3. (1 point) there are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remanining 2 people are technicians. in how many ways they can be seated in a row so that no two software engineers are together? show all your work step by step to get credit. final answers must be provided in decimal form

The equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

What is a parabola?

A parabola is defined as a collection of points such that the distance to a fixed point (the focus) and a fixed straight line (the directrix) are equal. But it's probably easier to remember it as the U-shaped curved line created when a quadratic is graphed.

To find the equation of the parabola that passes through the points (1,4) and (2,2), we can use the formula for the general form of the equation of a parabola:

y = a(x - h)² + k

where (h,k) is the vertex of the parabola, and a is a nonzero constant that determines the direction and shape of the parabola.

To find the values of a, h, and k that will give us the equation of the parabola that passes through the points (1,4) and (2,2), we can use the following steps:

Find the coordinates of the vertex of the parabola. The vertex of the parabola is the point where the parabola changes direction. In this case, the parabola changes direction at the midpoint of the two given points, which is the point (1.5,3).

Substitute the coordinates of the vertex into the formula for the general form of the equation of a parabola: y = a(x - h)² + k.

Substitute the coordinates of one of the given points into the equation to find the value of a. For example, if we substitute the coordinates of the point (1,4) into the equation, we get:

4 = a(1 - 1.5)² + 3

4 - 3 = a(-0.5)²

1 = a(-0.25)

a = -4

Substitute the values of a, h, and k into the formula for the general form of the equation of a parabola to find the equation of the parabola that passes through the points (1,4) and (2,2):

y = (-4)(x - 1.5)² + 3

Hence, the equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

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Statement on a population parameter that constitutes a statistical hypothesis. There's a chance it's true or not.

If the researchers predict a difference (or an impact) between two or more variables, this suggests that the observed pattern of the data is not the product of chance.

An equality declaration, such as =,, or, is present in a null hypothesis, which is a statistical hypothesis. A counterargument to the null hypothesis is an alternate hypothesis.  The likelihood of rejecting the null hypothesis when it is truly true is known as the level of significance. Error Type I is another name for it.

Determine the P-value for a Hypothesis Test

Find the P-value by choosing one of the following options: For a left-tailed test, P= (Area in left tail); For a right-tailed test, P= (Area in right tail); For a two-tailed test, P = 2. ( Area in tail of standardized test statistic)

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The students should draw the conclusion that the data might have been caused by the genetic connection if the null hypothesis is rejected.

Given information;

The students determine a crucial value of 7.82 and compare it to a chi-squared value of 92.86.

Which of the following results in the chi-square goodness-of-fit test being most complete?

The null hypothesis can be rejected, and the students should conclude that the data may have resulted from the genetic linkage.

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Volume of the solid (when squares divided into 4 equal parts in the lower left hand corners) = 318 cubic units.

Step-by-step explanation:

Paraboloid z=81-x2 -y2

The lower left hand corners of the squares are(0,0)(1,0)(0,1) and (1,1).

Then the volume can be estimated as,

Volume ≈ΔA [f(0,0)+f(1,0)+f(0,1)+f(1,1)]

            = 1[81+79+80+78]=318 cubic units.

b.) estimate the volume by dividing R into 4 equal squares and choosing the sample points to lie in the upper right hand corners.

Volume of the solid (when squares divided into 4 equal parts in the upper right hand corners) = 294 cubic units.

Paraboloid z=81-x2 -y2

The upper right hand corners of the squares are(1,1)(2,1)(1,2) and (2,2).

Then the volume can be estimated as,

Volume ≈ΔA [f(1,1)+f(2,1)+f(1,2)+f(2,2)]

            = 1(78+69+75+72)=294 cubic units

c.) what is the average of the two answers from a and b

Average of part a and b answer = (318+294)/2 = 712/2=306 cubic units

d.) using iterated integrals compute the exact value of the volume.

0202(81-x2 -y2) dy dx = 02[81y-x2y-⅓ y3]02 dx

                              = 02[162-2x2-8/3] dx

        = [162x-2x3/3-8/3 x]20

                              =644-16/3-16/3

                              = 644 cubic units.

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The best count on the tuition axis will be $5,000.

What is an expression?

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 senior counselor is making a histogram of the yearly cost of tuition of 20 colleges.

And, Tuition ranges from $5,000 to $51,000 a year.

Now,

Since, Tuition ranges from $5,000 to $51,000 a year.

And, There are 20 colleges.

Hence, We get;

The best count on the tuition axis will be $5,000.

Thus, he best count on the tuition axis will be $5,000.

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Given the following sample of three data points: 3, 6, 9, calculate the (estimated) standard error for the sample mean. Round to 3 decimal places.

s = √((3 - 8)² + (6 - 8)² + (9 - 8)²) / (3 - 1) = 4

2. Calculate the standard error of the sample mean:

SE = s / √n = 4 / √3 = 2.45

3. Round the standard error to three decimal places:

SE = 0.567

The standard error of the sample mean can be calculated by first finding the standard deviation of the sample (s). This is done by taking the sum of the squared differences between each data point and the mean, divided by the number of data points minus one. In this case, the standard deviation is 4. The standard error is then calculated by dividing the standard deviation by the square root of the number of data points, which is 3. The result is 2.45, which can be rounded to 0.567.

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The best approximation to the solution of the system of equations is (2, 3)

From the question, we have the following parameters that can be used in our computation:

Equation 1 is 5 x plus 2 y equals 16.

Equation 2 is x plus 3 y equals 12.

Rewrite the equations properly

So, we have the following representation

5x + 2y = 16

x + 3y = 12

Make x the subject in the second equation

So, we have

x = 12 - 3y

Substitute x =12 - 3y in the equation 5x + 2y = 16

So, we have

5(12 - 3y) + 2y = 16

Open the brakects

This gives

60 - 15y + 2y = 16

Evaluate the like terms

-13y = -44

Divide both sides by -13

y = 3.39

Substitute y = 3.39 in x = 12 - 3y

x = 12 - 3 * 3.39

Evaluate

x = 1.83

Approximate the solutions

x = 2 and y = 3

Hence, the solution is (2, 3)

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The number of aerobic classes would be 7 to make the cost of both gyms the same in the first month.

What are linear equations?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are those in which the linear equation contains two variables.

Let x= number of months, and a=no of aerobic classes.

Let Gym A charge a $10 membership fee plus $20.25 per month plus $5.50 per aerobics class.

So we get the equation:

y= 10+20.25x+5.50a

y=30.25+5.50a ------------ as (x=1)

Next, for Gym B, it charges $46 per month plus $3.25 per aerobics class.

So the equation is:

y=46x+3.25a

y=46+3.25a ------------------as (x=1)

Now since we need to find the number of aerobic classes, we equate both equations:

30.25+5.50a = 46+3.25a

2.25a = 15.75

a = 7

Therefore, there must be 7 aerobic classes that would make the cost of both gyms to be the same.

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The number of tickets that will be sold is 5560.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets sold will be = 94520/17 = 5560.

Hence, the number of tickets that will be sold is 5560.

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Answer:

The slope is [tex]\frac{-2}{3}[/tex]

Step-by-step explanation:

An order pair is in the form (x y).  The slope is the change in y over the change in x.  From the 2 points our y's are 2 and 4.  From the 2 points our x's are  1 and -2.  to find the change you subtract.

[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]

There are total percentage of 56% of red gumballs and 44% of blue gumballs in 4000 gumball machine.

Percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given,

Total gumballs in the machine = 4000

Red gumballs in the machine = 2240

Blue gumballs in the machine = 1760

Percentage of each gumballs,

Percentage of red gumballs,

Value/Total × 100%

2240/4000 × 100

0.56 × 100

56%

Percentage of blue gumballs,

1760/4000 × 100%

0.44 × 100%

44%

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Answer:

Step-by-step explanation:

it is C because 65 is a one Time thing and 30x means every month u rent it times the money.

Answer:

3(13/2)+2y=9 the answer is y=-21/4

The circumference of the circle with radius 17 millimeter is 106.76 millimeter

The radius of the circle = 17 millimeter

The circumference of the circle is defined as the linear distance around the circle

The radius of the circle is the distance between the center of the circle to the any point of the circumference.

The circumference of the circle = 2 × π × r

Where r is the radius of the circle

The value of the π = 3.14

Substitute the values in the equation

The circumference of the circle = 2 × 3.14 × 17

Multiply the numbers

= 106.76 millimeter

Therefore, the circumference of the circle is 106.76 millimeter

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Answer:

Step-by-step explanation:

To solve this problem, we need to divide 3/10 gallons by 1 gallon, which is equal to 4 quarts.

First, let's convert the fraction 3/10 to a decimal by dividing the numerator by the denominator: 3 / 10 = 0.3

Then, we can divide 0.3 gallons by 1 gallon to get the equivalent number of gallons in quarts: 0.3 gallons / 1 gallon = 0.75 quarts

Since 1 quart is equal to 0.25 gallons, 0.75 quarts is equivalent to 3/4 of a gallon.

Finally, we can add the number of quarts given in the problem (11 quarts) to the number of quarts equivalent to the number of gallons (3/4 of a gallon, or 3 quarts). This gives us a total of 14 quarts, which is equivalent to 3 and 1/2 gallons.

Therefore, the final answer is 3 gallons and 11 quarts.

Answer:

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

Average rate of change for this case is:

The line chart can be created using insert tab and then click line symbol in charts group.

Line chart is a type of chart with line visualization to show information of changing values over time.

Insert tab is tab in excel to insert object, symbol, chart, etc.

To create line chart,

I'm attaching a image for microsoft excel 365 version, your excel version may be different, but the line chart is still in the insert tab.

Thus, to create the line chart use insert tab and in chart group click line symbol.

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Therefore the solution to the given problem is  the each of the congruent base angles is 70°

In Euclidean geometry, an angle is the figure generated by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are in the plane where the rays are located. The intersection of two planes also forms angles. We refer to these as dihedral angles.

Here,

As the triangle is an isosceles triangle therefore it will have 2 same angles

thus,

Sum of the 3 angles of a triangle=180°

Vertex angle =40°

Sum of two congruent angles=180°–40°=140°

Measure of each base angle=70°

Therefore the each of the congruent base angles is 70°

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The correct answer is (B) 99.73%..

For a process in control, we expect 99.73% of the points on a process control chart to fall within the upper control limit (UCL) and the lower control limit (LCL).

A process control chart is a tool used in statistics and quality control to monitor and analyze a process over time. It consists of a line graph that plots the measured values of a process variable, such as the temperature or weight of a product, over time. The UCL and LCL are horizontal lines that are drawn on the graph at a predetermined distance above and below the average value of the process variable.

The expected percentage of points within the UCL and LCL is determined by the chosen level of statistical significance and the distribution of the process variable. In this case, the expected percentage of points within the UCL and LCL is 99.73%.

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Complete Question:

For process in control, we expect Pfo of the points on process control chart to fall within the UCL and the LCL:

A)0.27

B)99.73

C)100

Proving  that the maximum spanning tree of g contains the widest paths between every pair of vertices .

Suppose now we were to add an edge from the widest path into the spanning tree in a place that it won't cause a cycle.

so every path between our two nodes must contain some edge between two previously unconnected nodes.

The weight of the edge we removed was equal to the width of the original path, and because the path was that every edge in the new path must have had more weight than that edge.

This means that our new spanning tree must have strictly more total weight than the original, which contradicts the definition of the original 'maximum' spanning tree.

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Answer:

  73.3%

Step-by-step explanation:

You want to know the percentage adopted when 4 of 15 were not adopted.

The percentage can be found by multiplying the fraction by 100%. The fraction of dogs adopted was 11 out of 15, or 11/15. The percentage is ...

  11/15 × 100% ≈ 73.3%

About 73.3% of the dogs were adopted.

Answer:

b

Step-by-step explanation:

did the math?

8 is the best estimate of [tex]8\frac{1}{8}[/tex].

In simple words, the ratio of the two numbers is called a fraction.

Mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number.

For example, 2 (1/3) is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Step 1: Multiply the denominator with the whole number,

i.e. Multiply 8 with 8 in the given example, 8(1/8).

                                            8× 8  =64

Step 2: Add the numerator of the Fraction to the result in step 1. i.e.,             Add                                      1+ 64=65.

Step 3: Keep the Denominator same i.e. 8.

Step 4: The Improper fraction obtained is: 65/8.

Given number can be denoted as 8+[tex]\frac{1}{8}[/tex] = 8+0.15 = 8.15

So the number is nearest to 8 itself.

i.e. 8 is the best estimate.

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The vertex of the function g(x) = |x - 8| + 6 is (8, 6)

From the question, we have the following parameters that can be used in our computation:

g(x) = |x - 8| + 6

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex is

Vertex = (8, 6)

Remove the x value

y = 6

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 6

So, the range is y ≥ 6

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The graph of this inequality shows a region to the left at x = 12.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality (1/2)x < 6.

Multiplying both sides of the inequality by 2 we get,

2×(1/2)x < 2×6.

x < 12.

The graph of this inequality shows a dotted line at x = 12 and the region is left side to it.

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Hence for miles greater than 45, the Company A will charge less than Company B.

Given:

Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

we are asked to find for what mileages will Company A charge less than Company B = ?

from the question we frame  the inequality as:

⇒ 91< 55+0.80m

⇒ 36<0.80m

⇒ 45<m

or

m>45

Check answer

55+45(0.8)=91 check

Hence for miles greater than 45, the Company A will charge less than Company B.

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The image of the point after the transformation D₂,₀ T₋₄,₋₅ is (-6, -15)

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The coordinates of the point are given as

(-1, -3)

The transformation is given as D2 0 T-4,-5

This transformation, when properly expressed is

D₂,₀ T₋₄,₋₅

This represents

As mentioned above,

D₂,₀ T₋₄,₋₅

Mathematically, we have

(x, y) ⇒ (2x - 4, 2y - 5)

Substitute (-1, -3) in (x, y) ⇒ (2x - 4, 2y - 5)

So, we have

(x, y) ⇒ (2(-1) - 4, 2(-5) - 5)

Evaluate

(x, y) ⇒ (-6, -15)

Hence, the coordinates of the image are (-6, -15)

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According to Ritchie et al., a typology is a set of ordered categories occurring at discrete positions along a continuum is a True statement. often helps researchers gain insight into the underlying dynamics of the items being studied.

A typology is an organized classification of distinct types of entities, such as people, places, or objects. It is used to create order and structure out of seemingly unrelated items and to identify relationships between them. According to Ritchie et al. (2015), a typology is a set of ordered categories occurring at discrete positions along a continuum. This allows for a more comprehensive understanding of the items being classified, as it allows for further comparison and contrast between the categories. This type of ordered structure often helps researchers gain insight into the underlying dynamics of the items being studied.

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The probability that the sample mean is less than 5, is 0.92135.

Let X1,X2,...,X32 be a random sample from an exponential distribution with a mean of 4.

We have to find an approximate probability that the sample mean is less than 5.

Let X = [tex]\frac{\Sigma_{i=1}^{n}x_{i}}{n}[/tex]

X = [tex]\frac{\Sigma_{i=1}^{32} x_{i}}{32}[/tex]

Then required probability is P(X<5).

Now we have to find the distribution of X where [tex]x_{i}[/tex]……. x_{32}.

Follow exponential with mean 4.

[tex]x_{i}[/tex]→exponent(λ=1/mean)

[tex]x_{i}[/tex]→exponent(λ=1/4)

[tex]x_{i}[/tex]→exponent(λ=0.25)

Now we have result:

If [tex]x_{1}[/tex] ………… x_{n} are exponential with α.

Then [tex]\Sigma{x_{i}}[/tex] has Gamma Distribution with (α=0.25, n=32)

Now we have result

X→G(α, λ) then c X→G(α/c, λ)

Here, we have

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α=0.25, n=32)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α/(1/n), n)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(nα, n)

X→Gamma(32*0.25, 32)

X has Gamma distribution with α=8, λ=32.

Required probability is;

P(X<5) = [tex]\int_{0}^{5}f(x) dx[/tex]

P(X<5) =[tex]\int_{0}^{5}\frac{\alpha }{\sqrt{\lambda}}e^{-\alpha x}x^{\lambda-1} dx[/tex]

Now to approximate this probability using normal as

X-mean(X)/SD(X)  = N(0,1)

X→Gamma(α=8, λ=32)

E(X) = λ/α                                            Var(X)= λ/α^2

E(X) = 32/8                                          Var(X)= 32/(8)^2

E(X) = 4                                               Var(X)= 0.5

Now P(X<5)=P[{(X-E(X))/√Var(X)}<{ (5-4)/√0.5}]

P(X<5)=P[{z< 1/√0.5}]

P(X<5) = P(z<1.4142

From the normal probability table

P(X<5) = 0.92135

Hence, the probability that the sample mean is less than 5, is 0.92135.

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The good practice to protect the classified information is labelling them with markings.

In the question ,

we have been asked about the good practice that can help in protecting the classified information .

we know that ,

the term Classified means when something is arranged in classes. and

the term Labeling means that when something is assign to a category.

So , the best practice is to Ensure the proper labeling by appropriately marking all the classified material and when required, sensitive material.

Therefore , the best practice is Ensure proper labeling by appropriately marking all classified material .

The given question is incomplete , the complete question is

What is a good practice to protect classified information ?

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The given function models the amount in the account after t years is true.

What is compounded quarterly?

The process of calculating the interest earned quarterly on a fixed deposit or investment, computed based on the principal amount plus the interest earned for previous periods, is known as quarterly compounding.

Given:

Albert deposits $3250 in an account that earns 4.3% interest compounded quarterly.

P = $3250

r = 4.3% = 0.043

n = 4

t = t years

So, the function models the amount in the account after t years is,

[tex]A = P(1+\frac{r}{n})^n^t\\ A = 3250(1+\frac{0.043}{4})^4^t[/tex]

This equation is same as the given equation.

Hence, the given function models the amount in the account after t years is true.

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Complete question:

Complete question is attached below.