What percent is represented by the shaded area?

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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The mean and variance of Z=2 are 1 and 0.5 respectively, and the probability that Z=2 is 0.25.

Let's first calculate the mean and variance of N as follows -

The mean of N is 6 * 0.5 = 3, since each nickel has a 0.5 probability of landing heads up.

The variance of N is 6 * 0.5 * 0.5 = 1.5.

Since N determines the number of dimes that are tossed, the mean and variance of Z will depend on N.

Let's assume N = 2, then Z is the number of tails observed when tossing 2 dimes.

Each dime has a 0.5 probability of landing tails up, so the mean of Z would be 2 * 0.5 = 1.

The variance of Z would be 2 * 0.5 * 0.5 = 0.5.

To find the probability that Z=2, we can use the binomial probability formula as follows -

P(Z=2) = \(\binom{2}{2} * (0.5)^2 * (1-0.5)^{(2-2)}\) = 0.25.

Hence, the probability that Z=2 is 0.25.

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The complete question is -

Six nickels are tossed, and the total number N of heads is observed. Then N dimes are tossed, and the total number of Z of tails among the dimes is observed. Determine the mean and variance of Z and the probability that Z=2.

Answer:

19/5

Step-by-step explanation:

17= 5k - 2

Answer:

Julio's gross income before the tax deductions is $ 405.

Step-by-step explanation:

Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:

547 - 142 = X

405 = X

Therefore, Julio's gross income before the tax deductions is $ 405.

A point that best represent the location for them to put the science project is: A. (6.5, 6).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(5 + 8)/2, (8 + 4)/2]

Midpoint = [(13)/2, 12/2]

Midpoint = (6.5, 6).

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Answer:

52nd percentile

Step-by-step explanation:

The sorted data :

36.0, 37.0, 39.5, 40.0, 40.5, 43.0, 44.0, 45.5, 45.5, 46.5, 48.0, 48.00, 49.0, 50.0, 51.5, 52.5, 53.0, 53.5, 54.0, 57.3, 57.5, 58.0, 58.5, 59.0, 59.5, 60.0, 61.0, 61.0, 61.0, 61.5, 62.0, 62.5, 63.0, 63.0, 63.5, 64.0, 64.0, 64.0, 64.5, 65.0, 66.0, 67.5, 67.5, 68.5, 70.0, 70.5, 71.5, 72.0, 72.5, 72.5, 72.5, 73.5, 74.5, 77.5

The total size of the data = 54

The value 61.0 occurs in position ; 27th, 28th and 29th

Taking the position average :

(27+28+29)/3 = 84/3 = 28th position

This means the percentile score of 61 is :

(Position average / total size) * 100%

(28/54) * 100%

0.5185185 * 100%

= 51.85%

This means that 61 inch length falls in the 52nd percentile

Answer:

12. 10.5 cm

13. 16 m

14. 8 m

15. 50.24 m

16. 200.96 m2

17. (16+4 =20 ÷2 =10 ·10·π =314 ÷2 =157) + (16·4 =64) =221 in2

18. (1.1 · 1.2 =1.32) + (1.2 · 4 =4.8 ÷2 =2.4) =3.72 in2

19. 10·5=50

20. c.(1/2 d)^2·π

Answer: 138

Step-by-step explanation:

\(\angle KLJ \cong \angle MDF\) by the corresponding angles theorem.

Group C ran more miles than Group D

the central value of a set of data is expressed by the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.

Average = Total Values / Total Values

Group C = 27/4 = 6.75

Group D = 39 /6 = 6.5

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Answer:

t = 23

Step-by-step explanation:

line DG and FG are congruent

t - 1 = 4t -70

subtract t from both sides (-1 = 3t -70)

add 70 to both sides (69 = 3t)

divide each side by 3 (t = 23)

Answer:

t = 23

Step-by-step explanation:

Recall that the diagonals of a parallelogram intersect dividing each one in equal segments, therefore segment DG must equal the length of segment GF.

Then we can construct the following equation based on DG = GF

t - 1 = 4 t - 70  

then we can solve for t

subtract t from both sides

- 1 = 3 t - 70

add 70 to both sides

70 - 1 = 3 t

69 = 3 t

divide both sides by 3 to isolate t

69 / 3 = t

then

t = 23

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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The option C is correct.

In the given statement is:

Solve the inequality for x and identify the graph of its solution.

|x+2|<2

Here, The question is :

|x+2|<2

The modulus sign means that the absolute value of x + 2 is less than 2. This means that

-2 < x + 2 < 2

This is what is called double inequality. We must treat it as two separate inequalities.

From the left we get -2 < x + 2 and by subtract 2  to both sides we obtain

-4 < x.

On the right we have x + 2 < 2 , and by subtract 2 to both sides we get,

x < 0

We can write these solutions together as :

-4 < x < 0

and this range of values of x is illustrated on the number line see the image :

Hence, The option C is correct.

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Answer: -1

Step-by-step explanation:

    We will find the answer to this question by isolating the x variable.

    Given:

2(3x – 1) ≥ 4x – 6

    Distribute the 2 with multiplication:

6x – 2 ≥ 4x – 6

    Add 2 to both sides of the equation, and subtract 4x from both sides of the equation:

2x ≥ – 4

    Divide both sides of the equation by 2:

x ≥ -2

    The only value given that is greater than or equal to -2 is -1, leaving us with an answer of;

                 -1

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The solution set of the inequality  2(3x - 1) ≥ 4x - 6 is [-2, ∞). So, -1 belongs to the solution set, i.e., -1 ∈ [-2, ∞).

Mathematically, an inequality is a mathematical assertion that compares the comparative size or order of two quantities. It shows that one quantity is greater than, less than, or not equal to another. The symbols often used to show inequalities are (≥), (≤), or (≠).

The given inequality is

2(3x - 1) ≥ 4x - 6

6x - 2  ≥ 4x -6

6x - 4x ≥ -6 + 2

2x ≥ -4

\(x \geq -\frac{4}{2}\)

x ≥ -2

x ∈ (-2, ∞).

The correct answer is -1, as -1 belongs to the solution set of the given inequality.

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Answer: The vertex of the graph of \(y=x^2\) is shifted to the right 4 units and up 3 units.

If a company makes two models of television.

a The measurements of the larger screen are 55cm by 40cm.

b. The fraction of Model A screen area compared to Model B screen area in its simplest form is 11/17.

a) Model B has a screen that is 5:4 larger than Model A, so if the width of Model A is 44cm,

The width of Model B is:

44cm * 5/4 = 55cm

The height of Model B is:

32cm * 5/4 = 40cm.

So, the measurements of the larger screen are 55cm by 40cm.

b) The area of Model A is:

44cm * 32cm = 1408cm²

The area of Model B is:

55cm * 40cm = 2200cm²

So, the fraction of Model A screen area compared to Model B screen area is: 1408cm² / 2200cm².

To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor, which is 128:

(1408cm² / 128) / (2200cm² / 128) = 11 / 17

So, the fraction of Model A screen area compared to Model B screen area in its simplest form is 11/17.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

The angle is: \(\frac{4\pi}{3}\)

Step-by-step explanation:

Given

The attached plot

Required

The measure of the red arrow

Let the angle be \(\theta\)

So, we have:

\(\theta =180 +\)the green arrow

This gives:

\(\theta = 180 + \frac{\pi}{3}\)

180 degrees in radian is:

\(180 \to \pi\)

So, we have:

\(\theta = \pi + \frac{\pi}{3}\)

Take LCM

\(\theta = \frac{3\pi+\pi}{3}\)

\(\theta = \frac{4\pi}{3}\)

The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).

In the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.

To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).

If we subtract each value in column 1 from the corresponding value in column 2, we find that:

11 - 1 = 10

22 - 2 = 20

33 - 3 = 30

44 - 4 = 40

By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.

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Answer:

These equations cannot be simplified anymore than what they are. Unless there is a certain way the teacher want it.

Step-by-step explanation:

In this session we will focus on question a). Note that as the cake is made with a pan. the shape of the cake mostly the same as the one from the pan. So, we can assume that the cake has a diameter of 9 inches and a height of 1.5 inches too.

We want to calculate the surface area of a cylinder. Recall that we can think of a cylinder as the edge joined to two circles. So, the surface area of the cylinder is simply the sum of the area of both circles and the area of the edge

Recall that the area of a circle of radius r is given by the formula

Since we have two circles, then the area asociated to the circles would be

In our case, we have that r is one half of the diameter of the cake, which would be 4.5 inches. So the area of both circles would be

For the other part, note that it is a rectangle with the following dimensions

since the base is 2*pi* r and the height is h then the area of this portion would be

so, in our case we have r=4.5 inches and h=1.5 inches. So we have that

so the total surface area of the cake would be

so the total surface area of the cake is 169.646 squared inches

Answer:

u = 12

Step-by-step explanation:

formula : (base x height) / 2

60 x 2= 120

120 / 10 = 12

Answer:

100

Step-by-step explanation:

square root(L^2 + W^2)

Answer:

1. 135°

2. 62°

3. 148°

4. 180-x

Step-by-step explanation:

Supplementary angles are two angles that add to 180 degrees (a straight line).

Therefore, subtract the angle measure they give you from 180.

Hope this helps!

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

15/4

Step-by-step explanation:

Whenever you are working with a question of rate where two different quantities are being compared, the required units will indicate which quantity is to be divided by which.

3/4 divided by 1/5

3/4 times 5/1 (multiply reciprocal)

=15/4

I havent done this in a while so im not entirely sure.

Answer:

5 cups of flour.

Step-by-step explanation:

I know the wording of the problem may be confusing at first, but if you look at it a little bit, it's just multiplication and division.

To start,

12 biscuits require 2 cups of flour,

meaning that 6 biscuits (half of the original) only require 1 cup.

(12/2 = 6)

Next,

We need to find how much flour is in 30 biscuits.

We know that 1 cup is in 6 biscuits, and if you were to find how much was in 30 biscuits, you would just need to divide 30 by 6.

(30/6 = 5)

5 cups of flour would be your answer.

To put it mathematically,

(12/2 = 6), (30/6 = 5)

Answer:

Angle BPQ = 64°

Step-by-step explanation:

4x + 12 +2x = 90

6x + 12 = 90

     - 12    -12

6x = 78

x = 13°

BPQ = ((4(13) + 12)°

           (52 + 12)°

            64°