7) when constructing a confidence interval for the population mean when the standard deviation is unknown, what is the formula for standard error?

The probability that a family with 4 children has no more than 3 boys is 15/16.

To find the probability that a family with 4 children has no more than 3 boys, we can use the binomial distribution.

The binomial distribution is used to calculate the probability of obtaining a certain number of successes (boys in this case) in a fixed number of trials (children in this case), where each trial has only two possible outcomes (boy or girl) and the trials are independent.

Let X be the number of boys in the family. We want to find P(X ≤ 3), which is the probability of having no more than 3 boys. Since the probability of having a boy is 1/2 and the trials are independent, we can use the binomial distribution formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (1/2)⁴ + 4(1/2)⁴ + 6(1/2)⁴ + 4(1/2)⁴

= 15/16

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer: A =350 (1.05)^t

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form; 5/100=0.05)

t= years

A = population after t years

Replacing with the values given:

A = 350 (1+0.05)^t

A =350 (1.05)^t

Feel free to ask for more if needed or if you did not understand something.

Answer:

m a th wa y

Step-by-step explanation:

Answer:

  B. 1/4(x-5) = 13

Step-by-step explanation:

You want to know which number sentence has one solution.

Typically, an inequality has an infinite set of solutions. The inequalities here are linear inequalities in one variable, so will have an infinite solution set consisting of numbers greater than, or less than, some boundary value.

If the equation can be arranged to be in general form, ax +b = 0, where a ≠ 0, then it will have exactly one solution: x = -b/a.

The set of number sentences contains exactly one equation. That is the number sentence that has exactly one solution:

  B. 1/4(x-5) = 13

Answer: 1,073,741,824,000 amebas

Step-by-step explanation:

Bipartición significa que la población de amebas se duplica cada día.

Entonces si inicialmente hay 1000, después de un día van a haber:

2*1000.

Después del segundo día se vuelven a duplicar, entonces van a haber:

2*(2*1000) = (2^2)*1000

Después del tercer día, lo mismo:

2*(2^2)*1000 = (2^3)*1000.

A esta altura ya se puede ver el patrón, podemos concluir que después de N días, la población de amebas va a ser:

P(N) = (2^N)*1000.

Entonces respondiendo a la pregunta:

¿Cuántas amebas habrá al cabo de 30 días después que se inició el cultivo?

Tenemos que tomar N = 30

P(30) = (2^30)*1000 = 1,073,741,824,000 amebas

Los miembros de la sororidad tiene un porcentaje de 14 % de estudiantes procedentes de la especialización de ingeniería.

El enunciado describe las características de un diagrama circula, en donde el 100 % de los miembros de la sororidad representan a los 360° del ángulo central del círculo, esto es, una revolución completa del círculo.

El porcentaje de los miembros que se especializan en ingeniería mediante la siguiente fórmula:

e = (E / 360°) × 100 %

Donde E es el ángulo asociado a la cantidad de estudiantes de la especialización de ingeniería, en grados sexagesimales.

e = (50.4° / 360°) × 100 %

e = 14 %

Los estudiantes que especializan en ingeniería corresponden a un porcentaje de 14 % de los miembros de la sororidad.

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If the population grew to 35203 by the year 2019 , then the equation to model this situation is y = 1174x + 29333 .

We use the given data points to create a linear equation to model the population growth over the years.

Let , x₁ = 0 represents the year 2014

⇒ y₁ = 29333 represents the population in the year 2014

⇒ x₂ = 5 represents the year 2019

⇒ y₂ = 35203 represents the population in the year 2019

Using these variables, we can find the slope of the line that represents the population growth:

So , slope = (y₂ - y₁)/(x₂ - x₁)

⇒ slope = (35203 - 29333)/(5 - 0)   ;

⇒ slope = 5870/5 = 1174  ;

Now , by using the point-slope form of a linear equation

we get ;

⇒ y - y₁ = m(x - x₁)  ;

⇒ y - 29333 = 1174(x - 0)  ;

Simplifying this equation ;

we get ;

⇒ y = 1174x + 29333 ;

Therefore, the equation for the model is y = 1174x + 29333, where y represents the population and x represents the number of years since 2014.

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The given question is incomplete , the complete question is

The population in a small us city has been increasing linearly. in 2014, the population of this town was 29333. and by the year 2019, it grew to 35,203. Find the equation for this model ?

To find the position of the particle, we need to integrate the acceleration function twice with respect to time, starting from the initial conditions of position and velocity.

Given:

a(t) = 2t + 9 (acceleration function)

s(0) = 8 (initial position)

v(0) = -4 (initial velocity)

First, let's integrate the acceleration function to find the velocity function:

v(t) = ∫(2t + 9) dt

    = t^2 + 9t + C1

Using the initial velocity condition, we can solve for the constant C1:

v(0) = 0^2 + 9(0) + C1 = -4

C1 = -4

Therefore, the velocity function becomes:

v(t) = t^2 + 9t - 4

Next, we integrate the velocity function to find the position function:

s(t) = ∫(t^2 + 9t - 4) dt

    = (1/3)t^3 + (9/2)t^2 - 4t + C2

Using the initial position condition, we can solve for the constant C2:

s(0) = (1/3)(0^3) + (9/2)(0^2) - 4(0) + C2 = 8

C2 = 8

Therefore, the position function becomes:

s(t) = (1/3)t^3 + (9/2)t^2 - 4t + 8

Thus, the position of the particle is given by the function s(t) = (1/3)t^3 + (9/2)t^2 - 4t + 8.

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The percentage of people in each of the age groups that die in a given year is creasing The formula implies that even one will be dead by age 112.

What is the exponential function?

Although the exponential function was derived from the concept of exponentiation (repeated multiplication), contemporary formulations (there are numerous comparable characterizations) allow it to be rigorously extended to all real arguments, including irrational values.

Here, we have

Given: The percentage of people of any particular age group that will die in a given year may be approximated by the formula

P(t) =  0.00236 \(e^{0.0953t}\)....(1)

(a) We have to find the value of P(25).

When t = 25

Now we put the value of t in equation (1) and we get

P(25) =  0.00236 \(e^{0.0953(25)}\)

= 0.02556

P(25) = 0.026

We have to find the value of P(50).

When t = 50

Now we put the value of t in equation (1) and we get

P(50) =  0.00236 \(e^{0.0953(50)}\)

P(50) = 0.277

We have to find the value of P(75).

When t = 75

Now we put the value of t in equation (1) and we get

P(75) =  0.00236 \(e^{0.0953(75)}\)

P(75) =  2.999

(b) We have to find the value of P'(25)

When we differentiate equation (1) and we get

P'(t) = 0.00236×0.0953\(e^{0.0953t}\)....(2)

When t = 25

Now we put the value of t in equation (2) and we get

P'(25) = 0.00236×0.0953\(e^{0.0953(25)}\)

P'(25) = 0.0024

We have to find the value of P'(50)

When t = 50

Now we put the value of t in equation (2) and we get

P'(50) = 0.00236×0.0953\(e^{0.095350)}\)

P'(50) = 0.026

We have to find the value of P'(75)

When t = 75

Now we put the value of t in equation (2) and we get

P'(75) = 0.00236×0.0953\(e^{0.0953(75)}\)

P'(75) = 0.286

(c) Let P(t) = 100

100 = 0.00236 \(e^{0.0953t}\)

t = 112

Hence, The percentage of people in each of the age groups that die in a given year is creasing The formula implies that even one will be dead by age 112.

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The formula suggests that even at age 112, there will be some mortality rate within the population.

The given formula, P(t) = 0.00236, represents the percentage of people in any particular age group who will die in a given year.

(a) To find the value of P(25), we substitute t = 25 into the equation:

P(25) = 0.00236

Therefore, P(25) = 0.00236 or approximately 0.026.

Similarly, for P(50):

P(50) = 0.00236 or approximately 0.277.

And for P(75):

P(75) = 0.00236 or approximately 2.999.

(b) To find the value of P'(25), we differentiate the equation P(t) = 0.00236:

P'(t) = 0.00236 × 0.0953

Substituting t = 25:

P'(25) = 0.00236 × 0.0953

Therefore, P'(25) = 0.0024.

Similarly, for P'(50):

P'(50) = 0.00236 × 0.0953 or approximately 0.026.

And for P'(75):

P'(75) = 0.00236 × 0.0953 or approximately 0.286.

(c) If we set P(t) = 100, we can solve for t:

100 = 0.00236

Solving for t, we find:

t = 112

This implies that according to the given formula, the percentage of people in each age group dying in a given year, even one person will be dead by the age of 112.

Therefore, the formula suggests that even at age 112, there will be some mortality rate within the population.

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500 J, is the required work to pull the bucket of water to the top of the well.

From the given question we have the following information

the weight of the bucket is 3kg.

length of rope (h) = 5m

Weight of rope: 7kg

Total weight (rope + bucket) = 10kg

Required Work Done = force × distance travelled (length of rope ) = mgh, where

M = total weight in kg

g--> acceleration due to gravity

h--> length of rope ( height )

g = 10 m/sec² ( default value )

Put all the values in the above formula.

Required work done = 100× 5 = 500 Joules .

So, the bucket of water will require 500J work done for pulling.

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Answer:

When we have a function f(x), the domain of the function is the set of all the inputs that "work" (Not only in a mathematical way, the context is also important) with the function f(x)

In this case, we have a function M(p) = $2*p

This function represents the amount of money collected depending on the number of people who ride on the ferris whell.

Then p can be only a whole number (we can not have 1.5 people, only whole numbers of people).

And we also know that the maximum capacity of the ferris is 64 people.

Then:

p ≤ 64

And we also should add the restriction:

0 ≤ p ≤ 64

(Because p can't be smaller than zero)

Such that p should also be an integer, then, the domain is:

D: p ∈ Z, p ∈ {0, 1, 2, ..., 64}

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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There are 30 cubic feet of water in the pipe at time t = 0. 76.570 cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 ≤ t ≤ 8.

\(\int\limits^8_0\)   [R(t) dt = \(\int\limits^8_0\) 20 sin \(\frac{t^2}{35}\) dt = 76.570

What Is Time Interval?

The amount of time between two given times is known as time interval. In other words, it is the amount of time that has passed between the beginning and end of the event. It is also known as elapsed time.

INTERVAL types are divided into two classes: year-month intervals and day-time intervals. A year-month interval can represent a span of years and months, and a day-time interval can represent a span of days, hours, minutes, seconds, and fractions of a second.

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Main Answer:The circumstances under which the shape of the sampling distribution of pn is approximately normal.

Supporting Question and Answer:

What is the Central Limit Theorem and how does it relate to the shape of the sampling distribution of pn?

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean (or sum) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This theorem is applicable to the sampling distribution of pn (proportion) because the proportion can be considered as the sample mean of a binary variable (success or failure). As the sample size increases, the Central Limit Theorem ensures that the sampling distribution of pn becomes more approximately normal, making it a useful approximation for making inferences about the population proportion.

Body of the Solution:The shape of the sampling distribution of pn (proportion) is approximately normal under certain circumstances. These circumstances are related to the properties of the population being sampled and the sample size. Here are the key factors:

1.Large sample size: The sampling distribution of pn tends to become more approximately normal as the sample size increases. This is known as the Central Limit Theorem. As the sample size grows larger, the distribution of sample proportions approaches a normal distribution regardless of the shape of the population distribution.

2.Random sampling: The sample should be selected randomly from the population to ensure that each member of the population has an equal chance of being included in the sample. Random sampling helps to ensure that the sample is representative of the population.

3.Independence assumption: The sampled observations should be independent of each other. This means that the selection of one observation should not influence the selection or behavior of other observations. Independence is crucial to ensure that the sampling distribution accurately reflects the population distribution.

4.Adequate population size: If the population size is sufficiently large,

relative to the sample size, the shape of the sampling distribution of pn is approximately normal. In practice, if the population is at least 10 times larger than the sample size, this condition is considered to be met.

5.Binomial distribution approximation: The shape of the sampling distribution of pn is also approximately normal when the underlying population distribution follows a binomial distribution. The binomial distribution is characterized by a fixed number of trials and two possible outcomes (success or failure) for each trial.

Final Answer: These circumstances increase the likelihood of the sampling distribution of pn being approximately normal, it does not guarantee it in all cases. In practice, checking the normality of the sampling distribution can be done using statistical tests or graphical methods, such as a histogram or a normal probability plot.  

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The circumstances under which the shape of the sampling distribution of pn is approximately normal.

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean (or sum) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This theorem is applicable to the sampling distribution of pn (proportion) because the proportion can be considered as the sample mean of a binary variable (success or failure). As the sample size increases, the Central Limit Theorem ensures that the sampling distribution of pn becomes more approximately normal, making it a useful approximation for making inferences about the population proportion.

The shape of the sampling distribution of pn (proportion) is approximately normal under certain circumstances. These circumstances are related to the properties of the population being sampled and the sample size. Here are the key factors:

1.Large sample size: The sampling distribution of pn tends to become more approximately normal as the sample size increases. This is known as the Central Limit Theorem. As the sample size grows larger, the distribution of sample proportions approaches a normal distribution regardless of the shape of the population distribution.

2.Random sampling: The sample should be selected randomly from the population to ensure that each member of the population has an equal chance of being included in the sample. Random sampling helps to ensure that the sample is representative of the population.

3.Independence assumption: The sampled observations should be independent of each other. This means that the selection of one observation should not influence the selection or behavior of other observations. Independence is crucial to ensure that the sampling distribution accurately reflects the population distribution.

4.Adequate population size: If the population size is sufficiently large,

relative to the sample size, the shape of the sampling distribution of pn is approximately normal. In practice, if the population is at least 10 times larger than the sample size, this condition is considered to be met.

5.Binomial distribution approximation: The shape of the sampling distribution of pn is also approximately normal when the underlying population distribution follows a binomial distribution. The binomial distribution is characterized by a fixed number of trials and two possible outcomes (success or failure) for each trial.

These circumstances increase the likelihood of the sampling distribution of pn being approximately normal, it does not guarantee it in all cases. In practice, checking the normality of the sampling distribution can be done using statistical tests or graphical methods, such as a histogram or a normal probability plot.  

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Answer:

NO

Step-by-step explanation:

We can know the answer by using the Pythagorean Theorem.

In a triangle with uneven sides, the longest side is called the hypotenuse. In this case, it is 50.

   Using the theorem: a² + b² = c²  

(Let's say c is the hypotenuse and a and b are the other sides)

    10² + 35² = 50²

    100 + 1225 = 2500

    1325 ≠ 2500

So the answer is NO

Answer:

False

Step-by-step explanation:

Answer:

C. the average total cost for the first month of a gym membership

Step-by-step explanation:

x=1 is for month 1,

the value of y includes 1-month fee and one off payment, so this is the average total for the first month of membership

Answer:

It is the average total cost for the first month of a gym membership

Step-by-step explanation:

y = 34.99x+49

The 49 is the cost to join the gym and the 34.99 is the monthly cost

Let x =1 which is the cost after one month

It includes the cost to join and the 1st month membership

It is the average total cost for the first month of a gym membership

The formula used is \($N(t) = N_0 e^{rt}$\). If a new social network has 1000 users currently and at growth rate of 10% per month, it can be predicted that there will be approximately 2452 users in seven and a half months assuming similar exponential growth.

In the formula used in the spreadsheet model for measuring exponential growth i.e. \($N(t) = N_0 e^{rt}$\)

N(t) is the number of cases at time t

N₀ is the initial number of cases

e is the mathematical constant approximately equal to 2.71828

r is the growth rate (expressed as a decimal)

To adapt this formula to predict the number of users of a new social network, we can replace the variables with the appropriate values. For example, if the new social network has 1000 users currently and is growing at a rate of 10% per month, we can write:

N(t) = 1000 x \(e^{rt}$\)

To find the predicted number of users in seven and a half months, we can substitute t = 7.5 into the equation and solve for N(7.5):

N(7.5) = 1000 x \(e^{rt}$\)

N(7.5) ≈ 2452.22

Therefore, we would expect to have approximately 2452 users on the new social network in seven and a half months if it continues to experience similar exponential growth.

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The complete question is :

What is the formula used in the spreadsheet model discussed in this module for measuring exponential growth of an epidemic, and how can it be adapted to predict the number of users of a new social network at a future date assuming similar exponential growth? In particular, if the new social network has 1000 users currently and is growing at a rate of 10% per month, how many users would we expect to have in seven and a half months?

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

D

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\) , then

\(log_{2}\) x = 4.3 ⇒ x = \(2^{4.3}\) ≈ 19.70 ( to 2 dec. places )

Answer:

question 1:

step #1:divide both sides by x

step #2:multiply both sides by 4

step #3: plug it into equation

Step-by-step explanation:

question 1:

step #1: divide both sides by x

you get x/4 = 1

step #2:multiply both sides by 4

you get x = 4

step #3: plug it into equation

4 squared/4 = 4

a. To solve the initial value problem using Laplace transforms, we start by taking the Laplace transform of both sides of the given differential equation. The Laplace transform of y(t) is denoted as Y(s). The Laplace transform of the second derivative y"(t) can be expressed as s²Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions. The Laplace transform of 48t is simply 48/s².

Applying the Laplace transform to the given differential equation, we get:

s²Y(s) - sy(0) - y'(0) + 16Y(s) = 48/s²

Substituting the initial conditions y(0) = 5 and y'(0) = 2, we have:

s²Y(s) - s(5) - 2 + 16Y(s) = 48/s²

Simplifying this equation gives the corresponding algebraic equation in terms of Y(s).

b. Now, we solve the equation obtained in part (a) for Y(s). Rearranging the terms, we have:

(s² + 16)Y(s) = 48/s² + s(5) + 2

Combining like terms, we get:

(s² + 16)Y(s) = (48 + 5s² + 2s) / s²

Dividing both sides by (s² + 16), we obtain:

Y(s) = (48 + 5s² + 2s) / (s²(s² + 16))

So, Y(s) is equal to the Laplace transform of y(t).

c. To find y(t), we take the inverse Laplace transform of Y(s) obtained in part (b). We can use partial fraction decomposition and the properties of Laplace transforms to simplify the expression and find the inverse Laplace transform.

Taking the inverse Laplace transform of Y(s), we find:

y(t) = L^(-1){Y(s)} = L^(-1){(48 + 5s² + 2s) / (s²(s² + 16))}

The inverse Laplace transform can be calculated using tables or software, and it yields the solution y(t) to the initial value problem.

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Answer:

2/15

Step-by-step explanation:

BRANIEST PLS

Answer: 2/15 is the answer hope this help

Step-by-step explanation:

One-sided confidence interval which have the smallest margin of error.

Given that;

Researchers want to decrease the margin of error by adjusting the confidence level.

You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.

one-sided confidence interval:

The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.

Hence, we use one-sided confidence interval which have the smallest margin of error.

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Occupation is a qualitative variable with a nominal level value, annual salary is a quantitative variable with ratio level value, price of a shirt (in dollars) on clearance rack is quantitative with a ratio level value.

Variables can be divided into quantitative or qualitative (categorical).

Quantitative variables are those variables in which the data measures values or counts and is expressed as amounts or numbers. Qualitative variables are any variables whose data are descriptive rather than numerical.

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Step-by-step explanation:

Let Jack's present age be x

Hence, his fathers present age=4x

Jacks age after 5 years= (x+5)

Jacks Fathers age after 5 years= (4x+5)

We know.. that the difference between their ages fives years later is 10.. hence

4x+5-(x+5)=10

4x+5-x-5=10

3x = 10

x= 3.3 years old...

Hence,

Jacks present age = 3.3 years

Fathers present age= 13.2 years...

Hope it helps .. I know that the answer comes in decimals... but the questions' like that..

The external angle theorem states that the measure of the external angle of a triangle is equal to the sum of the two opposite internal angles.

In this case

Then

∠4 is greater than ∠2 and ∠1, so A and B check

And F also checks

We know that the sum of the internal angles of a triangle add up to 180º so that:

And we also know that ∠3 and ∠4 are a linear pair, this means that they also add up to 180º:

Since both expressions are equal to 180º we can conclude that they are equal:

Subtract ∠3 from both sides of the equation and we get that

As stated by the external angle theore, the measure of the external angle, ∠4, of a triangle is equal to the sum of the opposite interior angles, ∠1+∠2 → With this, is proven that F is correct

If angles 1 and 2 add up to angle 4, then, by logic, their measure has to be less than angle 4

→ and this is how you know that ∠1 and ∠2 are less than ∠4

To order the given expressions from least to greatest, we need to find the values of each expression. However, since we do not have the function p(x), we cannot find the values of p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10). Therefore, we cannot order the expressions from least to greatest.

It is important to note that the sign of each expression will depend on the function p(x) and its derivative p′(x). If p′(x) is positive, then the function p(x) is increasing at that point. If p′(x) is negative, then the function p(x) is decreasing at that point. Without the function p(x), we cannot determine the sign of each expression and therefore cannot order them from least to greatest.

In conclusion, without the function p(x), we cannot order the expressions p′(1), p′(3), p′(6), p′(7), p′(9), and p′(10) from least to greatest.

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Answer:

450

Step-by-step explanation: