-10-1/7x^3+4x in standard form

(A) dy/dx = - x/y will be the differential equations will a slope field show nothing but negative slopes in the fourth quadrant.

The slope field is utilized when you want to see the tendencies of solutions to a DE, given that the solutions pass through a certain localized area or set of points. The beauty of slope field diagrams is that they can be drawn without actually solving the DE. Slope fields allow these people to view the probable trends of a certain population based on its conditioning factors without actually solving their DE's.

In differential equations you can find what is called a "general solution" even if no initial conditions are given. If you do have initial condition, then you can transform your general solution into a "particular solution".

With the slope field visualization, you saw Sal draw several particular solutions, each one dependent of the initial conditions that he choose

As the differential equation dy/dx is a function of y, plugging in the y-value 6 gives

dy/dx = 6/6 × (4-6) = 1 ×-2 = -2,

the slope you mentioned. If you look at the point (1, 6) on the slope field diagram, you can see a short downward sloping line, of approximately slope -2.

If the slope were pi at a point, you would see an upward sloping line of approximately 3.14159

We can solve for which points this would be at:

dy/dx = π = y/6 × (4-y)

π6 = 4y-y²

multiply both sides by 6, then distribute on the right

0 = -1*y² +4 × y - 6×π,

add 6×π to the right side

The quadratic should get the y-values where the slope is π

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Answer:

a)  \(x=\frac{y}{k}\)

b) \(y=0.6k\)

c) \(x=\frac{38.5}{k}\)

Step-by-step explanation:

From the question we are told that:

  \(y=38.5\)

  \(x=0.6\)

Generally the equation for the directly proportional variable is mathematically given by

 \(y \alpha x\)

 \(y=kx\)

Where

\(K=proportionality\ constant\)

a)

    The Formula in terms of x

   \(x=\frac{y}{k}\)

b)

  \(y=k(0.6)\)

  \(y=0.6k\)

c)

   \(38.5=kx\)

   \(x=\frac{38.5}{k}\)

Answer:

-14 + 23 = 9

Step-by-step explanation:

if you borrow 14 dollars and pay23 dollars you have a change of 9 dollars

Answer:

The answer is 6. commutative property of multiplication states that no matter the order, as long as all numbers are there, it equals the same amount.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

It's more like the missing property. This question is an example of the commutative property for multiplication. It does not matter what order you do the multiplying. 4*6 is the same as 6 * 4

Answer:

x = 28*

Step-by-step explanation:

We know that Line M is parrallel to line N , so angle x = 28 degrees because the Alternate interior angles of a transversal are equal.

Hope it helps.

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

The solution of -34 < x < 10 can be expressed in three different ways: Interval Notation: (-34, 10), Set-Builder Notation: {x | -34 < x < 10}, Inequality Notation: -34 < x < 10.

Interval notation is a concise and standardized way of representing an interval of real numbers.

In interval notation, we use parentheses "(" and ")" to indicate open intervals (excluding the endpoints) and square brackets "[" and "]" to indicate closed intervals (including the endpoints).

The left parenthesis "(" indicates that -34 is not included in the interval. It signifies an open interval on the left side, meaning that the interval starts just to the right of -34.

The right parenthesis ")" indicates that 10 is not included in the interval. It signifies an open interval on the right side, meaning that the interval ends just to the left of 10.

Therefore, the interval (-34, 10) represents all real numbers x that are greater than -34 and less than 10, but does not include -34 or 10 themselves.

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Answer:

A

Step-by-step explanation:

Answer:

a = \(\frac{1}{2}\)

Step-by-step explanation:

since (2, - 3 ) lies on the graph then it makes the equation true.

substitute x = 2 and y = - 3 into the equation and solve for a

2(- 3) = a(2) - 7 , that is

- 6 = 2a - 7 ( add 7 to both sides )

1 = 2a ( divide both sides by 2 )

\(\frac{1}{2}\) = a

(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

1/6 im not sure how to explain it but u have 5/6 chance of not rolling it

The limit of cos(πx) as x approaches -2 is option C 1/16.

What is limit?

A limit in mathematics is a point at which a function approaches the outcome for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

To find the limit of the function cos(πx) as x approaches -2, we can simply evaluate the function at x = -2, since cos(πx) is a continuous function.

cos(πx)

= cos(π(-2))

= cos(-2π)

We know that the cosine function has a period of 2π, meaning that cos(x + 2π) = cos(x) for any value of x.

Therefore, we can add any multiple of 2π to -2π without changing the value of cos(-2π).

cos(-2π)

= cos(-2π + 2π)

= cos(0)

= 1

So, the limit of cos(πx) as x approaches -2 is equal to cos(-2π) = 1.

Therefore, the value is obtained as 1/16.

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Answer: One answer

Step-by-step explanation:

Answer:

17.a)  See below.

17.b)  x = 34.3 cm, y = 34.3 cm

18.a)  See below.

18.b)  r = 8 m

Step-by-step explanation:

Given information (see attachment 1):

According to the Similar Triangles Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.  Therefore, triangles ABC and ADE are similar (refer to attachment 1).

As corresponding sides of similar triangles are always in the same ratio, the ratio of the base to height of the smallest triangle is equal to the ratio of the base to height  of the largest triangle:

\(\implies \sf DE:AD=BC:AB\)

\(\implies y:80-x=60:80\)

\(\implies \dfrac{y}{80-x}=\dfrac{60}{80}\)

\(\implies 80y=60(80-x)\)

\(\implies y=\dfrac{60(80-x)}{80}\)

\(\implies y=\dfrac{3(80-x)}{4}\)

The maximum area of a rectangle is when the length and height are equal:

\(\implies x=y\)

Therefore, to find the value of x when the area of the rectangle is at its maximum, substitute x = y into the equation from part (a) and solve for x:

\(\implies x=\dfrac{3(80-x)}{4}\)

\(\implies 4x=3(80-x)\)

\(\implies 4x=240-3x\)

\(\implies 7x=240\)

\(\implies x=\dfrac{240}{7}\)

\(\implies x=34.3\; \sf cm\;\;(nearest\;tenth)\)

Therefore, the dimensions of the rectangle of maximum area to the nearest tenth are:

--------------------------------------------------------------------------------------------

Given information:

The formula for the volume of a cone is:

\(V=\dfrac{\pi r^2 h}{3}\)

If the sum of the base radius r and the height h is 12 metres then:

\(\implies r + h = 12\)

\(\implies h=12-r\)

Substitute the expression for h into the volume of a cone formula to create an equation for V in terms of r:

\(\implies V=\dfrac{\pi r^2 (12-r)}{3}\)

\(\implies V=\dfrac{12\pi r^2-\pi r^3}{3}\)

\(\implies V=\dfrac{12\pi r^2}{3}-\dfrac{\pi r^3}{3}\)

\(\implies V=4\pi r^2-\dfrac{1}{3}\pi r^3\)

To find the radius of the cone that yields the maximum volume, differentiate V with respect to x:

\(\implies \dfrac{\text{d}V}{\text{d}x}=2 \cdot 4\pi r^{2-1}-3 \cdot \dfrac{1}{3}\pi r^{3-1}\)

\(\implies \dfrac{\text{d}V}{\text{d}x}=8\pi r-\pi r^2\)

\(\implies \dfrac{\text{d}V}{\text{d}x}=\pi r(8-r)\)

Set the differentiated equation equal to zero and solve for x:

\(\implies \pi r(8-r)=0\)

\(\implies 8-r=0\)

\(\implies r=8\)

(Note: r is also equal to zero, but we can discard that solution since the radius has to be more than zero).

Therefore, the radius of the cone that yields the maximum volume is 8 m.

Answer:

Infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = -2x + 4

2x + y = 4

Step 2: Solve for x

Substitution

Here we see that 4 does indeed equal 4.

∴ the systems of equations has an infinite amount of solutions.

Answer:

Infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right  

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra I

Terms/Coefficients

Coordinates (x, y)

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

y = -2x + 4

2x + y = 4

Step 2: Solve for x

Substitution

Substitute in y:                                                                                                  2x + (-2x + 4) = 4

Combine like terms:                                                                                         4 = 4

Here we see that 4 does indeed equal 4.

∴ the systems of equations has an infinite amount of solutions.

Answer:

32

Step-by-step explanation:

Green : black

3             4

We have 24 green

3+8=24

so  multiply each side by 8

Green : black

3*8         4*8

24            32

There are 32 black grapes

Answer:

32

Step-by-step explanation:

By Question :-

Let :-

Therefore,

The sampling method that assumes a sample's average audited value will, for a certain sampling risk and allowance for sampling risk, represent the true audited value of the population is point estimation.

Point estimation is an estimate of the value of a quantity based on an observed sample of that quantity. A point estimator estimates the value of an unknown parameter in a statistical model. In point estimation, a single value (known as a statistic) is used to infer the unknown population parameter value. It is determined by applying a formula to the sample data, resulting in a single numerical value (known as a point estimate). This value is used to estimate the parameter of the population. In the process of auditing, allowances refer to the amounts that a company sets aside for doubtful accounts receivable and sales returns and allowances.

True Audited Value refers to the assessed value of a property that has been audited to determine its correct value. True Audited Value is often utilized by tax authorities in order to assess property tax or for property appraisal.

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Answer:

h(2) = 0

Step-by-step explanation:

Simply plug in 2 in for x in h(x)!

h(2) = -(2) + 2

h(2) = -2 + 2

h(2) = 0

And we have our final answer!

Answer:

H(2) = 0

Step-by-step explanation:

All you need to do is replace x with 2 in the function and solve:

H(2)= -2 + 2

H(2)= 0

Option D is the constructions that would construct a line of reflection from point A to point B. Make a line parallel to line AB.

A line parallel to line AB will generate a line of reflection that connects points A and B because a parallel line never intersects, resulting in direct imagery of Line AB.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect. They can be both horizontal and vertical in orientation.

We have,

-Make a perpendicular bisector of segment AB.

A perpendicular bisector does not create a line of reflection that connects points A and B, but rather divides the line AB into two equal parts.

-Draw a line through B that is perpendicular to segment AB.

A perpendicular line through B to segment AB WILL NOT Make a line of reflection from point A to point B.

-Build the line that connects A and B.

A line passing through A and B will NOT create a line of reflection that connects points A and B, but will instead create Line A and B and not its reflection.

Hence,

Make a line parallel to line AB.

A line parallel to line AB will generate a line of reflection that connects points A and B because a parallel line never intersects, resulting in direct imagery of Line AB.

To summarize

Option D is the constructions that would create a line of reflection from point A to point B.

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Answer:

£55.2

Step-by-step explanation:

Five day earning is £276

Earning per day is £276/5=£55.2

Answer:

(0,-4)

Step-by-step explanation:

The value of P is approximately 0.0082027.

To find the probability of selecting exactly three claims from one coverage and exactly two claims from one of the other coverages, we need to calculate the total number of ways to choose three claims from one coverage and two claims from another coverage, and divide it by the total number of ways to choose five claims from the portfolio.

First, let's calculate the total number of ways to choose three claims from one coverage and two claims from another coverage. We have 10 bodily injury claims and 10 property damage claims to choose from, so the number of ways to choose three claims from one coverage is 10 choose 3 (denoted as C(10, 3)), and the number of ways to choose two claims from another coverage is 10 choose 2 (denoted as C(10, 2)). Multiplying these two combinations gives us the total number of ways to choose three claims from one coverage and two claims from another coverage.

Next, let's calculate the total number of ways to choose five claims from the portfolio. We have a total of 10 bodily injury claims, 10 property damage claims, 10 worker's compensation claims, and 10 comprehensive claims to choose from, so the number of ways to choose five claims from the portfolio is 40 choose 5 (denoted as C(40, 5)).

Finally, to find the probability, we divide the total number of ways to choose three claims from one coverage and two claims from another coverage by the total number of ways to choose five claims from the portfolio.

Therefore, the probability that the selected claims contain exactly three claims from one coverage and exactly two claims from one of the other coverages can be calculated as:

P = (C(10, 3) * C(10, 2)) / C(40, 5)

P = (C(10, 3) * C(10, 2)) / C(40, 5)

ChatGPT

To solve the expression P = (C(10, 3) * C(10, 2)) / C(40, 5), we can substitute the values into the combination formulas and perform the calculations:

C(10, 3) = 10! / (3!(10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

C(10, 2) = 10! / (2!(10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45

C(40, 5) = 40! / (5!(40-5)!) = 40! / (5! * 35!) = (40 * 39 * 38 * 37 * 36) / (5 * 4 * 3 * 2 * 1) = 658,008

Now, we can substitute these values into the expression:

P = (C(10, 3) * C(10, 2)) / C(40, 5) = (120 * 45) / 658,008

Performing the calculation:

P = 5,400 / 658,008

Simplifying the fraction:

P ≈ 0.0082027

Therefore, the value of P is approximately 0.0082027.

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Miguel's salary after 5 years will be equal to $89,500 and after t years the equation for salary will be S = $67000 + $4500(t).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

As per the data given in the question,

Annual salary of Miguel = $67000

Increment every year = $4500

So,

Miguel's salary after t years,

S = $67000 + $4500(t).

Here, S is the total salary and t is the time in years.

So, Miguel's salary after 5 years,

S =$67000 + $4500(5)

S = $89,500.

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To determine whether the number of customers, which is expected to be 15 each day, follows a uniform distribution, a chi-square test for goodness of fit should be performed with a specified significance level (alpha).

The chi-square test for goodness of fit is used to determine if observed data follows an expected distribution. In this case, we want to test whether the number of customers each day, which is expected to be 15, follows a uniform distribution.

To perform the test, we need to collect data on the number of customers over a period of time and compare it to the expected uniform distribution. The observed frequencies for each category (e.g., the number of days with 0 customers, 1 customer, 2 customers, etc.) would be obtained.

Then, the chi-square test statistic can be calculated based on the observed and expected frequencies. The test statistic measures the discrepancy between the observed and expected distributions.

To interpret the test results, we compare the calculated chi-square value to the critical chi-square value at the chosen significance level (alpha). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis and conclude that the number of customers does not follow a uniform distribution. Conversely, if the calculated chi-square value does not exceed the critical value, we fail to reject the null hypothesis, indicating that the number of customers can be considered to follow a uniform distribution.

Please note that the specific calculations and decision-making process require additional data and the use of statistical software or tables to obtain the critical chi-square value.

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The given statement, "We can use the normal distribution to approximate the sampling distribution of the average (\(\bar X\)) for a small sample (n<30) even if our sample has clear outliers." is false.

Several random samples of a predetermined size are taken from the same population to generate a sampling distribution, which is a sort of probability distribution. You can better understand how a sample statistic fluctuates from sample to sample by using these distributions.

The given statement is false because when the sample size is small (n < 30) and the data have clear outliers, the normal distribution may not be a suitable approximation for the sampling distribution of the average (\(\bar X\)). In such cases, the presence of outliers can significantly affect the distribution, causing it to deviate from a normal distribution.

For small samples with outliers, it is generally recommended to use alternative methods or non-parametric tests that do not assume a specific distribution. These methods take into account the non-normal nature of the data and provide more robust and reliable results.

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Answer:

The answer is B. 600

Step-by-step explanation:

Hope that helps!

Answer:

B. $600.00

Step-by-step explanation:

every 10hrs worked you are getting $120.00 so just add $120.00 every 10 hrs

Answer:

8πcm² = 8pi cm²

Step-by-step explanation:

The formula for area of a sector = ½r²θ

Where r = radius = 6cm

θ = central angle = 4pi/9 in radians = 4π/9

Area of the sector = 1/2 × 6² × 4π/9

Area of the sector = (144π/18)cm²

Area of the sector = 8πcm²

Therefore, Area of the sector =

8πcm² = 8pi cm²

Answer:

8πcm² = 8pi cm²

Step-by-step explanation:

trust

After applying a reflection over the x-axis and a shift of 5 units up, the transformed function is:

g(x) = -3x + 5

Here we start with the linear function:

f(x)= 3x

There are some transformations that we need to apply to this function, first we need to apply a reflection over the x-axis, let's define this for a general function f(x). The reflection can be written as:

g(x) = -f(x)

After that, we apply a shift upwards of 5 units, to get that we just need to add 5 units, so we get:

g(x) = -f(x) + 5

Now we just replace f(x) by the given function to get

g(x) = -3x + 5

That is the transformed function.

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