Find the average rate of change of the function on the interval specified for real number b.
f(x) = 4x2 − 7 on [1, b]

Vector of the average velocity = 3.33 km\hr towards the south.

Distance covered by the student=7miles 7*6 = 42km

Total displacement =  10km in the south.

Total time is taken =  20mins 20/60=0.33hr

Note:

Odometer reading is the distance covered while straight-line distance is the displacement which is the shortest route

Distance is a scaler where as displacement is a vector quantity.

Scaler has only magnitude while vector has magnitude and direction.

We have to find the average velocity.

Average velocity = Ratio of total displacement and total time.

⇒ Average velocity (v) = displacement/time.

⇒ Plugging the values.

⇒ (v) = 10/0.33

⇒ (v) =3.33 km\hr

So the vector of the average velocity = 3.33 km\hr towards the south.

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Answer:

x on the horizontal axis and y on the vertical axis.

The type of statistical methods used to draw conclusions about the population based on a sample is called inferential statistic.

Statistical inference refers to the process of generating inferences about a population from a sample or subset of the data. The goal of inferential statistics is to extrapolate from sample data to the population as a whole by comparing the parameters of multiple samples. Two major categories of inferential statistics use distinct strategies to extrapolate information from samples of the population. These are regression analysis and hypothesis testing. Inferential statistics, including hypothesis testing, examines sample data to draw conclusions about the whole population. It entails establishing a null hypothesis and an alternative hypothesis, then doing a statistical test of significance to determine which one is more likely to be correct. The impact of one variable on another can be measured with the use of regression analysis.

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The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.

(a) R(n) = r(n) * n = (8 − 0.05(n − 80)) * n

(b)

n r (dollars per person) R (dollars)

80 8 640

90 7.5 675

100 7 700

(c) This formula for the rate is not ideal, as it does not take into account factors like the distance traveled or any additional services that the bus company may offer. It also does not account for any additional fees or taxes. I would not use this formula, as it does not provide an accurate representation of the price the bus company should charge for its services.

The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.

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Answer:

9 x - 5

Step-by-step explanation:

Simplify the following:

6 x - 3 - (-3 x + 2)

-(-3 x + 2) = 3 x - 2:

6 x - 3 + (-2 + 3 x)

Grouping like terms, 6 x - 3 - 2 + 3 x = (6 x + 3 x) + (-3 - 2):

(6 x + 3 x) + (-3 - 2)

6 x + 3 x = 9 x:

9 x + (-3 - 2)

-3 - 2 = -(3 + 2):

9 x + (-(3 + 2))

3 + 2 = 5:

Answer: 9 x - 5

By solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.

What is Elimination Method?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Now solving the both equation by using elimination method;

5x +4y = 12                                                     ----------------------------eq(1)

3x - 3y = 18                                                     ----------------------------eq(2)

Multiply equation (1) by 3 and equation (2) by 4,  we get;

15x + 12y = 36

12x - 12y = 72

Now, same equation will beb together;

15x + 12y + 12x - 12y = 36 + 72

15x + 12x = 36 + 72

27x = 108

x = 108/27

x = 4

Now, we calculate for the y ;

3x - 3y = 18

3 * 4 - 3y = 18

12 - 3y = 18

12 - 18 = 3y

3y = -6

y = -6/3

y = -2

(x, y) = (4, -2)

So, by solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.

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The distance 4450× 10⁶ km between the Neptune and the sun in AU is 29.75 AU

The astronomical unit is a unit of length, roughly the distance from Earth to the Sun and approximately equal to 150 million kilometres or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.

An astronomical unit is the average distance between the Earth and the Sun. Estimates of this distance have varied over time. It is now defined as exactly 149,597,870.7 kilometers.

if 149,597,870.7 kilometers = 1 AU

then 4450× 10⁶ km = 4450× 10⁶ ÷149,597,870.7

= 29.75 AU

Thefore the distance between the sun and neptune is 29.75 AU

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The size of each group will be half as big.

There will be twice as many groups.

We want to find out what is going to happen if we divide by 8/4 instead of 4/5.

The total of the tape diagram is 3¹/₅ = 16/5 and as such if we are going to divide by 4/5 we will have;

16/5 ÷ 4/5 = 4

However if we are dividing by 8/5, it means that the solution is;

16/5 ÷ 8/5 = 2

Thus, the solution will be half as big.

There will be twice as many groups.

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Answer:

here are the answers to the questions in order

Step-by-step explanation:

7. -7

8. 73

9. -8

10. 1

The given sample of the randomly selected players from the teams as described is a stratified sample. Hence, the right answer is option A.

In a stratified sample, the population is divided into groups (or strata) based on some characteristic, and a random sample is selected from each group. In this case, the population is the football players, and the groups are the varsity and junior varsity teams. The coach randomly selects one of these teams and then asks all players from that team their opinion on a new logo.

This type of sampling is used when the population is divided into subgroups that are different in some way, and the researcher wants to ensure that these subgroups are represented in the sample. In this case, the coach wants to ensure that both varsity and junior varsity players are represented in the sample, as they may have different opinions on the new logo.

It's not a simple random sample because he selected the team first and then the players. Also, it's not a voluntary response sample because the coach is selecting the players.

It's not a cluster sample because the coach is not selecting the players based on location or geographic proximity, and it's not a systematic sample because he is not selecting the players based on the order in which they appear in a list or a database.

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The value of x in the figure is calculated using the linear pair theorem to be 6 degrees

The linear pair postulate or linear pair theorem in mathematics states that the sum of the measurements of two angles that make up a linear pair is 180°.

Because o the linear pair postulate we have that

150 + 5x = 180

collecting like terms

5x = 180 - 150

5x = 30

Isolating x

5x / 5 = 30 / 5

x = 6

hence x is solved to be 6

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Answer:

3/10

Step-by-step explanation:

2 cans of tomato soup, 3 cans of chicken noodle soup, 2 cans of Italian wedding soup, 2 cans of potato soup, & 1 can of split pea soup = 10 cans of soup

P( chicken noodle soup) = cans of chicken noodle soup / total cans

                                         = 3/10

The true statements regarding the construction are statement 2) and statement 5)

"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.

Given that, A design began from the construction of a regular hexagon.

The true statements made on the construction is;

2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.

5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.

Hence, The true statements regarding the construction are statement 2) and statement 5)

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The equation for the line is y=x+7.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation.

In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given, the line's points are (2,9), (3,10), (4,11), and (5,12). (6,13)

Assuming that the line's equation is y=x+7, adding the points to the equation results in

(2,9) 9=2+7

(3,10) 10=3+7

The equation is also valid for every point on the graph.

Hence, The line's equation is y=x+7.

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Complete Question -

The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units

To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:

= Amount won x ( 1 + periodic  rate ) ^ number of periods

Periodic rate :

= 6 % / 4 quarters per year

= 1. 5 %

The number of periods is:

= 3 years x 4 quarters per year

= 12 quarters

The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²

= 1, 195, 618. 17 currency units

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The length of each bar is given as follows:

3.5 inches.

As a mixed number, the length of each bar is given as follows:

3 and 1/2 inches.

The length of each bar is obtained applying the proportions in the context of this problem.

The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:

7/2 = 3.5 inches.

The fraction equivalent to a decimal of 0.5 is given as follows:

1/2.

(which is used to construct the mixed number).

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Answer:

h minus three

Step-by-step explanation:

The proportional relationship is given by the equations -

y = mx     or     y = kx     or     y = mx + b     or    y = kx + b.

Given are the statements describing proportional relationship.

        {K} = y/x = constant.

        y = mx     or     y = kx     or     y = mx + b     or    y = kx + b

Therefore, the proportional relationship is given by the equations -

y = mx     or     y = kx     or     y = mx + b     or    y = kx + b.

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The impulse equation is given by pf = p0 + ∫tL₀F(t)dt. With the given information, the integral is ∫tL₀(-28t² + 7.0)dt.

This integral can be solved using the power rule for integration, which states that the integral of xⁿ is xⁿ⁺¹/(n+1). Thus, the integral of -28t² + 7.0 is -28/3t³ + 7t. This can be evaluated from t=0 to t=0.5 to get the change in momentum due to the applied impulse. Substituting the values into the impulse equation, pf = 0 + (-28/3(0.5)³ + 7(0.5)) = -2.167. Thus, the correct expression for pf is pf = -2.167.

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a) Using the summation notation to write the sum is 3∑n=1 3n.

b) The total amount that Jummy will save during the first 3 weeks of his new job is $18.

The summation notation is the representation of a series in a compact form, using the capital sigma symbol (Σ) to indicate the sum of a number of similar terms.

Using the summation notation, one can write a long sum in a single expression.

In this situation, the expression can be read as the sum of 3n as n goes from week 1 to week 3, representing the first three weeks Jimmy will spend on the job.

3∑n=1 3n

= 3 x 1 + 3 x 2 + 3 x 3

= 3 + 6 + 9

= 18

Thus, we have used the summation notation to find that Jimmy will save $18 during the first three weeks at his new job.

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Answer:

Step-by-step explanation:

the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.

1. This is an example of stratified sampling, since the students are divided into three groups (Sophomores, Juniors, and Seniors) and a sample is taken from each group. This allows for a more representative sample of the overall population.

2. This is an example of random sampling, since each name has an equal chance of being selected from the bag. This ensures that the sample is unbiased and allows for a fair representation of the population.

3. This sampling plan results in a random sample, since the schools were randomly selected from the district. A random sample ensures that every member of the population has an equal chance of being selected.

4. This sampling plan results in a systematic sample, since the polling company selected every 20th person from the list. Systematic sampling allows for a more representative sample of the population, since it ensures that each person in the population is equally likely to be selected.

5. This sampling plan does not result in a random sample, since only the female employees who attended the meeting were selected. This means that those who did not attend the meeting had no chance of being selected in the sample, thus biasing the results.

This answer demonstrates the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.

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The fraction of a pound of granola Marty buys is 3/4.

A fraction is a part of a whole number, value, and variable.

There are proper and improper fractions, including complex fractions.

Proper fractions are those with the numerator less than the denominator. An improper fraction produces a whole number with a remainder when the denominator divides the numerator.

On the other hand, complex fractions are rational expressions that have some fractions in their numerators, denominators, or both.

1 pound = 16 ounces

The quantity of granola Marty buys = 12 ounces

The fraction of a pound of granola Marty buys = 3/4 (12/16)

Thus, we can conclude that Marty buys 3/4 or 75% of a pound of granola.

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The number of members for counseling groups of children should generally be smaller as compared to counseling groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. Smaller groups also allow for more individualized attention and support.

The recommended number of members for counseling groups of children should generally be smaller than that of groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. This can lead to a lack of engagement and little benefit from the group counseling sessions. Smaller groups also allow for more individualized attention and support, which is important for young people to feel comfortable expressing their thoughts and feelings. Additionally, smaller groups can help create a more intimate environment for participants to safely share their experiences and feelings with one another. As such, reducing the size of the group for counseling sessions with children can help ensure a more successful therapeutic experience.

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Answer:

the 4 represents how many times 5 can go into 20

A call center required the number of agents is equal to 18.

One of the most frequent themes in quantitative aptitude that is tested in government exams is time and work. One of the subjects that candidates are knowledgeable about even before they begin preparing for competitive exams.

The idea of time and effort is still the same, but there may be some variation in the questions that are posed. The majority of the questions on this topic are 1-2 word problems, but candidates should also be ready for questions about data sufficiency and data interpretation that may come up over the course of their work.

A 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works Tuesday Saturday and rests on Sunday and Monday.

total working day of call center = 7

agent's working day =5

so, required the minimal number of agents-

[tex]=\frac{7!}{2!.5!}\\\\=\frac{35}{2}\\\\= 17.5 = 18[/tex]

So, at least required number of agents = 18.

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Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.

How to find vertex of a parallelogram?

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Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.

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Answer:

dividir

Step-by-step explanation:

PEMDAS

you must Divide first, since its's left most

The infinite product measure [tex]$\mu$\\[/tex] is uniquely defined on the product measure space[tex]$(\Omega, \mathcal{A}, \mu)$[/tex] by Dynkin's theorem, since [tex]$\mu$\\[/tex] is finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite.

Let [tex]$\mathcal{A}_1, \mathcal{A}_2, \ldots$[/tex] be a sequence of sigma algebras defined on [tex]$\Omega_1, \Omega_2, \ldots$[/tex] respectively. Let [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] be the product measure space, where [tex]\Omega = \prod_{i=1}^{\infty} \Omega_i$ and $\mathcal{A} = \bigotimes_{i=1}^{\infty} \mathcal{A}_i$[/tex].

We want to prove that the infinite product measure [tex]$\mu$[/tex] is uniquely defined. To do this, we will use Dynkin's theorem.

According to Dynkin's theorem, a measure [tex]$\mu$[/tex] is uniquely determined on a product measure space [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] if the following conditions are satisfied:

1. [tex]$\mu$[/tex] is finitely additive on [tex]$\mathcal{A}$[/tex]

2. [tex]$\mu$[/tex] is countably subadditive on [tex]$\mathcal{A}$[/tex]

3. [tex]$\mu$[/tex] is [tex]$\sigma$[/tex]-finite on [tex]$\mathcal{A}$[/tex]

It is easy to see that the infinite product measure [tex]$\mu$[/tex]satisfies these conditions, since it is defined as a product of finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite measures. Thus, by Dynkin's theorem,[tex]$\mu$[/tex] is uniquely determined on the product measure space [tex](\Omega, \mathcal{A}, \mu)$.[/tex]

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The population of the given study in the polling organization contacts is given by :

Option B. Teenagers who are 13 to 17 years of age and live in the United States.

Total number of people attended by the polling organization = 1398

Population is represented by all teenagers of United States in the age group of 13 to 17 years of age.

Those who attended the concert represents the sample of particular category.

Therefore, the population of the required study is given by :

Option B. Teenagers belongs to 13 to 17 years of age and live in the United States .

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