Find each product or quotient.

−5(−6)

We need to find how long a person has to wait on average to have their question answered, how many people will be in line on average, what percent of the day will the information booth be busy.

The average time that each person takes is 1 minute. Therefore, 30 people can be helped per hour by a single employee. And since the fair lasts for 8 hours a day, a total of 240 people can be helped every day by a single employee. The fair is visited by approximately 1000 people.

Therefore, the percentage of the day that the information booth will be busy can be given by; Percent of the day the information booth will be busy= (240/1000)×100 Percent of the day the information booth will be busy= 24% Therefore, the information booth will be busy 24% of the day.2.

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The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.

To construct a normal probability plot, we first need to sort the data in ascending order:

6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9

Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.

To determine the sample standard deviation, we can use the formula:

s = sqrt[(∑(xi - x)²) / (n - 1)]

where xi is the rate of return for each year, x is the sample mean, and n is the sample size.

Sample mean:

x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433

Sample standard deviation:

s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]

= 3.059

Therefore, the sample standard deviation is 3.059.

To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:

CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]

where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).

For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:

χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337

Plugging in the values, we get:

CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]

= [1.946, 26.557]

Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.

The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.

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Answer:

Concept:

The formula used to calculate the equation of a line when two points are given is given below as

Where the coordinates are given are

By substituting the values, we will have

Hence,

The equation of the line is y =-x+8

By graphing the line, we will have the image to be given below as

Answer:

f(2) = 2

Step-by-step explanation:

We are given
f(x) = x² - 7x + 4

To find f(2), just plug in 2 wherever you see an x and simplify

f(2) = 3 · 2² - 7 · 2 + 4

= 3 · 4 - 7 · 2 + 4

= 12 - 14 + 4

= 2

We are given the following equation and we must state the reason behind each of the steps taken to solve it:

In the first step after giving the equation 21 is being substracted from both sides of the equation. Remember that the substraction property of the equality states that any value substracted from one side of the equal sign must also be substracted from the other side. Therefore the reason behind this step is the substraction property.

Then the substractions on each side are performed. In the left side we get 21-21=0 so the constant term dissapears and on the right we obtain 21-15=6. This means that during this step only a simplification was performed.

In the following step a number 2 is multiplied to each side of the equal sign. Remember that the multiplication property of equality states that whatever is multiplied in one side of the equal sign must also be multiplied in the other side. Then the reason behind this step is the multiplication property of equality.

In the final step in the left side the 2 multiplying is simplified with the number 2 dividing and in the right side the product between -6 and 2 is performed. Then this step is also a simplification.

Then the reasons in order are:

- Substraction Property of Equality

- Simplifying

- Multiplication Property of Equality

- Simplifying

In regression analysis , the error term ε is a random variable with expected value of 0.

What is regression analysis?

A set of statistical procedures known as regression analysis is used to estimate the relationships between a dependent variable and one or more independent variables.

Main Body:

In regression analysis, the model in the form is called regression model.

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β0 + β1x, is known as regression equation.

So the answer  to error term is 0.

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Answer:

B)120º

Step-by-step explanation:

70+50=x

120=x

Sum of two interior angles=exterior angle

\(\\ \sf\longmapsto 50+70=x\)

\(\\ \sf\longmapsto x=120\)

Option B

Answer:

79.5

Step-by-step explanation:

10^7 = 10^6 * 10

then 10*7.95 = 79.5

Answer:

27

Step-by-step explanation:

According to the general rule, the sample distribution of means will be roughly normal if n is more than 30. However, any sample size will result in a normal.

A sampling distribution is the name given to this statistic's probability distribution. And the term "standard error" refers to this statistic's standard deviation. Whether we sample with or without replacement, the sampling distribution has essentially the same standard error if the population size is significantly bigger than the sample size. The probability distribution of a specific statistic based on a random sample is called a sampling distribution, also referred to as a finite-sample distribution, in statistics. The sampling distribution is the probability distribution of the values that would be used to compute the statistic from an arbitrary large number of samples, each containing multiple observations (data points).

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The value of the square root of 140 lies between 11 and 12. The square root of 140 is 11.83

The volume of the solid (cylinder) is 6π unit³,

The volume of an object is the amount of space occupied by a three dimensional object.

A solid with a circular base and a vertical cross section is a cylinder.

Therefore the solid shown in the problem above is a cylinder.

A unit circle has a radius of 1, hence the radius of the cylinder = 1 unit, diameter = 2 * radius = 2 * 1 = 2 unit

Height of cylinder = 3 * diameter = 3 * 2 = 6 unit

Volume of cylinder = π * radius² * height = π * 1² * 6 = 6π unit³

The volume of the solid (cylinder) is 6π unit³.

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Answer:

33%

Step-by-step explanation:

(68/206) × 100 = 33%

the answer is 33%

Answer:

B

Step-by-step explanation:

1/x+2 + 1/x+2 = 2/x+2 = 1/x+1.

The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.

The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).

So we can write an equation to represent the total cost:

0.62x + 0.52 (5000 - x) = 2798

Expanding the second term:

0.62x + 2600 - 0.52x = 2798

Combining like terms:

0.10x = 198

Finally, solving for x:

x = 1980

So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

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Answer:

$4.50

Step-by-step explanation:

6/4=1.5 $1.50 per container. 1.50×3 is $4.50

(check comment)

Answer: the last question at the very bottom

Step-by-step explanation:

the graph is not a scatter plot, so its a line plot .

Answer:

2 and x=-2

Step-by-step explanation:

The area of the rectangle is increasing at a rate of 166 cm^2/s when the length is 15 cm and the width is 13 cm.

To find the rate at which the area of the rectangle is increasing, we need to use the formula for the area of a rectangle, which is A = lw (where A is the area, l is the length, and w is the width).

We can differentiate both sides of the equation with respect to time (t) to obtain:

dA/dt = (dl/dt)w + l(dw/dt)

Here, dl/dt is the rate of change of the length, which is given as 7 cm/s, and dw/dt is the rate of change of the width, which is given as 5 cm/s.

We can substitute these values along with the given values of length and width (l = 15 cm and w = 13 cm) to obtain:

dA/dt = (7 cm/s)(13 cm) + (15 cm)(5 cm/s)

dA/dt = 91 cm^2/s + 75 cm^2/s

dA/dt = 166 cm^2/s

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To use the tangent ratio in a triangle, you need to know the lengths of two sides or the measures of two angles in the triangle. The tangent ratio relates the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.

The tangent ratio is a trigonometric ratio that relates the length of one side of a right triangle to the length of another side. It is defined as the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle.

In order to use the tangent ratio, you must have knowledge of the triangle's sides or angles. If you know the lengths of two sides of a right triangle, you can use the tangent ratio to find the measure of one of the acute angles in the triangle. Conversely, if you know the measure of one of the acute angles, you can use the tangent ratio to find the ratio of the lengths of the sides in the triangle.

Essentially, to apply the tangent ratio, you need to have sufficient information about the triangle to identify the sides or angles involved in the ratio calculation. This information can be provided in terms of lengths of sides or measures of angles, allowing you to use the tangent ratio to solve for missing values or determine specific relationships within the triangle.

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Based on the given Poisson distribution, the probability there is at least one error in a five-page document is 0.981 or 98.2%.

The Poisson distribution refers to a discrete probability distribution that provides the probability of a given number of events occurring in a fixed interval of time or space such that the events happen with a known constant mean rate. The probability formula for Poisson distribution is given by:

P\left(x\right)=\frac{e^{-\lambda}*\lambda^x}{x!}

Where λ is an average rate of value, x is the random variable, and e is the base of the algorithm.

The number of typing errors on a page follows a Poisson distribution. The average of typing errors on a page is 0.8 per page, hence the average rate for five-page document is 0.8*5 = 4 per document. Hence, the probable at least one error is found in the document is given by P(x ≥ 1) = 1 – P(x = 0)

Hence, find the probability that the number of error is 0 is given by:

P\left(0\right)=\frac{e^{-4}*4^0}{0!}\ =\ e^{-4}

Therefore,

P(x\ \geq\ 1)\ =\ 1\ -\ e^{-4}\ =\ 0.981

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raAnswer:

x = 5

Step-by-step explanation:

Original equation = \(\sqrt{2x+6}\) - \(\sqrt{x+4}\) = 1

Remove square roots

\(x^{2}\) + 2x +1 = 4x +16

Subtract 16 from both sides

\(x^{2}\)+ 2x +1 = 4x +16

           -16       -16

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

\(x^{2}\)  + 2x- 15= 4x

Subtract 4x from both sides

\(x^{2}\) + 2x - 15 - 4x= 4x - 4x

= \(x^{2}\) - 2x - 15 = 0

THIS EQUATION HAS 2 rational roots. {x1,x2} = {5,-3}

CHECK THAT THE FIRST SOLUTION IS CORRECT (5)

    Original equation, root isolated, after tidy up

  \(\sqrt{2x+6}\) = \(\sqrt{x+4}\)

     Plug in 5 for  x

\(\sqrt{2\cdot (5)+6}\) = \(\sqrt{(5)+4+1}\)

        Simplify

      \(\sqrt16}\) = 4

  Solution checks !!

     Solution is: x = 5

CHECK THAT THE SECOND SOLUTION IS CORRECT (-3)

 Original equation, root isolated, after tidy up

  \(\sqrt{2x+6}\) = \(\sqrt{x+4}\)

   Plug in  -3 for  x

  \(\sqrt{2\cdot (-3) +6}\) = \(\sqrt{(-3)+4+1}\)

       Simplify

\(\sqrt{0}\) = 2

 Solution does not check

          0 ≠ 2

   So, the answer is x = 5

Hope this helps!

Answer:

Slope: −2-2

y-intercept: (0,4)

Answer:

(-8,7)

Step-by-step explanation:

5x+9y=23

-2x+y=23

 Step 1. When looking at the equation you need to find out what method you must use and a good way to find out if you use subtraction is to look for a variable of 1

just like -2x+y=23 has the variable 1y

 Step 2. solve for y in the second equation

-2x+y=23

+2x       +2x

y=2x+23

Step 3. rewrite your equation

5x+9y=23

y=2x+23

 Step 4. replace your y variable with the expression you just made

5x+9(2x+23)=23

Step 5. Distribute the 9 and solve

5x+18x+207=23

23x+207=23

23x=-184

x=-8

Step 6. enter your x value into the equation you solved in step one

y=2(-8)+23

y=-16+23

y=7

Step 7. determine if consistent or inconsistent

Because you have a x and y you have an consistent

...you can also graph it

Step-by-step explanation:

Angles in a quadrilateral add to 360 degrees. So, x = 360-88-142-106=24 degrees

The average rate of change between the given values of the variable is 21

A function can be defined as an expression or rule showing the relationship between a dependent and an independent variable.

Given the function;

h(t) = 2t^{2}\) − t

For t =2

Substitute the value of t as 2 in the function, we have;

h(2) = 2 (2)² - (2)

Find the square

h(2) = 2(4) - 2

h(2) = 8 - 2

h(2) = 6

For t = 9

Substitute the value of t as 9 in the function, we have;

h(9) = 2(9)² - 9

Find the square

h(9) = 2(81) - 9

h(9) = 153

The average change = 153 - 6 = 147/ 9 -2 = 147/ 7 = 21

Thus, the average rate of change between the given values of the variable is 21

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The location of point P such that the ratio AP / PB = 2 / 3 is (1, - 2).

In this question we have the location of two endpoints of a line segment, point A (3, 0) and point B (- 2, - 5). About the line segment, we are asked to find the coordinates of a point P such that the following ratio is met:

AP / PB = 2 / 3

3 · AP = 2 · PB

3 · [P(x, y) - A(x, y)] = 2 · [B(x, y) - P(x, y)]

3 · P(x, y) - 3 · A(x, y) = 2 · B(x, y) - 2 · P(x, y)

5 · P(x, y) = 3 · A(x, y) + 2 · B(x, y)

P(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

P(x, y) = (3 / 5) · (3, 0) + (2 / 5) · (- 2, - 5)

P(x, y) = (9 / 5, 0) + (- 4 / 5, - 10 / 5)

P(x, y) = (9 / 5, 0) + (- 4 / 5, - 2)

P(x, y) = (1, - 2)

The location of point P is (1, - 2).

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Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

The calculated value of the circumference of the circle is 31.4 units

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

Radius, r = 5

Using the above as a guide, we have the following:

Circumference = 2 * π * r

Substitute the known values in the above equation, so, we have the following representation

Circumference = 2 * 5 * 3.14

Evaluate the products

Circumference = 31.4

HEnce, the value of the circumference is 31.4 units

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