MATHEMATICS COLLEGE

A data related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is Routput of the relationship between X and Y. Coefficients: Estimate Std. Error t value Pro> tl) (Intercept) 9.4764 9.6266 0.98 0.354 2.0315 0.0070 4.51 0.CO2 ** X Signif. codes: 9 ****' 0.001 ***' 0.01 **' 0.05, 0.1' '1 Residual standard error: 17.9 on 8 degrees of freedom Multiple R-squared: 0.717, Adjusted R-squared: 0.682 F-statistic: 20.3 on 1 and 8 DF, p-value: 0.00198
a) Write the regression equation with parameters from the R output.b) Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine?c) What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter.d) What is the value of the correlation coefficient?e) Calculate a 95% confidence interval for the slope of the model.f) Based on the confidence interval, is there a linear relationship between X and Y?

Answers

Answer 1
Answer:

Answer:

Y = 0.0315x + 9.4764

Residual = 2.35

Correlation Coefficient = 0.847

Step-by-step explanation:

From the R output given :

Intercept = 9.4764

Slope = 0.0315

x = number of manufacturing enterprise employing 20 or more workers

y = annual mean concentration of Sulphur dioxide

The regression equation :

y = bx + c

b = slope ; c = intercept

y = 0.0315x + 9.4764

Prediction using the regression equation :

The predicted y value, when x = 250

y = 0.0315(250) + 9.4764

y = 17.3514

The residual, if actual annual concentration = 15

Y residual = 17.35 - 15 = 2.35

The correlation Coefficient value, R

R = √R²

R = √0.717

R = 0.847

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The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?A.
The maximum value of f(x) is greater than the maximum value of g(x).
B.
The maximum value of g(x) is greater than the maximum value of f(x).
C.
The minimum value of f(x) is greater than the minimum value of g(x).
D.
The minimum value of g(x) is greater than the minimum value of f(x).

Answers

ANSWER

D.
The minimum value of g(x) is greater than the minimum value of f(x).

EXPLANATION

It was given that;

f(x)
has a vertex at

(9,8)

and opens upwards.

This means that f(x) is a minimum graph and hence have a minimum value of 8.

Also ,

g(x) = 4 {(x - 8)}^(2) + 9

When we compare this function to

y = a {(x - h)}^(2) + k

We can see that,a=4, h=8 and y=9.

The vertex is

(8,9)

Since a>0, the graph opens upwards.

The graph has a minimum point which is (8,9) and hence the minimum value is 9.

We can see that, the minimum value of g(x) is greater than the minimum value of f(x).

Therefore the correct answer is D.

What are the advantages of a closed​ question? A. Closed questions allow the respondent to go​ in-depth with their answers. B. It is possible to automate the collection of results for closed questions. C. Closed questions allow for new solutions to be introduced. D. It is easy to quantify and compare the results of surveys with closed questions.

Answers

Answer:

closed questions are questions with fixed answer options

A. Closed questions allow the respondent to go​ in-depth with their answers.

  • no, it is relevant to open questions

B. It is possible to automate the collection of results for closed questions.

  • yes

C. Closed questions allow for new solutions to be introduced.

  • no, it allows to collect statistical data but not good for new solutions, it better works with open questions when new ideas, solutions may appear

D. It is easy to quantify and compare the results of surveys with closed questions.

  • yes

Rock concert tickets are sold at a ticket counter. Femalesandmalesarriveat times of independent Poisson processes with rates 30 and 20 customers per hour. (a) What is the probability the first three customers are female

Answers

Answer: The probability that the first three customers are female is 0.216

Step-by-step explanation:

The attachment below shows the calculations clearly.

A coin is flipped three times. James is declared the winner if there are at least two tails. Peter is declared the winner if there is a head flipped.a. How many different outcomes are there?
b. What is the probability that James wins?
c. What is the probability that Peter wins?
d. Is the game fair?
e. Are there any outcomes where the game would be tied?
f. Are there any outcomes where no one would win?

Answers

 A______is your answer

Help to solve   y'''-y''-4y'+4y=5-e^x+e^2x

Answers

By solving the equation "y'''-y''-4y'+4y=5-e^x+e^2x" we get "y = Ae^x+Be^(2e)+Ce^(-2x)+(5)/(4)+(xe^x)/(3) +(xe^(2x))/(4)".

As we know the auxiliary equations,

  • m^3-m^2-4m+4=0
  • (m-1)(m-2)(m+2) =0

here,

m = 1, 2, -2

Thus,

The general equation will be:

→ y = Ae^x+Be^(2x)+Ce^(-2x)

Particularly,

  • 5 = (5)/(4)
  • e^x= x((1)/(1-4)e^x ) = -(xe^x)/(3)
  • e^(2x) = x((e^(2x))/((2+2)(2-1)) )= (xe^(2x))/(4)

hence,

The complete equation will be:

→ y = Ae^x+Be^(2e)+Ce^(-2x)+(5)/(4)+(xe^x)/(3) +(xe^(2x))/(4)

Thus the above answer is right.

Learn more:

brainly.com/question/22449567

Answer:

Step-by-step explanation:

First of all write the auxialary equation as

m^3-m^2-4m+4 =0\n(m-1)(m-2)(m+2)=0

m=1,2,-2

Hence general solution is

y=Ae^x+Be^(2x) +Ce^(-2x)

Particular solution of 5 is

(5)/(4)

Particular solution of e^x is

x((1)/(1-4) e^x =(-xe^x)/(3)

Particular solution of e^2x is

x(e^(2x) )/((2+2)(2-1)) =(xe^(2x) )/(4)

Together full solution is

y=Ae^x+Be^(2x) +Ce^(-2x)+(5)/(4) +(xe^x)/(3) +(xe^(2x) )/(4)

Subtract and write the difference in simplest form 12 5/8 - 7 1/3

Answers

Answer:

5 7/24

Step-by-step explanation:

Given the following mathematical expression;

12 5/8 - 7 1/3

First of all, we would subtract the whole numbers;

12 5/8 - 7 1/3 = (12 - 7) 5/8 - 1/3

12 5/8 - 7 1/3 = 5 [5/8 - 1/3]

Next, we subtract the fractions from each other;

5/8 - 1/3

Lowest common multiple (lcm) = 24

5/8 - 1/3 = (15 - 8)/24

5/8 - 1/3 = 7/24

Combining the two parts, we have;

12 5/8 - 7 1/3 = 5 7/24
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