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- An analysis of first-year students at a college revealed that 1/5 of the first-year women were from homes where both parents were professionals. Of these, 3/4 were interested in the same profession as one or both of their parents. If this latter group is made up of 15 students, how many first-year women are there?In February 2022, suppose that a group of 100 students are taking UCR test as follows: 40 are taking Econ 107 , 40 are taking Econ 105B , and the remaining students are taking Econ 104A . Suppose the grades are given as follows: Econ 107 results: 10 students scored 60 out of 100 points, 20 students scored 80 out of 100 points, and rest scored 90 out of 100 points. Econ 105B results: 30 students scored 80 out of 100 points, 5 students scored 90 out of 100 points, and rest scored 100 out of 100 points. Econ 104A results: 10 students scored 88 out of 100 points, 5 students scored 80 out of 100 points, and rest scored 96 out of 100 points. Give the information above, please solve the following questions: i. Find all marginal and joint probabilities for each class and grade? ii. Find the probability of that the grade is 60 given that students are taking Econ107 ? Find the probability that a student is taking 104A given that he/she scored 80 points? iii. Find the mean and the variance of all…Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.
- Suppose that in a closed economy GDP is equal to 11,000, taxes are equal to 2,500, consumption equals 7,000, and government purchases equal 3,000, the outcome is private saving and public savings2,500 and -1500,respectively. Select one: a. True b. Falseassume that the 160 students who take this exam will receive one of 24 grades i. What does the pigeonhole principle tell us about the exam results of these students? ii. Regardless of the scores assigned, how many other students must get the same grade as you?7.) Suppose that thirty-two students signed up for classes during an orientation session. If exactly twenty of them signed up for Chemistry and exactly sixteen of them signed up for English, how many of them signed up for both Chemistry and English?
- Here's a problem that was used as the basis of a television show to illustrate the difference between the way a human mind approaches such a problem and the brute-force approach of a computer that finds the solution by trying all possible 40,320 different arrangements of the digits. Place the digits from 1 though 8 in the eight circles shown in the diagram, but with this restriction: no two digits next to each other in serial order may go in circles that are connected by a direct line. (For example: if 2 is placed in the top circle, neither 1 nor 3 may be placed in any of the three circles in the horizontal row beneath it because each of these circles is connected to the top circle by a direct line.) There is only one solution.Suppose that 4 Pistons need to be installed in a new engine block. there is a production run of 100 Pistons. if the new pistons to be installed in the engine block must come from this production run, how many different possible ways are there to install these pistons?(I am reposting because I just need the answer to part D now, and was told to post it seperately after getting the answers to the rest of it.)
- How would you prove #14 and #15 using either postulate SSS or SAS? And can a problem be proven by both or just one?1. Due to the high incidence of crime, a company is giving its employees new and secured access to the company. Instead of leaving the doors open, they are installing a card system. To open the door, employees must insert a card into a slot. If a green light comes on, it is okay to turn the handle and open the door; if a yellow light comes on it indicates the door is locked from inside and you cannot enter. Suppose that 90% of the time when the card is inserted, the door should open because it is not locked from the inside. When the door should open, the system makes errors 2% of the time. That is, the green light will appear 98% of the time. When the door should not open, the system makes errors 5% of the time (green light appears). Suppose you inserted the card and the light is green, what is the probability the door will open?is there a step missing after "Hence"?