The sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

To find the approximate standard deviation of X, we can use the formula:
σ = √(np(1-p))
Where n is the sample size (1500 in this case), p is the probability of success (0.04 in this case), and (1-p) is the probability of failure (0.96 in this case).
Substituting the values, we get:
σ = √(1500 x 0.04 x 0.96)
σ = √57.6
σ ≈ 7.59
Therefore, the approximate standard deviation of X is 7.59. Option C is the correct answer.
The standard deviation is a measure of how spread out a set of data is from the mean. In this case, the standard deviation of X represents how much the number of people who support the increase in the state sales tax varies from sample to sample.
As per the given information, 4% of all adults in Ohio support the increase. We can assume that this is the population proportion. Since we are dealing with a sample of 1500 adults in Ohio, we need to calculate the standard deviation of the sample proportion (X), which is an estimate of the population proportion.
Using the formula σ = √(np(1-p)), we find that the standard deviation of X is approximately 7.59. This means that if we were to take multiple random samples of 1500 adults from Ohio and ask them about their support for the sales tax increase, we can expect the number of supporters to vary by about 7.59 on average.
It's important to note that this is only an estimate, and the actual standard deviation of X may differ slightly from 7.59 due to sampling error. However, as the sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

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Adding and subtracting polynomials worksheets assist pupils in becoming acquainted with the idea of polynomial addition and subtraction.

Adding and subtracting polynomial worksheets provide pupils with a platform to access a variety of well-structured problems. Because these worksheets progress in complexity, they are simple to use and allow pupils to reinforce their concepts.

Children must study in accordance with their learning curve, and these worksheets are designed to allow young brains to work at their own speed. These math worksheets also address the logical and reasoning aspects of arithmetic, assisting pupils in real-life situations.

Students may have a better grasp and explore these worksheets more quickly with the aid of pictures. These worksheets' step-by-step approach helps pupils better comprehend ideas and reinforce their comprehension.

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Therefore , the solution of the given problem of function comes out to be Oy=-0.5z²+z+4.

On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

We must make use of the data provided in the challenge in order to identify the quadratic function.

=>  f(z) = a(z + 4)(z - 2)

where an is a constant we need to figure out.

We can use the position (-6, -8), which is where the function passes through, to determine the value of a:

=>  -8 = a(-6 + 4)(-6 - 2)

=>  -8 = a(-2)(-8)

=>  -8 = 16a

=>  a = -1/2

Inputting this number of an into the quadratic function equation yields the following results:

=>  f(z) = -1/2(z + 4)(z - 2)

By extending this phrase, we get:

=> f(z) = -1/2(z² - 2z - 8)

Further simplification results in:

=>  f(z) = -0.5z² + z + 4

The quadratic function's corresponding equation is thus:

=>  Oy=-0.5z²+z+4

The following is the appropriate decision from the options provided:

=> Oy=-0.5z²+z+4

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Answer:

181

Step-by-step explanation:

Emily = 62

Collin = 3 years + Emily = 3 + 62 = 65

Dan = Emily - 8 years = 62 - 8 = 54

So, for finding the combined age,

=> 62 + 65 + 54

=> 181

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Answer:

Square

Step-by-step explanation:

Its easy, duh

Answer:

Step-by-step explanation:

For every time you have a probability of getting 1 is:

For all 6, the probability of outcome of 1 is:

Probability of 1

Probability of 6

P(1×6)

Answer:

1) D. \(y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10\)

2) E. The coefficient of \(x\) is -16.

Step-by-step explanation:

1) A polynomial is an algebraic expression of the form \(p(x) = \Sigma \limits_{i = 0}^{n} c_{i}\cdot x^{i}\), where \(n\) is the grade of the polynomial. In this case, the only equation that satisfies this definition is:

\(y = -\frac{3}{2}\cdot x^{12} -7\cdot x^{5}+\frac{2}{3}\cdot x -10\)

Correct answer: D

2) Let \(p(x) = (2\cdot x + 1) \cdot (5\cdot x^{3}-8\cdot x +4)\), we proceed to expand the expression by algebraic means:

\(p(x) = (2\cdot x + 1)\cdot (5\cdot x^{3}) -(2\cdot x +1)\cdot (8\cdot x) + 4\cdot (2\cdot x + 1)\)

\(p(x) = 10\cdot x^{4}+5\cdot x^{3}-16\cdot x^{2}+4\)

We see that coefficients for \(x^{2}\) and \(x\) are -16 and 0, respectively. Hence, the incorrect answer is E.