Please help me ASAP and I have more so PLEASE

Please Help Me ASAP And I Have More So PLEASE

Answers

Answer 1

The answer is B part

As the requirement for the student is either a senior or one who studies maths or both.

So, just add the values within the two venn circles divide it by total no of values.

=> 240+40+110/240+40+110+840

=> 360/1200

Answer 2

Answer:

B

Step-by-step explanation:

840 people aren't senior or don't takes math.

210 + 40 = 250 are seniors

110 + 40 = 150 people take math

In this class has 840 + 210 + 40 + 110 = 1200 people => All

210 + 40 + 110 = 360 people are seniors or take math. => P( S U M)

Probabilty that a randomly selected student is a senior or takes math =>\(\frac{P(S U M)}{All}\)

\(\frac{P(S U M)}{All} = \frac{360}{1200}\)

Hope this helps ^-^


Related Questions

A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities

Answers

The probabilities that the at least one tie is too tight is 0.878 and more than two ties are too tight is 0.323 and none are too tight is 0.122 and at least 18 are NOT too tight is 0.67.

According to the statement

We have given that the in a survey showing that the approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain.

And we have to find the probability on the some given conditions.

So, For this purpose, we know that the

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

Now,

A. Here n = 20, P = 0.1, And  X ≥ 1. Then

The probability that at least one tie is too tight P(≥ 1) = 1 - P(0)

P(≥ 1) = 1 - 0.12

P(≥ 1) = 0.878.

And

B. Here P(≤2) = 0.67 Then

The probability that more than two ties are too tight P(≥ 3) = 1 - P(≤2)

P(≥ 3) = 1 - 0.67

P(≥ 3) = 0.323

And

C. The probability that none are too tight P(0) = 0.122.

And

D. Here n =20, P = 0.1 and X≤2

The probability that at least 18 are NOT too tight P(X≤2) = 0.67.

So, The probabilities that the at least one tie is too tight is 0.878 and more than two ties are too tight is 0.323 and none are too tight is 0.122 and at least 18 are NOT too tight is 0.67.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

A research team conducted a study showing that approximately 20% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 15 businessmen, all of whom wear ties, what are the following probabilities

A. What is the probability that at least one tie is too tight?

B. What is the probability that more than two ties are too tight?

C. What is the probability that none are too tight?

D. What is the probability that at least 18 are NOT too tight?

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Richard can make 8 dough balls in two hours. If the amount of time is directly proportional to the number of dough balls,
how many hours have passed if he made 18 dough balls?

Answers

2 1/2 hours long hope this helped :)
Well.. let’s see... It would take him 2 hours to make 8 dough balls... So, 1 hour would give him 4.... and 1/2 hour would make 2... So, 4 hours would have him at 16 dough balls, then add a half hour to get 18 dough balls!! So, it’d take 4 and 1/2 hours to make 18 dough balls!

please help wth my mathsssssssss

please help wth my mathsssssssss

Answers

Answer:

A = 1

B = 5

Step-by-step explanation:

When Point A is plotted at (2, -3) and Point B is plotted at (2, 3) what axis is inbetween them?

Options

y axis


origin


x axis

Answers

Answer:

x - axis

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y )

(2, - 3 ) → (2, 3 ) is thus a reflection in the x- axis

Load the Tutorial 8 dataset tute8_smoke.csv in R. Run the following regression using the subsample of mothers who are smokers: - Regression 1 - dependent variable: birthweight independent variables: alcohol, tripre1, tripre2, tripre3, unmarried, educ, age Test the joint null hypothesis that: 1. the coefficient on 'alcohol' equals the coefficient on 'unmarried' 2. the coefficient on 'tripre2' equals the coefficient on 'unmarried' 3. the coefficient on 'tripre1' equals the coefficient on 'tripre3' 4. the coefficient on 'educ' equals the coefficient on 'age' against the alternative that at least one of these conditions does not hold. Given the sample size, Regression 1's specification, and the joint test, what is the distribution of the test statistic corresponding to this joint test? F(7,578) F(7,575) F(4,582) F(4,574)

Answers

The distribution used is F-distribution for the test statistic corresponding to the given joint test will be F(4, 582).

The regression 1 and its specification is dependent variable is birthweight and independent variables are alcohol, tripre1, tripre2, tripre3, unmarried, educ, and age.

The hypothesis is testing for joint null hypothesis, as stated below, that is

H0: βalcohol = βunmarried

H0: βtripre2 = βunmarried

H0: βtripre1 = βtripre3

H0: βeduc = βage

Against the alternative that at least one of these conditions does not hold.

The formula for the F-distribution is:

F = (SSR1 – SSR2 / r) / SSE2 / (n – r – 1)

Where,

SSR1: Residual sum of squares for the full model

SSR2: Residual sum of squares for the reduced model

r: Number of restrictions

SSE2: Residual sum of squares for the reduced model

n: Sample size

Given the sample size, Regression 1's specification, and the joint test, the distribution of the test statistic corresponding to this joint test will be F(4, 582). Hence, the correct option is F(4, 582).

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What is the amplitude of this function f (2) ?
f(x) = 3/4cos (3x) + 4
Enter your answer in the box.

Answers

Answer:

3/4

Step-by-step explanation:

The amplitude always comes before the operation(cos, tan...)

Express E in its simplest form- b) Express 36 : '22 in its simplest form. 4 3 2 c) Express the fractions — . I and E as equivalent fractions with a denominator of It} 20. x 3 2 d) Workout;+;—§ e) Find the mean of the following dataset: 301, 285, 21]. 351. 35. 2135. 311. 25. 45. 310. 301. 305 Round your answer to two decimal places.

Answers

a) , 36 : '22 in its simplest form is 18 : 11., d) the mean is 301.25.

a) To express 36 : '22 in its simplest form, we need to find the greatest common divisor (GCD) of 36 and 22. The GCD of 36 and 22 is 2. Divide both numbers by the GCD to simplify the fraction. 36 ÷ 2 = 18 and 22 ÷ 2 = 11. So, 36 : '22 in its simplest form is 18 : 11.

b) To express the fractions x 3 2 and I in equivalent fractions with a denominator of 20, we need to multiply the numerator and denominator by the same number. For x 3 2, multiply both the numerator and denominator by 10. This gives us x 3 2 = 10 x 3 2 ÷ 2 10 ÷ 2 = 15 1. For I, multiply both the numerator and denominator by 20. This gives us I = 1 x 20 2 x 20 = 20 40.

c) To evaluate Workout;+;—§, substitute the values into the expression: 2 + 5 - 4 ÷ 2. Start by performing the division: 4 ÷ 2 = 2. Then, perform the addition: 2 + 5 = 7. Finally, perform the subtraction: 7 - 2 = 5.

d) To find the mean of the dataset: 301, 285, 21, 351, 35, 2135, 311, 25, 45, 310, 301, 305, add up all the numbers and divide by the total number of values. Adding all the numbers together gives us 3615. Since there are 12 numbers in the dataset, the mean is 3615 ÷ 12 = 301.25. Rounded to two decimal places, the mean is 301.25.

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What is the slope of the line that passes through (-1, 3) and (-1, 8)?
due today

Answers

Answer:

Slope of the line is undefined

Step-by-step explanation:

(x₁, y₁) = (-1 , 3)  and (x₂, y₂) = (-1 , 8)

The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.

Use Venn diagrams to obtain the conclusion that is validly implied by each of the following sets of premises. If no conclusion can be validly drawn, write "no conclusion
1.All M are P.
All S are M.
2.Some M are not P.
All M are S.
3.Some M are P.
All S are M.
I did help figure these solutions
Example
1.Some P are M.
All M are S
Answer:
Some P are M.
All M are S
Some S are P.

Answers

Let's analyze each set of premises using Venn diagrams to determine the valid conclusions:

All M are P.

All S are M.

Venn diagram representation:

P: S:

| M |

Conclusion: Some S are P.

Explanation: Since all S are M, and all M are P, it is valid to conclude that there is an overlap between S and P, indicating that some S are P.

Some M are not P.

All M are S.

Venn diagram representation:

P:

| M |

S:

| M |

Conclusion: No conclusion.

Explanation: The given premises do not provide enough information to determine any valid conclusion. The Venn diagrams show that there can be overlap between M and S, but there is no information about the relationship between P and S.

Some M are P.

All S are M.

Venn diagram representation:

P:

| M |

S:

| M |

Conclusion: Some S are P.

Explanation: Since all S are M, and some M are P, it is valid to conclude that there is an overlap between S and P, indicating that some S are P.

In summary:

Some S are P.

No conclusion.

Some S are P.

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In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

Answers

Answer:

0 ≤ x ≤ 30

Step-by-step explanation:

In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

f(x) = 250(1.25)ˣ

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 250

0 ≤ x ≤ 30

All positive integers greater than 100

All real numbers

Solution:

Given that f(x) = 250(1.25)ˣ, where x is the number of days and f(x) is the population of the birds after x days. This means that at the beginning of the month of September (i.e. at x = 0), the population of the birds was 250. And as each day goes by, the population of the bird increases by a factor of 1.25.

The domain of a function is the set of all possible independent variables. In this case the number of days (x) is the independent variable. Since in the month of September there are 30 days, therefore the domain is:

0 ≤ x ≤ 30

f(x)=-3x^2+10x+13, find f(-1)

f(x)=-3x^2+10x+13, find f(-1)

Answers

f(-1)=0.

What is quadratic function?

A quadratic function is a polynomial function with one or more variable with highest degree of two.

Given, \(f(x)=-3x^{2} +10x+13\)

At x=-1, f(x)=f(-1)= \(-3(-1)^{2} +10(-1)+13\)

f(-1)=0.

Hence, \(f(x)=-3x^{2} +10x+13\) , at x=-1 is 0.

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Anyone know the answer?

Anyone know the answer?

Answers

Answer:

A≈18.38

Step-by-step explanation:

Solve for area

Shape: Parallelogram

Formula: Base*Height

5.25*3.5=18.375

Round answer

Hope this helps.

Find the 9th term of the geometric sequence 9,27,81...

Answers

Answer:

59049

Step-by-step explanation:

The pattern is that it multiplies by 3 every time.

9*3=27, and 27*3=81.

81*3 = 243

243*3 = 729

729*3=2187

2187*3=6561

6561*3=19683

19683*3 = 59049

We can also use such a statement as a question to the knowledge base, to ask: is it
the case that all apples in the knowledge base are known to be red or green?

Answers

Yes, you can use the statement as a question to the knowledge base to inquire about the color of apples in the base.

Specifically, the question seeks to confirm whether all apples in the knowledge base are either red or green.
1. Review the knowledge base to identify all statements related to apples.
2. Examine each statement to determine if it contains information about the color of the apples.
3. Check if the color mentioned in each statement is either red or green.
4. If all the relevant statements in the knowledge base confirm that apples are either red or green, then the answer to your question is "yes." Otherwise, the answer is "no."
In this process, the terms "knowledge," "statement," and "red or green" are used to analyze the information stored in the knowledge base and draw a conclusion about the colors of apples.

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Solve y''+2y'+y = e^(-t)sqrt(1+t), t > -1
14.) Solve y" + 2y' + y = e¯¹√1+t, t > −1

Answers

The solution to the differential equation y'' + 2y' + y = e^(-t)sqrt(1+t), t > -1 is y = e^(-t)(C1 + C2t) + (1/3)e^(-t)sqrt(1+t), where C1 and C2 are constants. To solve the given second-order linear homogeneous differential equation y'' + 2y' + y = e^(-t)sqrt(1+t), we first find the complementary solution by solving the corresponding homogeneous equation y'' + 2y' + y = 0.

The auxiliary equation is obtained by substituting y = e^(mt) into the homogeneous equation:

m^2 + 2m + 1 = 0

Solving the auxiliary equation, we find a repeated root m = -1. Therefore, the complementary solution is y_c = (C1 + C2t)e^(-t), where C1 and C2 are constants.

To find the particular solution, we assume a particular form of y_p = Ae^(-t)sqrt(1+t), where A is a constant to be determined. Plugging this into the original non-homogeneous equation, we differentiate y_p twice and substitute them back into the equation:

y_p'' + 2y_p' + y_p = A(1 + t)^(-1/2)e^(-t) + A(1 + t)^(-1/2)e^(-t) + A(1 + t)^(-1/2)e^(-t)sqrt(1 + t) = e^(-t)sqrt(1 + t)

Matching the coefficients of the same terms on both sides, we find A = 1/3. Thus, the particular solution is y_p = (1/3)e^(-t)sqrt(1 + t).

The general solution to the non-homogeneous equation is obtained by adding the complementary and particular solutions:

y = y_c + y_p = (C1 + C2t)e^(-t) + (1/3)e^(-t)sqrt(1 + t)

Therefore, the complete solution to the given differential equation is y = e^(-t)(C1 + C2t) + (1/3)e^(-t)sqrt(1 + t), where C1 and C2 are constants.

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In the United States, among a representative group of 6,006 white men and 1,126 black men, ages 70-79 at diagnosis with stage IV prostate cancer, 2,337 white men and 344 black men developed a second cancer of some kind after 5 years of follow-up. What is the incidence of a second cancer in the white population

Answers

Answer:

White men diagnosed with stage IV prostatic adenocarcinoma within the age bracket of 70-79 are 1.27 times more likely to survive five years after the diagnosis of stage IV prostatic adenocarcinoma than black men.

Step-by-step explanation:

The exposure is race and the outcome is survival.  

Race   Alive    Dead           T

W       2337     3669         6006

B         344        782          1126  

Relative Risk -  1.27  

White men diagnosed with stage IV prostatic adenocarcinoma within the age bracket of 70-79 are 1.27 times more likely to survive five years after the diagnosis of stage IV prostatic adenocarcinoma than black men.

Nila has r red peppers and 88 green peppers. Write an algebraic expression that tells how many total peppers she has.

Answers

Answer:

X= R +88

Step-by-step explanation:

X for total peppers

The figure shows the measurements, in inches, of a rectangular prism. 8 in 12 in 7 in What is the volume of the prism

A:92 in B: 236 in C: 472 D: 672

Answers

Answer:

672 in.³

Step-by-step explanation:

V = LWH

V = 8 in. × 12 in. × 7 in.

V = 672 in.³

Answer: D 672

Step-by-step explanation: The formula for volume is L x W x H = V so if you plug all those numbers in and multiply u get 672

The slope of the graph is -1. Which statement describes how the slope is related to the burning of a candle?

Answers

Answer: candle burns down 1 cm per hour

Step-by-step explanation:

Answer:

d.

Step-by-step explanation:

7. What values will be increased if the practitioner forgets to ice and ABG sample and leaves it at room temperature for 45 minutes

Answers

Various values that are being measured in the sample will increase, which can make the interpretation of the results difficult and potentially confusing.

When a practitioner forgets to ice and ABG sample and leaves it at room temperature for 45 minutes, some of the values that will be increased include the following:1. pH levels:The pH level of the sample is going to rise, leading to an increase in the alkalinity of the blood.2. PaO2:PaO2 (partial pressure of oxygen) is going to decrease since oxygen dissolved in blood will diffuse out into the air.

This will lead to an increase in the level of PaCO2 (partial pressure of carbon dioxide) since the respiratory rate will increase in order to get rid of more CO2.3. PCO2:The partial pressure of carbon dioxide (PCO2) in the sample is going to increase. The increase in PCO2 level in the sample will cause it to become more acidic due to the increase in carbon dioxide.4.

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Besides being simple for its own sake, what other advantage do simple models usually have?
a) Higher accuracy
b) Greater complexity
c) Easier interpretation
d) More detailed predictions

Answers

The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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simply the following expression

simply the following expression

Answers

Answer:

\( \dfrac{4r^6}{st^8} \)

Step-by-step explanation:

\( (4r^{-2}st^4)(r^{-4}st^6)^{-2} = \)

Use laws of exponents to simplify the right set of parentheses.

\(= (4r^{-2}st^4)(r^{8}s^{-2}t^{-12})\)

Now use the law of exponents for a product of powers with the same base.

\( = 4r^6s^{-1}t^{-8} \)

Finally, use the definition of a negative exponent.

\( = \dfrac{4r^6}{st^8} \)

What is the solution to the system of equations y equals 1.5 x 4?

Answers

The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6). The correct answer is D.

The solution to the system of equations can be calculate as follows

From the question we can conclude that the equations are :

y = 1.5x - 4

y = -x

to find the value of x and y  we can substitute y = -x in the first equation so it became

-x = 1.5x - 4

-1.5x - x = -4

-2.5x = -4

x = 1.6

after we found the value of x we can find the value of y by Substitute

x = 1.6 in y = -x

y = -1.6

Therefore, the solution to the y = 1.5x - 4 and y = -x  is (1.6,-1.6).

Your question is incomplete but most probably your full question was

What is the solution to the system of equations y = 1.5x – 4 y = –x

a.(–1.6, 1.6)

b.(–1.5, 1.5)

c. (1.5, –1.5)

d. (1.6, –1.6)

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please solve please be right

please solve please be right

Answers

Answer:

152

Step-by-step explanation:

Substitute 6 in for x since x = 6:

8(3(6) + 1)

8(18 + 1)

8(19)

= 152

hope this helps!

An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. A sample of 15 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded: x= the distance between the fire and the nearest fire station (in miles) y=cost of damage lin dollars) The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles.

Answers

A linear relationship between the cost of fire damage (y) and the distance from the house to the nearest fire station (x) is being analyzed using the equation y = mx + c.

We have,

A sample of 15 recent fires and the variables recorded for each fire:

x = distance from the fire to the nearest fire station (in miles) and

y = cost of damage (in dollars).

The distances range from 0.7 miles to 6.1 miles.

To determine the linear relationship between the variables x and y, you can perform a linear regression analysis to find the equation of the best-fit line that represents this relationship.

This equation will help you predict the cost of fire damage based on the distance to the nearest fire station.

If you have the data points for the distances and costs of damage, you can use statistical software or tools to perform the regression analysis and find the equation of the line.

The equation will be in the form of:

y = mx + b

where:

y is the cost of damage

x is the distance to the nearest fire station

m is the slope of the line (reflecting the rate of change of cost with respect to distance)

b is the y-intercept (the cost when the distance is 0)

This linear equation will provide insights into how the cost of fire damage changes as the distance to the nearest fire station changes.

Thus,

A linear relationship between the cost of fire damage (y) and the distance from the house to the nearest fire station (x) is being analyzed using the equation y = mx + c.

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a. The critical value for testing if the correlation is significant at α=0.05 with a sample size of 15 is 0.524.

b. With a correlation coefficient of 0.961, the correlation between cost and distance is significant at α=0.05, as the computed correlation coefficient is greater than the critical value of 0.524.

c. The regression equation for predicting cost of damage from the distance between the fire and the nearest fire station is y = 4919x + 10278, where y represents the cost of damage and x represents the distance between the fire and the nearest fire station.

d. To predict the cost of damage for a house that is 0.5 miles from the nearest fire station, substitute x=0.5 into the regression equation to obtain y = 13877 dollars.

Here, we have to test if the correlation is significant, we need to calculate the critical value using the formula: critical value = t(α/2, n-2), where t is the t-distribution value and α is the level of significance.

With α=0.05 and n=15, the critical value is 0.524. As the computed correlation coefficient of 0.961 is greater than the critical value, we can conclude that the correlation between cost and distance is significant.

To find the regression equation, we use the formula: y = bx + a, where b is the slope and a is the y-intercept.

Given that the slope is 4919 and the y-intercept is 10278, the regression equation is y = 4919x + 10278.

This equation can be used to predict the cost of damage for any distance between the fire and the nearest fire station.

To predict the cost of damage for a house that is 0.5 miles from the nearest fire station, we substitute x=0.5 into the regression equation to obtain y = 4919(0.5) + 10278 = 13877 dollars.

This means that the predicted cost of damage for a house that is 0.5 miles from the nearest fire station is $13,877.

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complete question:

An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. A sample of 15 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded:

x= the distance between the fire and the nearest fire station (in miles)

y= cost of damage (in dollars)

The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles.

a. The correlation between cost and distance is 0.961. What is the critical value for testing if the correlation is significant at α=.05?

b. The correlation between cost and distance is 0.961. Test if the correlation is significant at α=.05.

c. What is the regression equation for predicting cost of damage from the distance between the fire and the nearest fire station when the slope is 4919, and the y-intercept is 10278 ?

d. Predict the cost of damage for a house that is 0.5 miles from the nearest fire station.

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.

y=-4x²+141x−703

Answers

The maximum amοunt οf prοfit the cοmpany can make is $543

What is prοfit?

Prοfit is the mοney yοu have left after paying fοr business expenses. There are three main types οf prοfit: grοss prοfit, οperating and net prοfit.

Grοss prοfit is biggest. It shοws what mοney was left after paying fοr the gοοds and services sοld. Operating prοfit is next. It shοws what's left after alsο paying οperating cοsts such as rent, electricity, phοnes and in sοme cases staff.

Net prοfit cοmes last. It shοws what yοu made after deducting all cοsts and tax. Yοu get tο hοld οntο net prοfit.

Let y represent the amοunt οf prοfit and x represent the selling price.

The relatiοnship between x and y is:

y = -4x² + 141x – 703

The maximum prοfit is at dy/dx = 0, hence:

dy/dx = -8x + 141

-8x + 141 = 0

8x = 141

x = 17.625

The maximum prοfit is:

y = -4(17.625)² + 141(17.625) – 703 = 543

The maximum amοunt οf prοfit the cοmpany can make is $543

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Explain what is wrong with the statement. If 0 = f (x) = g(x) and g(x) dx diverges then by the comparison test so f(x)dx diverges. x O If 0

Answers

The statement is incorrect due to the invalid assumption of f(x) = g(x) = 0, and the incorrect application of the comparison test.

The comparison test states that if 0 ≤ f(x) ≤ g(x) and the integral of g(x) dx diverges, then the integral of f(x) dx also diverges. However, the statement assumes that f(x) and g(x) are equal to zero, which means that 0 ≤ f(x) ≤ g(x) is not satisfied.

Additionally, the assumption that g(x) dx diverges does not necessarily imply that f(x) dx also diverges. For example, let g(x) = 1/x^2 and f(x) = 0 for all x. Then g(x) dx diverges, but f(x) dx converges to zero.

In conclusion, the statement is incorrect due to the invalid assumption of f(x) = g(x) = 0, and the incorrect application of the comparison test.

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act scores are normally distributed and from 2015 to 2017, the mean was 20.9 with a standard deviation of 5.6. to get accepted into u of m, you need at least a 31. what is the z-score you need to get accepted? enter your answer rounded to the nearest hundredth. question 3 options:

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To find the z-score needed to get accepted into the University of Michigan (U of M) with an ACT score of at least 31, we can use the mean and standard deviation of the ACT scores distribution from 2015 to 2017.

The mean is 20.9, and the standard deviation is 5.6.

The z-score measures how many standard deviations an individual's ACT score is above or below the mean. We can calculate the z-score using the formula: z = (x - μ) / σ, where x is the ACT score, μ is the mean, and σ is the standard deviation.

For the desired ACT score of 31, we can calculate the z-score as follows:

z = (31 - 20.9) / 5.6 ≈ 1.82

Therefore, the z-score needed to get accepted into U of M with an ACT score of at least 31 is approximately 1.82, rounded to the nearest hundredth.

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An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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List all the permutations of four objects m, I, n, and k taken two at a time without repetition. What is P? List all the permutations of four objects m, I, n, and k taken two at a time without repetition. Choose the correct answer below. O A. m, mn, mk, In, lk, nk OB. ml, mn, mk, Im, in, lk, nm, nl, nk, km, kl, kn OC. m. I, n,k OD. mm, ml, mn, mk, II, In, lk, nn, nk, kk What is P2?

Answers

The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.

P is the total number of permutations, which is equal to 12.

The correct answer is OB, which lists all 12 permutations.

P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.

There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.

Therefore, P2 is equal to 16.

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