Question: points A (-1,-2),B(7,2) and C (k, 4), where K is a constant, are the vertices of triangle ABC. Angle ABC is a right angle. Calculate the value of K?

Answers
ABC is a right angle thus AC is the hypotenuse.  Length of AB=sqrt((7+1)^2+(2+2)^2)=sqrt(64+16)=sqrt100=10.BC=sqrt((k-7)^2+(4-2)^2)=sqrt((k-7)^2+4)AC=sqrt((k+1)^2+(4+2)^2)=sqrt((k+1)^2+36)Pythagoras gives: AC^2=AB^2+BC^2 hence(k+1)^2+36=100+(k-7)^2+4Expand, simplify etc and you find the value of k.
marias
17 June 2018
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tausif045
17 June 2018
Have a go at drawing it out on graph paper. Plot the two points you've been given for A and B and connect them. Use your protractor to draw a line at a right angle perpendicular to the line AB at point B. Extend that line to where it intersects at y=4 and this point of intersection will give you the value of K. Hope that makes sense?
Sammi M.
20 June 2018
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Miriam F.
30 June 2018
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monika_yadav
03 July 2018
Gradient of side AB = (2 - (-2)) / (7 - (-1)) = 1/2So gradient of (perpendicular) side BC = -1 / (1/2) = -2Using y = mx + c , with m = -2 , we can sub in the (7,2) x,y coordinates from B to find the constant c. Hence we can use c and the y coordinate of point C to find x coordinate k:y = -2x + c2 = -14 + cc = 16So, for point C, x = k = (c - y)/2 = (16 -4) / 2 = 6k = 6
Calem C.
12 July 2018
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coolsubh13
25 July 2018
You have to find a value of k such that AB and BC are perpendicular lines, or their gradients multiply to give -1. The formula for the gradient is (y2-y1)/(x2-x1)gradient for AB(2--2)/(7--1) = 4/8 = 1/2gradient for BC (4-2)/(k-7) = 2/(k-7)now equate the product to -1 and rearrange(1/2)*(2/(k-7)) = -1k-7 = -1k = 6
Aleksandra J.
27 July 2018
IMG_20180729_143851_150.jpg
sanharshal
29 July 2018
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Precision Tree

Jim Sellers considers producing a new type of electric razor for men. If the market is favorable, he would get a return of 100000, but, if the market is unfavorable, he would lose60000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research Company to gather additional information about the razor market. Bush has suggested that Jim either use a survey, or a pilot study to test the market. The survey is a sophisticated questionnaire administered to a test market, and costs 5000. Another alternative is to run a pilot study. This would involve producing a limited number of new razors and trying to sell them in two representative American cities. The pilot study is more accurate but is also more expensive: it costs20000. Ron Bush has proposed Jim to conduct either the survey, or the pilot study before making any decision regarding the production of the new razor. Jim is however not convinced that the contribution of the survey, or that of the pilot study, is worth its cost.

Ron Bush has proposed Jim to conduct either the survey, or the pilot study before making any decision regarding the production of the new razor. Jim is however not convinced that the contribution of the survey, or that of the pilot study, is worth its cost. Jim estimates that the unconditional probability of a successful market is 0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7 and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study result given an unfavorable market is 0.9, and the probability of an unfavorable pilot study result given a favorable market for razors is 0.2. Jim wants to use these probability estimates to decide whether to do the survey, or the pilot study, or none.

A) Using PrecisionTree, draw a decision tree to solve Jims problem. Explain how you have calculated all the probabilities that you report on the tree. Define clearly each decision node, event node, decision that you can take, and possible outcome for the random variables.

Let: . FS denote the “favorable survey" outcome . US denote the “unfavorable survey" outcome . FP denote the “favorable pilot study" outcome . UP denote the “unfavorable pilot study" outcome . F denote the “favorable market" scenario . U denote the “unfavorable market" scenario

B) What is the best decision for Jim amongst opting for survey or pilot study or none? Include the decision tree in your analysis/report.

C) Suppose that the cost of the pilot study can be cut down to $15,000. Does it affect Jims best decision?

Probability trees

Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable he would get a return of 100,000, but if the market for this new type of razorwere unfavorable, he would lose60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested that Jimeither use a survey or a pilot study to test the market. The survey would be a sophisticated questionnaire administered to a test market. It will cost 5,000. Another alternative is to run a pilot study. This would involve producing a limited number of the new razors and tying to sell them in two cities that are typical of American cities. The pilot study is more accurate e but is also more expensive. It will cost20,000. Ron Bush has suggested that it would be a good idea for Jim to conduct either the survey or the pilot before Jim makes the decision concerning whether to produce the new razor. ButJim is not sure if the value of the survey or the pilot is worththe cost. Jim estimates that the probability of a successful market without performing a survey or pilot study is0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7, and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study given an unfavorable market is 0.9, and the probability of ann unsuccessful pilot study result given a favorable market for razors is 0.2.

Draw the decision tree for this problem without the probability values. Computer the revised probabilities needed to complete the decision, and place these values in the decision tree. What is the best decision for Jim? Use Expected MonetaryValue (EMV) as the decision criterion.

Total marks for this assignment are 100; this contributes 25% of the module. Task 1: (30 marks)

A student measured the data in the tables below by recording the time, t, it took two different cylinders (one solid and one hollow) with the same dimensions to roll, from rest, down a slope for a fixed distance.

Theory suggests that the hollow cylinder should take longer to travel the same distance as the solid cylinder. Hollow Cylinder times, t/s Solid Cylinder times, t/s 2.08 2.03 1.88 1.88 2.07 2.07 1.79 1.87 2.05 2.01 1.80 1.90 2.04 2.16 1.85 1.78 2.03 2.03 1.90 1.81 2.12 2.01 1.76 1.74 2.06 2.05 1.62 1.73 2.07 2.08 1.72 1.79 1.97 2.11 1.77 1.87 1.99 2.12 1.77 1.82 2.10 2.00 1.81 1.79 2.06 2.01 1.77 1.84 2.07 2.02 1.81 1.83 2.06 1.99 1.84 1.77 2.13 2.07 1.86 1.80 1.98 2.10 1.80 1.73 2.04 2.02 1.78 1.77 2.05 2.11 1.76 1.84 2.03 2.08 1.82 1.95 2.02 2.08 1.81 1.87 2.00 2.07 1.67 1.79 1.97 2.12 1.84 1.89 2.10 2.03 1.74 1.87

To analyse the data it is suggested to the student that she groups the data and produces a histogram for each cylinder showing the distribution of rolling times. The student consults her lecturer who suggests the following class intervals, where t is the rolling time in seconds: A B C 1.50

a.The student decides to use the class intervals shown in column C in the table, explain why this is an appropriate choice for the data from this experiment.

  1. Construct histograms for the experimental data using the class intervals shown in column C of the table above.

  2. Calculate the mean rolling time for each of the cylinders.

  3. Produce a spreadsheet to calculate the standard deviation in the rolling time for each cylinder – the spreadsheet table should show the additional columns required and a print out including the formulae you have used in each cell is required.

  4. Use the “Comparison of Means Test” (Shown below) to determine whether there is significant difference in the rolling time between the two cylinders.

Comparison of means test (i) Calculate the difference between the mean values of each data set.

(ii) Calculate the “Standard error of the difference” using the formula below:

Standard error of difference = √((S1/n1)+ ) (S2/n2) (the frist one is S1 2 and next is S2 2 )

Where: s1 is the standard deviation of data set 1, n1 is the number of measurements in data set 1, s2 is the standard deviation of data set 2 and n2 is the number of measurements in data set 2.

If the difference between the mean values of each data set is greater than twice the standard error of the difference then you can be 95% confident that there is a significant difference between the two sets of data i.e. whatever has been changed between one data set and the other has influenced the results.