find a particular solution to the nonhomogeneous differential equation y′′ 4y′ 5y=15x 3e−x.

Answer:

The answer is C.

Step-by-step explanation:

The value of x on the relative frequency table is  14%.

Percentage is fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.

Value of x = (number of people with green eyes that have other hair colour / total number of people) x 100

(114/881) x 100 = 14%

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Answer:

A. x = 14%

Step-by-step explanation:

Did the Unit Test Review on Edge 2022

Answer:

Ivan: 4

Caleb: 4, 4, 4, 4, 4, 4, 4

Step-by-step explanation:

For every 4 Ivan sees, Caleb sees 28. (4 times 7)

The population mean amount of paint included in a 1- gallon can is between 0.160 gallons to 1.814 gallons.

The confidence intervals (range estimates) over a specific level of confidence are excellent indicators for the true value of the parameter. The primary logic for computing the estimate is by means of point estimate and margin of error.

The confidence level is 99%

The significance level is 0.01 \((\alpha )\)

The z - table is used to obtain two - tailed critical value at 0.01 level of significance

\(2P(Z > z_\frac{\alpha }{2} )=\frac{\alpha }{2}\)

2P(Z > 2.58) = 0.01

The margin of error1 is:

ME = \(z_\frac{\alpha }{2} .(\frac{\sigma}{\sqrt{n} } )\)

ME = 2.58 \((\frac{2.58}{\sqrt{64} } )\)

ME = 0.832

The 99% confidence interval for the population mean amount of paint include in a 1- gallon can:

(x(bar) - ME ,x(bar) + ME ) = (0.992 - 0.832 , 0.992 + 0.832)

                                         = (0.160 , 1.814)

Therefore, the population mean amount of paint included in a 1- gallon can is between 0.160 gallons to 1.814 gallons.

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\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

The Correct choice is : C

\(\qquad \sf  \dashrightarrow \: it \: \: is \: \: on \: \: the \: x - axis\)

As we can observe, the y - coordinate ( ordinate ) of the given point (2 , 0) is 0. so it's obvious that it's distance from x - axis is Zero. In other words we can say that the point is lying on x - axis.

Answer:

answer is C

it's on the x-axis

Step-by-step explanation:

hope t     his helps!

Answer:

To solve a system of linear equation graphically, it is best to write both equations in slope-intercept form first. After you put them in slope-intercept form, you should be able to graph them easily.For one solution, the two lines have to intersect at exactly one point, since both equations are satisfied at the intersection.

For no solution, the two lines have to never intersect, which means they have to be parallel lines. In other words, no solution will satisfy both equation.

The graph of a system of equations with one solution intersects at a point.

The graph of a system of equations with infinitely many solutions has only one line.

The graph of a system of equations with no solutions has two parallel lines.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The graph of a system of equations with one solution.

The graph intersects at a point.

The graph of a system of equations with infinitely many solutions.

The graph has only one line.

The graph of a system of equations with no solutions.

The graph has two parallel lines.

Thus,

The graph of a system of equations with one solution intersects at a point.

The graph of a system of equations with infinitely many solutions has only one line.

The graph of a system of equations with no solutions has two parallel lines.

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SOLUTION

The diagram below would be very helpful in answering the question

(a) to find f'(-2), we find the slope m of the line that I have made in red.

We use the points (-1, 0) and (-3, 1) we have

Hence the answer is

(c) We should determine x, where f'(x) = 0

Now f'(x) = 0 at a where we call the maximum point. That is the highest point of the graph curved as "n" From the figure above we can see that at this point, y is 3, also tracing down to the x-axis plane, can see that x = 3

Hence the answer is x = 3

The probability that the no of copper rings received equals to no of brass rings received is 8.68 x 10^-6. That the number of copper rings equals the number of brass rings is not possible.

We can use the concept of combinations and permutations to solve this problem,

First, let's consider the number of ways to select pairs of employees and interns.

Given data:

no of employees = 10

no of intern = 10

To select a pair of employees let us consider there are 10 choose 2 ways = 10! / (2! * (10-2)!)

= (10 * 9) / 2

= 45 ways

To select a pair of interns let us consider that there are 10 choose 2 ways = 45 ways

Additionally, there are 10 x 10 = 100 ways to select a pair consisting of one employee and one intern.

Next, we need to consider the number of ways to distribute the rings.

number of pairs of employees = 45

number of pairs of interns = 45

number of ways, if we distribute the copper and brass rings in 45 choose 5,

= 45! / (5! * (45-5)!)

= 1,221,759 ways

no pairs consist of one employee and one intern = 100

Several ways we can distribute the silver rings in 100 choose 10 are

= 100! / (10! * (100-10)!)

= 173,103,094,564,400 ways.

Now consider that number of copper rings equals the number of brass rings

There are two ways which are

1) If we assume that all pairs consist of one employee and one intern, and each pair receives a silver ring.

In this case, the number of ways to distribute the silver rings is 100 choose 10

= 100! / (10! * 90!)

= 173,103,094,564,400 ways

2) If we assume that five pairs of employees receive copper rings, and five pairs of interns receive brass rings.

In this case, the number of ways to distribute the copper and brass rings is 45 choose 5 x 45 choose 5

= (45! / (5! * (45-5)!)) x (45! / (5! * (45-5)!))

= 1,488,087,002,625 ways

The total number of ways to distribute the rings

= 173,103,094,564,400 x 1,221,759 x 1,221,759

= 2.176 x 10^29.

The probability that the number of copper rings equals the number of brass rings is

= (173,103,094,564,400 + 1,488,087,002,625)/2.176 x 10^29

= 8.68 x 10^-6.

the probability is very low, and the number of copper rings that will be equal to the number of brass rings is not possible.

Therefore, the number of copper rings equals the number of brass rings is 8.68 x 10^-6

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The complete question is -

At a company, ten employees and ten interns line up to visit the CEO in ten randomly selected pairs. If each pair of employees receives a copper ring, each pair of interns receive a brass ring, and each employe-intern pair receives a silver ring what is the probability that the no of copper rings received equals to no of brass rings received?

Answer:

3/11

Step-by-step explanation:

You add both of the fractions so 2+1 is equal to 3 and 8+3 is equal to 11. You can not simply any further from 3/11

The researcher draws a random sample using a Multistage cluster sample

At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.

In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.

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Answer:

81, Option 2.

Step-by-step explanation:

\(3^{4}\) means 3 x 3 x 3 x 3, that is 3 multiplied 4 times with itself.

Here's how to do it:-

3 x 3 = 9

9 x 3 = 27

27 x 3 = 81

So, \(3^{4}\) would be 81, Option 2.

===================================================

Work Shown:

a^2+b^2 = c^2

15^2+20^2 = 25^2

225+400 = 625

625 = 625

Since the last equation is true, this makes the first equation true for those a,b,c values. Therefore, by the pythagorean theorem converse, this is a right triangle.

Side note: c is always the longest side.

The linear function is y = (-1/2)x + 4.

What is a linear function?

A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.

Here, we have

Given,

A linear function has an x-intercept of 8 and a y-intercept of 4.

So, The two points on the line are (8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 - 8).

slope(m) = -4/8.

slope(m) = -1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Hence, the linear function is y = (-1/2)x + 4.

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Answer:

\(\sqrt{x^2+y^2+1}=18\)

Step-by-step explanation:

We are given:

\(x^2=18x+y\qquad\qquad[1]\)

\(y^2=18y+x\qquad\qquad[2]\)

Subtracting [1] and [2]:

\(x^2-y^2=18x+y-(18y+x)\)

Operating:

\(x^2-y^2=18x+y-18y-x\)

Recall:

\(x^2-y^2=(x-y)(x+y)\)

Substituting:

\((x-y)(x+y)=18x+y-18y-x\)

Rearranging:

\((x-y)(x+y)=18x-18y-(x-y)\)

\((x-y)(x+y)=18(x-y)-(x-y)\)

Dividing by x-y (recall x≠y):

\(x+y=18-1=17\)

\(x+y=17\qquad[3]\)

Now we add [1] and [2]:

\(x^2+y^2=18x+y+18y+x\)

Rearranging:

\(x^2+y^2=18x+18y+x+y\)

\(x^2+y^2=18(x+y)+(x+y)\)

\(x^2+y^2=19(x+y)\)

Substituting from [3]

\(x^2+y^2=19*17=323\)

Adding 1:

\(x^2+y^2+1=324\)

Taking the square root:

\(\sqrt{x^2+y^2+1}=\sqrt{324}=18\)

Thus:

\(\mathbf{\sqrt{x^2+y^2+1}=18}\)

Answer:

(2,3)

Step-by-step explanation:

(2)(2) + (3)(3) = 13

The correct options are (a) and (d).

A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.

The given equation is as below,

2x + 3y = 12                              (1)

In order to find the correct answer all the options are considered one by one as follows,

(a) (0, 4)

Substitute x = 0 and y = 4 in equation to get,

LHS = 2× 0 + 3 × 4

       = 12

Since LHS = RHS, the given option is correct.

(b)  (3, 2)

Substitute x = 3 and y = 2 in equation to get,

LHS = 2× 2 + 3 × 2

       = 10

Since LHS ≠ RHS, the given option is not correct.

(c)  (2, 3)

Substitute x = 2 and y = 3 in equation to get,

LHS = 2× 3 + 3 × 3

       = 13

Since LHS ≠ RHS, the given option is not correct.

(d) (6, 0)

Substitute x = 0 and y = 4 in equation to get,

LHS = 2× 6 + 3 × 0

       = 12  

Since LHS = RHS, the given option is correct.

Hence, the points satisfying the given equation are (0, 4) and (6, 0).

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

See explanation.

Step-by-step explanation:

(0,-6) --> -6x-5y=30

(0,3) --> 3x+2y=6

(4,-1) --> x-4y=8

(1,-5) --> -5x+y=-10

Answer:

2%

Step-by-step explanation:

The probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have been given that a group of 12 dance competition contestants is wearing the numbers 1 through 12.

To determine the probability that the winners will be wearing numbers 2, 4 and 7

Here are favorable outcomes that the contestants wearing numbers 2, 4, and 7

So the number of favorable outcomes = 3

And there is a total number of outcomes = 12

Required probability = 3/12

Required probability = 1/4.

Thus, the probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.

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Answer:

y, because it crosses the y-axis.

b, because in y=mx+b b is the y-intercept.

Step-by-step explanation:

This is basically just memorization.

The real part of the complex number - 5 + 3i is ''-5''.

The complex part of the complex number - 5 + 3i is ''3''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The complex number is,

⇒ - 5 + 3i

Now,

Since, The complex number is,

⇒ - 5 + 3i

Hence, The real part of the complex number = -5

The complex part of the complex number = 3

Thus, real part of the complex number - 5 + 3i is ''-5''.

The complex part of the complex number - 5 + 3i is ''3''.

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Answer:

-5 complex and 3 imaginary complex

Step-by-step explanation:

Answer:

The answer of the question is C

24

Answer:

20 problems.

Step-by-step explanation:

She has 100 - 65 = 35% of her problems left.

35% is equivalent to 7 problems,

so, 100% = 7 * 100/35

               = 100/5

              = 20 problems

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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Answer:

it's not showing the question so how will I tell you

When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

What is statistical validity?

Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.

It can also be the statistics which are derived from the research works or studies.

What is frequency in statistics?

Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.

For a given set of data the frequency can either be 0 or more than that.

Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.

What is margin of error estimate?

The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.

The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the  interval.

Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

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Answer:

12

Step-by-step explanation:

\(\sqrt{8} * \sqrt{18} =12\)