Category: Mathematics Homework Help

I’m working on a calculus question and need a sample draft to help me learn.

Hello I need help with my Calculus homework. Please show work for each question. Please explain step by step for all the problems so it’s easy to follow and understand the work. Thank You.Pg.235, Sec.5.1, EX#13, 15, 17

Pg.244, Sec.5.2, EX#1, 5, 9, 33, 39, 51, 55, 57, 71

Sec.5.3, EX#5, 9, 13, 17, 21, 35

Sec.5.4, EX#7, 9, 21, 29

Sec.5.5, EX#3, 5, 7, 11, 29, 31

Sec.5.7, EX#5, 7, 9, 13, 17, 31, 35, 45, 67, 73

https://drive.google.com/file/d/1CHh4j2dPoe3vWqUrc…

Q1) A medicinal chemist working in a Singapore-based pharmaceutical company has been tasked
to develop a nutritional supplement which should contain a total of at least 16 units of
Magnesium and 24 units of Zinc by mixing two commercially available food grade
compounds: C1 and C2.

C1 costs $140 per kg while C2 costs $180 per kg. According to the supplier, every kg of C1
contains 4 units of Magnesium and 2 units of Zinc, while every kg of C2 contains 2 units of
Magnesium and 4 units of Zinc.

How should the chemist minimise the cost of such a mixture?

(1a) Develop an LP model that represents the problem by clearly stating the decision
variables, objective and constraints. You are not required to solve it at this stage.
Please limit your answer to within one page.
(15 marks)

(1b) Find the optimal solution to the problem using the graphical method or any other
manual method (show your workings) and explain by using the graph whether the
optimal solution is unique.
(20 marks)

(1c) Due to other nutritional consideration, the chief chemist has given the medicinal
chemist an additional instruction that the quantity of compound C2 should be at most
 times the quantity of compound C1 used ( > 0). Using the graphical method,
explain how the optimal solution in this new situation could be affected by differing
values of  ( > 0). You are required to re-work the new optimal solution, if different
from (b). Please limit your answer to within two pages.
(20 marks)

Q2) Describe one application of Linear Programming in healthcare, hospitality, manufacturing, or
supply chain. You are required to describe the scenario and explain how LP could be used in
solving the scenario. You do not need to formulate the problem into an LP model or solve it.
Please limit the answer to within 500 words.
(45 marks)

Topics:

Chapter 2 Probability: Sample space, events, probability of an event, rule of addition, conditional probability, multiplication and total probability rules, independence, and Bayes’ theorem

Chapter 3 Discrete Random Variables and Probability Distributions: Concept of a random variable, discrete random variables, probability mass function and cumulative distribution functions, mean and variance of a discrete random variable, discrete probability distributions (Binomial, Poisson, Geometric, and Hypergeometric)

Chapter 4 Continuous Random Variables and Probability Distributions: continuous random variables, probability density functions, cumulative distribution functions, mean and variance of a continuous random variable, continuous distributions (Uniform, Normal, Exponential, Erlang and Gamma, and Weibull), and Normal approximation to Binomial and Poisson

Need these 10 answers questioned in 1 hour. 10 minutes extra will be granted if needed. Need to show all work. Please upload each answer with the work shown as you answer it, please. I need all answers in by the latest 9 pm PST (California Time, United States). Make sure everything is legible and that I can read everything with full work shown. If all work isn’t shown I will have to refund. Thank you.

HERE IS THE LINK TO THE SCREENSHOTS OF QUESTIONS.

https://we.tl/t-Nn3dZK5Ksb

UNIT 5

Evaluate a statistical study.

Introduction

In this assessment, you will demonstrate your ability to critically evaluate surveys and their statistical findings. In the process, you will get to know important terms and methods that are used when conducting a survey and when presenting a report based on an evaluation of a survey and its statistical findings.

Demonstration of Proficiency

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies through the following assessment scoring guide criteria.

• Competency 2: Evaluate the adequacy of data collection methods.
  • Assess the appropriateness of a sample to represent a population.
  • Explain the rationale for using a particular sampling technique.
• Competency 5: Evaluate statistical arguments.
  • Interpret the meaning of the confidence interval in the context of survey results.
  • Evaluate the impact of question wording on participants’ responses.
  • Evaluate a study for evidence of bias.

This assessment is somewhat independent of the other assessments so far, in the sense that it does not involve your own survey. Instead, you will produce a report based on an evaluation of a Gallup survey and its statistical findings. Gallup reports on a variety of polls with explanations of the survey methods. Categories of polls include politics, economy, well-being, health care law, taxes, federal budget, and many other subjects.

For Assessment 5, you need to select a survey from Gallup then analyze it. You will find links to the most recent topics on the Gallup home page. You can search for surveys by keyword; alternatively, click on the news link at the bottom of the page and search by topic. Make sure the topic you select contains information about survey methods, particularly the sample size, sampling method, and margin of error.

To prepare for this assessment, go to the Gallup home page and do the following:

• Review a variety of polls on the site.
• Choose a poll to report on that closely aligns to your field of study or area of professional interest.
• Review the information in the Survey Methods section of the article. This section details how the study was conducted. Also, study all information contained in additional links at the bottom of this section. You will use this information to complete your assessment.

Then, answer the following questions about the Gallup poll you selected:

• What was the purpose of the poll? Write a brief summary. Include the title and link to the article within your summary.
• What were the population and sample? Why is this sample appropriate for the population? What was the sample size? Was the sample size large enough to reflect the opinions of the population?
• Were the results parameters or statistics? Why?
• What type of sampling technique was used (for example, stratified, clustered, random, convenience, or systematic)? Why was this technique used? How were the subjects contacted? Was this method appropriate?
• What was the confidence interval and margin of error? Interpret what the confidence interval means as it relates to the context of the survey.
• What were the exact questions asked? Do you think the wording of the questions influenced the participants’ responses?
• Did you find any evidence of bias in the poll? If so, describe the source of the bias. If not, how was bias avoided?

I’m working on a statistics test / quiz prep and need an explanation to help me learn.

Q1. A local charity is holding a prize raffle to raise money for their cause. The raffle is being run by a lottery, in which each participant picks a set of 3 numbers ranging from 1 to 21. The three winning numbers are selected at random, and the prize drawing is done only once. If you decide to buy a raffle ticket, what are your chances of winning?

Q2. The mean time for a 100 meter race at a college track meet is 13.2 seconds, with a standard deviation of 0.9 seconds. To win, the next sprinter needs to run the race in 12.5 seconds or less. Assuming this random variable is normally distributed, what is the probability of the sprinter running the race in a short enough time to take the lead?

Q3. A denim company sells its jeans both online and at a retail store. Assume that 80% of the company’s sales are retail, and 20% of sales are online.
a. What’s the probability that all of the next four pairs of jeans are sold online?
b. What’s the probability that three out of the next four pairs of jeans are sold online?
c. Use your answers from part (a) and (b) to derive a formula for p(x), the probability distribution of the binomial random variable x, the number of the next four pairs of jeans sold online.

Q4.A toy manufacturer needs to test its new product to make sure it doesn’t present a choking hazard to small children. It needs to estimate the fraction of toys that could potentially be defective, ρ, to be less than .01 with a 95% confidence interval. A sample fraction of defective toys from other testing, p̂, is 0.04. How many toys would the manufacturer have to randomly sample to make sure they aren’t defective?

Q5. An environmental scientist is catching fish from the Great Lakes and testing them for the presence of an invasive parasite. After a sample analysis that included 175 rounds of testing, the scientist finds that the sample mean infection rate, μ, is 54.37 fish per round and the sample standard deviation, σ, is 7.07 fish per round.
a. Construct a 95% confidence interval for the mean infection rate in the total fish population. Explain what this figure means.
b. Explain how your work in part would have been different if the sample size had been only 12 rounds of testing instead of 175.

International Tractor Motors (ITM) had recently undertaken an ad campaign aimed at agricultural owners in a certain country in Asia. The ad campaign was devoted to promoting the new IT-8 large specialty tractor. Four sales associates were assigned to sell in different medium to large farms throughout the country for many days. One associate was assigned to the northern part of the country. Another was assigned to the southern part. The other two were assigned to the west and east, respectively. Because of regulations, a sales associate can sell at most one IT-8 tractor per day and only one such tractor per farm, too. A sales associate was successful if he or she sold a tractor during the day. Thus, ITM can sell at most 4 tractors (4 total sales) per day in this country.

Download the file titled Tractor Successes. It contains a scatter plot of the number of successes versus frequency. To compare the results to the Binomial Distribution, complete the following:

1. Explain why this tractor sales scenario can be a binomial experiment.
2. Using the Tractor Successes scatter plot, construct a frequency distribution for the number of successes.
3. Compute the mean number of successes. The formula for the mean is as follows: ?(x?f)?f?(x?f)?f

The terms x represent the total number of successes (0, 1, 2, 3, 4) and f is the corresponding frequency (number of days where x successes occurred).

Explain what the numerical result means.

1. From the frequency distribution, construct the corresponding relative frequency distribution.

Explain why the relative frequency distribution table is a probability distribution.

Then, use Excel to create a scatter plot of the probability distribution:

Select the two columns of the probability distribution. Click on INSERT, and then go to the Charts area and select Scatter. Then choose the first Scatter chart (the one without lines connecting).

1. Using the frequency distribution, what is the tractor sales success average? In part 3, note that the numerator in the formula for the mean is the total number of successes. The total number of trials is the denominator of the formula for the mean multiplied by 4. What does this average mean?
2. The Binomial Distribution is uniquely determined by n, the number of trials, and p, the probability of “success” on each trial. Using Excel, construct the Binomial Probability Distribution for four trials, n, and probability of success, p, as the tractor sales success average in part 5. Here is an explanation of the BINOM.DIST function in Excel: https://support.office.com/en-ie/article/BINOM-DIST-function-c5ae37b6-f39c-4be2-94c2-509a1480770c?ui=en-USrs=en-IEad=I (Links to an external site.)

For example, In Excel

=BINOM.DIST(7,15,0.7, FALSE)

represents the probability of 7 successes out of 15 (n) trials. The 0.7 is the probability of success, p.

Using the above value of n=4 with probability of success, p, as the tractor sales success average in part 5, what is the probability of at least two successes?

1. Using the formula for the mean of the Binomial Distribution, what is the mean number of successes in part 6 above?
2. In Excel, create a scatter plot for the Binomial Distribution. The instructions for creating a scatter plot are in part 4 above.
3. Use the results above to compare the probability distribution of tractor sales successes and the Binomial Distribution. Compare the means in parts 4 and 6, too.

If the probability distribution of tractor sales successes and the Binomial Distribution differ, explain why that is so.

• Do you think the Binomial Distribution is a good model for the tractor sales success scenario? Why or why not?
• How can International Tractor Motors use the Binomial Distribution to approximate tractor sales in similar countries?
• In what other scenarios can International Tractor Motors use the Binomial Distribution? Explain.

Select the response that best completes the statement or answers the question.

1. Which ordered pair is not a solution of y = -9x + 1?

A. (1,-5) B. (2,1) C.(-1, 10) D. (-3, -1)

2. Which of the following ordered pairs is a solution to 3x – 4y = -1?

A. (3, 2) B.(4,3) C. (5, -4) D. (5, 4)

3. To the nearest degree, what is the measure of the central angle that

represents 32% in a circle graph?

A. 32°

B. 115° C. 328° D. 148°

4. Which two symbols cannot represent the same figure?

A. FD and DF B. XY and YX C. PQ and QP

D. RT and TR

5. AABC has vertices A(2, 3), B(6, 7), C(-3,3). AA’B’C’ is the image of AABC

after the translation (x, y)” (x + 5, y-1). What are the coordinates of B’?

A. (11,6) B.(-2, 4) C.(-1,3) D. (2,5)

6. What is the slope of the line that passes through points (-1, -14) and (5, 4)?

7. If each leg of a right triangle has a length of 6 inches, how many lines of

symmetry does the triangle have?

A. 1 line B. 2 lines C. 3 lines D. 6 lines

8. What is the slope of this line?

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9. What is the slope of the line that contains the points A(2, 4) and B(6, 1)?

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D. undefined

10. A truck tire travels about 11 feet in 1 full rotation. What is the diameter of the

wheel, to the nearest inch?

A. 3.5 in. B. 42 in. C. 94 in. D. 132 in.

11. What is the m26, given that lines A and B are parallel?

C

1200

B.60° C. 90°

D. 120°

12. If 41 and 42 are complementary angles, what could their measures be?

A. 36° and 24° B. 52° and 38° C. 61° and 61° D. 89° and 91°

13. The measure of two angles of a triangle are 589 and 28°. Classify the triangle

by its angles.

A. obtuse

B. acute

C. right D. equilateral

14. What type of triangle will have no congruent sides and one right angle?

A. obtuse isosceles triangle B. acute scalene triangle C. right equilateral triangle D. right scalene triangle

15. Which ordered pair is the solution of the linear system y= 2x + 16 and y = -x

+ 1?

A. (0, 16) B. (2, -1) C.(-5, 6) D.(-8,9)

16. Which of the following is never a quadrilateral with 4 right angles?

A. parallelogram B. rectangle C. square D. trapezoid

17. What is the slope of the line defined by 6x + y = 10?

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18. What is the domain of the relation {(8, 2), (6, 4), (4, 2), (2, 4)}?

A. 2,4 B. 2, 4, 6, 8 C.6,8 D. 2, 4, 8

19. If the measures of two angles of a triangle are 28° and 58°, what is the

measure of the third angle?

A. 28° B. 16° C. 94° D.58°

20. Which of the following is an angle vertical to LCAD in this diagram?

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A. ZGAF B. ZCAE C. ZGAC D. ZFAE

21. What is the approximate circumference of a circle with a radius of 5.7 ft?

A. 6 ft B. 12 ft C. 18 ft D. 36 ft

22. A Ferris wheel is 40 feet in diameter. Which is closest to the distance

traveled in three rotations by a point on the Ferris wheel? A. 125.6 ft

B. 251.2 ft

C. 376.8 ft

D. 753.6 ft

23. The ratio of the side lengths of a triangle is 4: 5: 6. Classify the triangle by its

side lengths. A. scalene B. equilateral C. isosceles D. acute

24. In AABC, MZA = 45°, and m2C = 115o. What type of triangle is SABC?

A. acute B. equilateral C. right D. obtuse

25. Find the perimeter of a square that has a side measure of 45 cm.

A. 90 cm

B. 135 cm C. 180 cm D. 225 cm

26. In the prism below, what is the relationship between CD and EF?

RAP

OL

A. parallel B. intersecting

C. skew

D. perpendicular

27. The graph of which of the following equations would have the greatest slope?

A. y = 2x B. y = x + 12 C. y = 15x – 1 D.y = -8x + 4

28. Which of the following relations is a function?

A. {(2, -3), (-3, 2), (2, 3), (-2,3)} B. {(5, -4), (-4, 5), (-5, 4), (4, -5)} C. {(8,-5), (-5, 8), (-5, -8), (-8,5)} D. {(-7, 6), (6, –7), (-7, 9), (10,3)}

29. Which ordered pair is a solution of the equation y=-3x + 4?

A. (3,-2) B.(-2, 10) C. (-4,-8) D. (8,9)

30

Which of the following ordered pairs is not a solution of 5x – 4y = 7?

A. (-9, -13) B.(-5, -9) C. (7,7) D. (11, 12)

31. What is the y-intercept of the graph of -x + 4y = -24?

A. -6

D. 24

32. The perimeter of a triangle is 36 feet. The length of a side is 10 feet. The

lengths of the other two sides are equal. How long is each of the other two sides?

A. 26 ft

B. 13 ft C. 23 ft

D. 10 ft

33. You weave wall hangings. You sell small ones for $30 and large ones for $50.

Your goal is to make $1,000. Let x represent the number of large wali hangings you sell, and let y represent the number of small wall hangings you sell. Which equation best models the situation? A. 50x + 30 = 1,000y B. 30x + 50y = 1,000 C. 1,000x – 30y = 50 D. 50x + 30y = 1,000

34. What is the y-intercept of the graph of 6x + 4y = 28?

35. Which ordered pair is a solution of the inequality 6x + 3y < 36?

A. (3, 8) B.(4,6) C. (6,4) D.(-2, 12)

36. If a regular octagon has a perimeter of 96 mm, what is the length of each

side?

A. 16 mm B. 24 mm C. 12 mm

D. 19.2 mm

37. Which ordered pair is the solution of the system of equations 2x + y = -10

and y = 2x + 2? A. (1, -8) B.(-1,0) C.(-3,-4) D.(3, 4)

38. When each member of a relation’s domain is paired with exactly one member

of the range, the relation is a

A. slope B. solution C. function

D. linear equation

39. Which of the following best identifies the triangle shown here?

Metro

A. obtuse B. acute scalene C. acute D. obtuse isosceles

40. What is the slope of the line through points (2, 3) and (4, 5)?

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41. What kinds of lines always intersect to form 90° angles?

A. intersecting B. parallel C. perpendicular

D. skew

42. Which point is a solution of the system? y = x + 2

y = 2x – 2

A. (6,4) B. (1,3) C. (4,6) D. no solution

43. What is the y-intercept of the line defined by y = 3x – 6?

A. -6

If 23 and 24 are supplementary angles, what could their measures be?

A 110° and 110° B. 97° and 83° C. 57o and 33° D. 82° and 41°

45. A circle has a radius of 3.6 cm. Find the circumference to the nearest tenth,

using 3.14 for it

A. 11.3 cm B. 22.6 cm C. 19.5 cm D. 29.5 cm

What is the slope of the line defined by -5x + y =

?

47. In the diagram, the m2 1 = 58°; what is the M22?

A. 32° B. 122° C. 107° D. 58°

48. Which of the following ordered pairs is a solution to x + y< 6; y = 7x – 3?

A. (1,4) B.(3,6) C. (2,5) D. (2, -1)

49. Which ordered pair is the solution of x – 2y = 3 and 3x + y = 2.

A. (1, -1) B. (-1,1) C. (3, 2)

D. (2. –

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I’m studying for my Statistics class and need an explanation.

Using the Gun Control dataset complete the following tasks:

• Run a regression on the variables: Education, AmericanOwn.
• Part 1: Identify and interpret the coefficient of determination (R²).
• Part 2: Identify and interpret the correlation coefficient (R).
• Part 3: Generate and interpret the regression equation.

Part 4: Type or copy and paste your answers to Parts 1-3 in the comment box and upload your output as an attachment