w(5)=w(-5) true or false

Answer: A. Mean = 9.56, Median = 11, Mode = 7

Step-by-step explanation:

The mean, median and the mode for the given data is 9.56, 9, and 7 respectively.

Given data below:

In order to find the mean, it can be calculated by dividing a sum of all the data points with the number of data points in the data set.

The formula is:

\(\bar{M}=\dfrac{\sum M}{N}\)

\(\bar{M}=\dfrac{4+6+7+7+9+11+13+14+15}{9}\)

\(\bar{M}=\dfrac{86}{9}\)

\(\bar{M}=9.56\)

Next, we will find the median.

In order to find the median, we got to place the numbers in value order and find the middle.

So,

\(\text{Median}=9\)

Lastly, we will find the mode.

To find the mode, order the numbers lowest to highest and see which number appears the most often.

So,

\(\text{Mode}=7\)

Thus, the mean, median and the mode for the given data is 9.56, 9, and 7 respectively.

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The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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The fitted model log( ) = 1.6 - 0.2c is equivalent to the models y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\)), y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\)), and y = 1.6 - 0.22.

The fitted model log( ) = 1.6 - 0.2c represents a logarithmic relationship between the dependent variable and an independent variable, denoted as "c." To identify equivalent models, we need to examine the given options.

Option 1: y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\))

This model is equivalent to the fitted model log( ) = 1.6 - 0.2c because the right side of the equation contains the term 1+\(e^(1.6-0.2c)\), which corresponds to the exponential function e^(1.6-0.2c). The coefficient -0.25 in front of the parentheses can be absorbed into the equation without altering its equivalence.

Option 2: y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\))

This model is also equivalent to the fitted model because it contains the term 1+e^(1.6+0.2) in the denominator. The coefficient -0.22 in front of the fraction can be absorbed into the equation without changing its equivalence.

Option 3: y = 1.6 - 0.22

This model is a simplified version of the fitted model. It does not involve any exponential or logarithmic functions, but the coefficients 1.6 and -0.22 remain the same as in the original equation.

Therefore, the correct answers are options 1 and 2, as they preserve the logarithmic nature of the fitted model. Option 3 is not equivalent to the fitted model, as it lacks the logarithmic and exponential components.

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Answer:

  C. 64 = 0.80 x n; 80

Step-by-step explanation:

In this context "of" means "times." The given relation can be translated to ...

  64 is 80% of what

  64 = 0.80 × what

If we let "n" represent the number that would answer "what", then this is ...

  64 = 0.80 × n

__

Dividing by the coefficient of n, we find the value of n to be ...

  64/0.80 = n = 80

The quantity of lemonade that Regan sold on saturday given the amount sold by Mark is 1 11/12 gallons.

Fractions are non-integers that consist of a numerator and a denominator. A proper fraction is a fraction in which the numerator is less than the denominator. e.g. 2/3. A mixed fraction is made up of a whole number and a proper fraction. An example is 2 7/8.

2 7/8 x 2/3

23/8 x 2/3 = 23/12 = 1 11/12 gallons

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Answer:

72

Step-by-step explanation:

80x.90= 72

Answer:

72 is your answer

Step-by-step explanation:

A simple random sample of 500 voters would be an appropriate method for a pollster to use in this situation.

In this method, each voter in the town is assigned a unique identifier and a list of all unique identifiers is created. Then, using a random number generator or a random number table, 500 unique identifiers are selected and those individuals are surveyed.

This method ensures that each voter in the town has an equal chance of being selected, so that the sample is representative of the population of voters. It also eliminates any potential biases that may be introduced if the pollster were to select individuals based on certain criteria (such as age, gender, or location).

By using a random sample, the pollster can have a good estimate of the true population parameter (voter preferences) with a high degree of confidence.

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91 percent of the 6th graders did not wear shorts to school on Friday.

To find out what percentage of 6th graders did not wear shorts on Friday, we first need to find out how many 6th graders did not wear shorts on that day.

If 27 students wore shorts, then the number of students who did not wear shorts is:

300 - 27 = 273

So, out of 300 6th graders, 273 did not wear shorts on Friday.

To find the percentage of 6th graders who did not wear shorts, we divide the number of students who did not wear shorts by the total number of 6th graders and multiply by 100.

273 / 300 = 0.91

0.91 x 100 = 91

Therefore, 91% of the 6th graders did not wear shorts to school on Friday.

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Answer:

1/3 + 2/4 + 1/2 = 4/

3

= 1 1/

3

≅ 1.3333333

Step-by-step explanation:

The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

x-int: (3,0)

y-int: (0,-10)

Step-by-step explanation:

The x-intercept is where the line intercepts the x-axis.

The y-intercept is where the line intercepts hte y-axis

Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.

Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.

A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.

The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.

32 = 4² × h/3

32 = 16 × h/3

Multiply both sides by 3

96 = 16 × h

Divide both sides by 16

H = 96/16

H = 6

Therefore, the height is 6 feet.

The complete question is:

Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.

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There are no values of c that satisfy the conclusion of Rolle's Theorem. Thus, the answer is N.

To apply Rolle's Theorem, we need to check if the function satisfies the following conditions:

f(x) is continuous on the closed interval [a, b].

f(x) is differentiable on the open interval (a, b).

f(a) = f(b).

The function f(x) = x² - 9x + 2 is a polynomial, so it is continuous and differentiable everywhere. We need to check the third condition.

f(0) = (0)² - 9(0) + 2 = 2

f(9) = (9)² - 9(9) + 2 = -61

Since f(0) is not equal to f(9), we can't apply Rolle's Theorem to this function on the interval [0, 9].

Therefore, there are no values of c that satisfy the conclusion of Rolle's Theorem. Thus, the answer is N.

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The constant term (36) represents the initial height of the ball, in feet, when it was thrown into the air.

In mathematics, a coefficient is a constant factor that appears in front of a variable or a term in an algebraic expression.

For example, in the expression 5x²  + 3x - 2, the coefficients are 5, 3, and -2. The coefficient 5 is in front of the variable x² , the coefficient 3 is in front of x, and the coefficient -2 is a constant term.

The function h(t) = −16t² + 48t + 36 models the height of a ball, in feet, at t seconds after being thrown into the air.

The coefficient of the t²  term (-16) represents the acceleration due to gravity, which is constant at approximately 32 feet per second squared. The negative sign indicates that the acceleration is directed downwards, opposing the motion of the ball.

The coefficient of the t term (48) represents the initial velocity of the ball, in feet per second, when it was thrown into the air. Since the coefficient is positive, the ball was thrown upwards.

The constant term (36) represents the initial height of the ball, in feet, when it was thrown into the air.

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Kamlu will have two chances to catch the apple.

Kamlu's friend is standing directly below her on the ground and tossing her an apple from five feet above the ground.

The apple is released with an initial velocity of 28 feet per second.

Since Kamlu's hands are 14 feet above the ground, the apple will have two chances to reach her. The first chance will be when the apple reaches her hands at 14 feet above the ground, and the second chance will be when the apple reaches the ground after falling from the initial velocity of 28 feet per second.

The time it takes for the apple to reach her hands and the ground will depend on the acceleration due to gravity.

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Answer:

x=12

Step-by-step explanation:

You have to do 60/5 which is 12
so x=12

Answer:

x=12

Step-by-step explanation:

5x=60

divide both sides by 5

x=12

answer: x=12

The center of a circle that circumscribes a triangle is known as the circumcenter of the triangle.

The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle. This point is equidistant from the three vertices of the triangle, which means that it lies on the perpendicular bisector of each side.

The circumcenter plays an important role in the geometry of triangles. One of its properties is that it is also the center of the circle that passes through the three vertices of the triangle, which is why it is called the circumcenter. This circle is known as the circumcircle of the triangle.

The circumcircle is a unique circle that can be drawn around any triangle, and its center is always the circumcenter. This circle has several important properties, such as:

The circumcircle passes through the three vertices of the triangle.

The circumcircle is centered at the circumcenter of the triangle.

The circumcircle has a radius that is equal to the distance from the circumcenter to any vertex of the triangle.

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer: x=-6

Step-by-step explanation:

Let's solve your equation step-by-step.

2(9−x)=3(x+16)

Step 1: Simplify both sides of the equation by distribution

\(2(9-x)=3(x+16)\\(2)(9)+(2)(-x)=(3)(x)+(3)(16)\\18+-2x=3x+48\\-2x+18=3x+48\\\)

Step 2: Subtract 3x from both sides.

\(-2x+18-3x=3x+48-3x\\-5x+18=48\)

Step 3: Subtract 18 from both sides.

\(-5x+18-18=48-18\\-5x=30\)

Step 4: Divide both sides by -5.

\(\frac{-5x}{-5} =\frac{30}{-5} \\x=-6\)

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

To determine the number of calories in a food, you would need to know the caloric content per gram for each macronutrient (carbohydrates, protein, and fat).

On average, carbohydrates contain about 4 calories per gram, protein also contains about 4 calories per gram, and fat contains about 9 calories per gram.

Using these values, we can calculate the calorie content of the food:

Calories from carbohydrates: 16 grams * 4 calories/gram = 64 calories

Calories from protein: 2 grams * 4 calories/gram = 8 calories

Calories from fat: 10 grams * 9 calories/gram = 90 calories

Total calorie content: 64 calories + 8 calories + 90 calories = 162 calories

Therefore, the food contains approximately 162 calories.

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Lets Solve

\( \\ \rm \longmapsto \: {x}^{2} - 8x - 7 = 0 \\ \\ \rm \longmapsto \: {x}^{2} - 8 {}^{}x = 7 \\ \\ \rm \longmapsto \: 4( {x}^{2} - 8x) = 4 \times 7 \\ \\ \rm \longmapsto \: {4x}^{2} - 32x = 28 \\ \\ \rm \longmapsto \: {(2x)}^{2} - 2 \times 2x \times 8 = 28 \\ \\ \rm \longmapsto \: (2x) {}^{2} - 2 \times 2x \times 8 + {8}^{2} = 28 + {8}^{2} \\ \\ \rm \longmapsto \: {(2x - 8)}^{2} = 64 + 28 \\ \\ \rm \longmapsto \: {(2x - 8)}^{2} = 92 \\ \\ \rm \longmapsto \: 2x - 8 = \underline{ + }9.3 \\ \\ \rm \longmapsto \:2x = 8 + 9.3 \: or \: 8 - 9.3 \\ \\ \rm \longmapsto \:2x = 17.3 \:or \: - 1.3 \\ \\ \rm \longmapsto \:2x = 17.3 \\ \\ \rm \longmapsto \:x = \frac{17.3}{2} \\ \\ \rm \longmapsto x = \:8.6\)

The intersection of sets A and B, denoted as A∩B, is the set of elements that are common to both sets. In this case, the intersection of sets A and B is {2, 9, 10}, as these elements appear in both sets.

The elements are listed in increasing order and enclosed in curly braces.The union of sets A and B, denoted as A∪B, is the set of all elements that belong to either set A or set B or both. In this case, the union of sets A and B is {1, 2, 4, 5, 6, 7, 8, 9, 10, 13, 15}, as these elements appear in either set A or set B or both. The elements are listed in increasing order and enclosed in curly braces.

To find the intersection, we compare the elements of set A with the elements of set B and select the common elements. In this case, the common elements are 2, 9, and 10.

To find the union, we combine all the elements from both sets, ensuring that each element is included only once. The resulting set includes all the elements from set A and set B without any repetition.

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We want to solve the following equation for x:

First, let's expand the parenthesis on the right side of the equation using the distributive property

To add the terms with x, we just need to add their coefficients.

Subtracting 5x from both sides of the equation:

Now, if we subtract 7 from both sides, we have

Since this is a first degree polynomial, it has only one solution and this solution is x = - 13.

To find the optimal solution for maximizing the overall profitability of sensor production for Sherpa Sensors Pty Ltd, Microsoft Excel's Solver tool can be used.

The goal is to determine the allocation of units, advertising budget, and salesforce effort among the four distribution methods. The decision variables include the number of units allocated to each method, the advertising budget allocated to each method, and the salesforce effort allocated to each method.

Constraints include the total number of units produced, the advertising budget, and the salesforce effort limit. By setting up the objective function to maximize the overall profitability, Solver can be used to find the optimal solution. The answer report generated by Solver will provide insights into the optimal allocation strategy.

To solve this problem using Microsoft Excel's Solver, you need to set up the spreadsheet with the relevant data and define the decision variables, objective function, and constraints. The decision variables are the allocation quantities and budgets for each distribution method. The objective function is the overall profitability, which needs to be maximized. The constraints include the total number of units produced, the advertising budget, and the salesforce effort limit. By specifying these parameters and running Solver, it will find the optimal solution that maximizes the overall profitability while satisfying the constraints.

The answer report generated by Solver will provide detailed information about the optimal solution, including the allocation quantities, budget allocations, salesforce effort allocations, and the resulting overall profitability. It will help guide Sherpa Sensors Pty Ltd in making decisions on the distribution strategy to maximize profitability for their temperature sensors.

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