Mathematics

3a. The probability of randomly selecting a car with two occupants.3b. The probability of randomly selecting a car with two or more occupants.3c. The probability of randomly selecting a car with between two and five occupants, inclusive.4. Scores. Scores for a qualification exam are normally distributed, with a mean of 80 and a standard deviation of 10. To be qualified for an interview, you must score in the top 10%. What is the lowest score you can earn and still be qualified for an interview?5. Coffee temperatures. You randomly select 25 coffee shops and measure the temperature of coffee sold at each. The sample mean temperature is one-hundred sixty-two degrees F with a sample standard deviation of 8.0 degrees F. Find the 95% confidence interval for the mean temperature. Assume the temperatures are approximately normally distributed.

Question 1.Find x and y so that [2x ???? y; x + 3y] = [1; 25]:Question 2.Write the vector [3; 5] as a linear combination of [6; 4] and [3; 1]:Question 3.Find the angle between the vectors [1; 2; 2] and [3; 4; 5]:Question 4.(a) Find the cross product [2; 3; 4] [7; 6; 5]:(b) Find a unit vector that is orthogonal to both [2; 3; 4] and [7; 6; 5]:(c) Compute the dot product of the unit vector that you found in Part (b) with each of [2; 3; 4] and [7; 6; 5]:Question 5.Find the shortest vector among the following 3 vectors:[3; 0; ????5]; [????1; 2; ????4]; [2; 3; 2]Question 6.Find the equation of the line that passes through the points 1; 3; 4) and (5; 8; 6):Question 7.Find the equation of the plane that passes through the point (1; 3; 4) and is normal to [4; 3; 2]:

The purpose of the statistics project is to go through the process that a statistician goes through when analyzing new data. You will be asked to do some Exploratory Data Analysis, describe the data using descriptive statistics and plots, answer some questions about probability of future information, create confidence intervals, and describe relations of the data through the use of correlations and linear regressions.For this project you will use StatCrunch (or any other software you are comfortable using.). You will use the data from the StatCrunch Website entitled “Sample College Data.” This is data sampled from universities from a few states on the East Coast and you will use it to work through the sections below. To find the data follow the link to StatCrunch from MyMathLab. In the Data box click the link to “Data sets” and use the search bar to find the data set “Sample College Data”, then open StatCrunch.Section 1 Exploratory Data Analysis: In this section of your analysis you will need to open the data, describe the data by data type, understand the sample size, the number of data points for each row etc.· Think about displaying the categorical (qualitative data) using pie charts or bar charts· For numerical (quantitative) look to show the data using histograms or other appropriate plots.For every plot or piece of information about the data you uncover, please summarize what the plots/information says about the “shape” of the data.Section 2 Descriptive Statistics: In this section you will describe the data using methods we learned for qualitative and quantitative data. This includes frequencies, measures of central tendency, measures of dispersion and any other statistics you may find within the data (percentiles, outlies, etc.).For all descriptive statistics that you find ensure that you summarize each and how/what is describes in the data.Section 3 Probabilities: In this section you will find the probability of several possible outcomes listed below. You will need to use the data to create these probabilities.1. Find the probability that a randomly selected university will be public.2. Find the probability that a randomly selected university will have an Admissions rate equal to 70% but less than 80%.3. Find the probability that a randomly selected university will have an admissions rate below 60% given that it is a private institution.Section 4 Confidence Intervals: In this section you will need to construct 95% Confidence intervals of the mean and variance of all the numerical (quantitative) data. For each please interpret the confidence interval and explain any surprising results.Section 5 Hypothesis Testing: In this section you will make some hypotheses about the data and then use what we learned in lecture/homework to test these hypotheses.1. Is the average Admissions Rate greater than 70?2. Is the average Retention Rate less than 80?3. Is the average Graduation Rate equal to 55?4. Is the average Admissions Rate for Private universities the same as that for Public?Section 6 Correlation and Regression: In this section you will calculate the correlation matrix and discuss any interesting findings or expected findings. You will also build a regression model and compare the coefficients to the correlation matrix.1. Calculate the correlation matrix for the qualitative columns.2. Build a regression model that takes the dependent variable Admissions Rate:a. Do a simple linear regression with SAT Reading as the independent variable.b. Do a simple linear regression with Average Financial Aid as the independent variable.c. Compare the two above outputs to the correlation matrix entries and discuss what you see.3. Build a regression model that takes the Variable Graduation Rate:a. Repeat a-c from part 2 and discuss the results.

The purpose of the statistics project is to go through the process that a statistician goes through when analyzing new data. You will be asked to do some Exploratory Data Analysis, describe the data using descriptive statistics and plots, answer some questions about probability of future information, create confidence intervals, and describe relations of the data through the use of correlations and linear regressions.For this project you will use StatCrunch (or any other software you are comfortable using.). You will use the data from the StatCrunch Website entitled “Sample College Data.” This is data sampled from universities from a few states on the East Coast and you will use it to work through the sections below. To find the data follow the link to StatCrunch from MyMathLab. In the Data box click the link to “Data sets” and use the search bar to find the data set “Sample College Data”, then open StatCrunch.Section 1 Exploratory Data Analysis: In this section of your analysis you will need to open the data, describe the data by data type, understand the sample size, the number of data points for each row etc.· Think about displaying the categorical (qualitative data) using pie charts or bar charts· For numerical (quantitative) look to show the data using histograms or other appropriate plots.For every plot or piece of information about the data you uncover, please summarize what the plots/information says about the “shape” of the data.Section 2 Descriptive Statistics: In this section you will describe the data using methods we learned for qualitative and quantitative data. This includes frequencies, measures of central tendency, measures of dispersion and any other statistics you may find within the data (percentiles, outlies, etc.).For all descriptive statistics that you find ensure that you summarize each and how/what is describes in the data.Section 3 Probabilities: In this section you will find the probability of several possible outcomes listed below. You will need to use the data to create these probabilities.1. Find the probability that a randomly selected university will be public.2. Find the probability that a randomly selected university will have an Admissions rate equal to 70% but less than 80%.3. Find the probability that a randomly selected university will have an admissions rate below 60% given that it is a private institution.Section 4 Confidence Intervals: In this section you will need to construct 95% Confidence intervals of the mean and variance of all the numerical (quantitative) data. For each please interpret the confidence interval and explain any surprising results.Section 5 Hypothesis Testing: In this section you will make some hypotheses about the data and then use what we learned in lecture/homework to test these hypotheses.1. Is the average Admissions Rate greater than 70?2. Is the average Retention Rate less than 80?3. Is the average Graduation Rate equal to 55?4. Is the average Admissions Rate for Private universities the same as that for Public?Section 6 Correlation and Regression: In this section you will calculate the correlation matrix and discuss any interesting findings or expected findings. You will also build a regression model and compare the coefficients to the correlation matrix.1. Calculate the correlation matrix for the qualitative columns.2. Build a regression model that takes the dependent variable Admissions Rate:a. Do a simple linear regression with SAT Reading as the independent variable.b. Do a simple linear regression with Average Financial Aid as the independent variable.c. Compare the two above outputs to the correlation matrix entries and discuss what you see.3. Build a regression model that takes the Variable Graduation Rate:a. Repeat a-c from part 2 and discuss the results.

Administer the data collection tool you created in the Topic 2 assignment. Using the data you collect, create an Excel table and complete the items below.Create two frequency tables based on two separate questions from your survey.Create a bar graph and a pie chart based on the data in the frequency tables.Determine the class intervals and create frequency distribution for each of the frequency tables.Create one frequency polygon of the data from the frequency distribution.Create an individual Excel document for each of the required items.

Considering Royal Hayat is based on Jabriya, explain in at least 500 words where you would put the facility to produce respirators. You have to discuss at least 5 factors and explain your reasoning by providing sufficient proof. You have to explain how you will bring the respirator, how will you make subcontracts, contracts with logistics, which road to use, lead times, raw materials to bring to your facility and so on. Your grade will be determined based on your ability to provide details and support of ideas. (50 Points)Important Note: Notice that based on your assumptions, design and thinking, each and every group gets different answers to these questions. Therefore, what you say, what you do, what you defend in your report is more important than simply obtaining an answer. Keep that in mind and always use systemic approach to this project, define your assumptions clearly and support them with your mind.The first factor is the integration management structure that includes all the activities involved in setting up the respirator assembly. It extends to the general infrastructure needed to meet the safety and quality requirements. In uwait it includes the medical device regulations defined by the Ministry of Health. Drug and Food control but in international terms it includes the necessary requirements from the World Health Organization. Additionally it includes the need to meet the quality control standards and the need to attain safety of consumer plus the use of such respirators in modern healthcare systems. Such medical requirement include the “Law of Soud Food and Drug Authority,” Article Five abbreviated as 25/1/1428H as issued from the Royal Decree. The regulations make it clear that Saudi Food and Drug Authority should monitor the health care equipment plus their conformity with their safe operation with other medical devices.The second factor is the scope associated with this respirator that includes the responsibilities of each stakeholder, healthcare providers handling the final respirators, the internal biomedical engineering department plus the requirements of all third part service contractors. Also it includes the manufactuer instructions for the PPM and CM, accuracy of the inventory information and maintenance management system, pre-installation and pre-procurement of medical devices, listing of manufactured respirators with market authorization or listing numbers, review of published data with respect to technical difficulties.The third factor is the resources associated in the assembly of this respirators; scheduling, human-related and organization. The scheduling includes the time frames needed to complete manufacturing the respirators in meeting the local and international demands. The human-resources includes the labor and compensation schemes of workers both technical and non-technical all working to deliver quality respirators for the public. The organizational includes the financial resources needed to set-up the infrastructure, train the team members, manage the sales, logistics and marketing ventures. In this part the most important factor is the source of these funds and direct/indirect costs involved in manufacturing the respirators.The fourth factor is the risk management involved in overcoming the manufacturing defect rates. It includes the technological/innovational risk associated with future improvement in the structure, aesthetics or working of the current respirators and how it should meet international expectations. Ethical and legal risks composed of the regulations, policies, and standards from a local, regional, and international perspective. The social/cultural risks attributed to various norms and practices by the citizens that affect directly or indirectly the finished product of these respirators. Finally, the economic risk that includes the competition from other manufacturing firms producing respirators.

Please bid if you understand and can finish in 2 hoursHow does the idea of a differential equation tie into finding integrals from Calculus II?2. Please give an example of a differential equation to solve.3. Give a totally unrelated example of an integral to solve.4. Solve each of the problems that you wrote in parts 2 and 3.5. Include a graph of the each original function along with a graph of their solution.6. Include a url that you used or would help others.

Is Sun Microsystems a good “Strategic” fit for Oracle? Why or why not?

Similar problem in LN, § 5.3, Example 5.3.6, 5.3.7. 1. (10 points)Find the critical points (also called equilibrium solutions) of the predator-prey systemx? =?3 x + 2 x y y? = 7 y?8 x yCritical PointsNote: A point is an ordered pair (x,y), and your answer must be a comma separated list of points.Similar problem in LN, § 5.3, Example 5.3.6, 5.3.7. 2. (10 points)Find the critical points (also called equilibrium solutions) of the competing species systemx? = 3 x?x2 ?2 x y y? = 2 y?y2 ?x yEquilibrium Points:Note: A point is an ordered pair (x,y), and your answer must be a comma separated list of points.See in LN, § 5.3, See Examples 5.3.8-5.3.10. 3. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =?9 x + x3y? =?2 y(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 0] , x2 =[ x2 0] .where x1 > 0 > x2. Find these components.x1 = x2 =Part 2: The Jacobian Matrix 1Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2 See in LN, § 5.3, See Examples 5.3.8-5.3.10. 4. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =?16 x + x3y? = 3 y(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 0] , x2 =[ x2 0] .where x1 > 0 > x2. Find these components.x1 = x2 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2 See in LN, § 5.3, See Examples 5.3.8-5.3.10. 5. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systex? = 4 y?y3y? =?9 x?y2

Miran Anwar, mth 235 ss21 1: Hw19-5.4-SDE-2x2NS-PP-NP. Due: 04/26/2021 at 11:00pm EDT. See in LN, § 5.4, See Subsection 5.4.3. 1. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 2x + xyy? = 3 2y? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 y1] .Find these components.x1 =y1 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1See in LN, § 5.4, See Subsection 5.4.3. 2. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 4x + 1 2xyy? = y? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ x1 y1] .Find these components.x1 =y1 =Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X01Part 4: The Jacobian Matrix at X1See in LN, § 5.4, See Subsection 5.4.4. 3. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systemx? =? 1 4x + 1 2xyy? = y? 1 2y2 ? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ 0 y1] , x2 =[ x2 y2] .Find these components.y1 =x2 =y2 = Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2See in LN, § 5.4, See Subsection 5.4.4. 4. (10 points) Part 1: Critical Points Consider the two-dimensional autonomous systex? =?x + xyy? = 9 8y? y2 ? 1 2xy(a) The critical points of the system above have the formx0 = [0 0] , x1 =[ 0 y1] , x2 =[ x2 y2] .Find these components.y1 =x2 =y2 = 2Part 2: The Jacobian Matrix Part 3: The Jacobian Matrix at X0 Part 4: The Jacobian Matrix at X1 Part 5: The Jacobian Matrix at X2See in LN, § 5.4, See Example 5.4.5. 5. (10 points)