VExample 3-27. If p1 = P(A), P2 = P (B), P3 = P (AnB), (Pi, P2 P3 > 0), express the following in terms of p1, p2, P3 (a) P (A U B ) , (b) P(Ā UB), (c) P (Ā OB), (d) P (Ā UB), (e) P (Ā O B) () P (An B ), (g) P (A IB), (h) P (B I A), (i) P[Ā O(A UB)].
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- Population Genetics-First Cousins This is a continuation of Exercise 5. Double first cousins are first cousins in two waysthat is, each of the parents of one is a sibling of a parent of the other. First cousins in general have six different grandparents whereas double first cousins have only four different grandparents. For mating between double first cousins, the proportions of the genotypes of the children can be accounted for in terms of those of parents, grandparents, and great-grandparent: 3=122+14+18. a. Find all solutions to the cubic equation above and Identify which is 1. b. After 5 generations, what proportion of the population will be homozygous? c. After 20 generations, what proportion of the population will be homozygous? 5. Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?Producing one lot of doohickeys requires 0.4 lots of doohickeys and 1.7 lots of thingomajigs; producing one lot of thingomajigs requires 0.1 lots of doohickeys and 0.2 lots of thingomajigs.In a particular class, exams are worth 50%50% of the overall grade, quizzes are worth 30%30% of the overall grade, homework is worth 15%15% of the overall grade, and class participation is worth 5%5% of the overall grade. A particular student has earned an average score of 82.2%82.2% on the exams, 76.3%76.3% on the quizzes, 90.0%90.0% on the homeworks, and 100.0%100.0% on class participation. What is this student's overall grade in the course? Report the answer with one digit after the decimal point. overall grade:
- Jo, a store owner, has an option of selling hot drinks or halu-halo during a championship game. The profits will depend on weather conditions. On a clear day, the profits will be P 1,500 and P9,000 on a rainy day if she sells hot drinks. If she sells halu-halo, her profits will be P 10,000 on a clear day and P5,000 an a rainy day. It was learned that during the time of the year 65% of the days are clear and 35%) are rainy. What type of refreshments should the owner sell? Make a decision tree and state your decision.In a classic study of problem solving, Duncker (1945) asked participants to mount a candle on a wall in an upright position so that it would burn normally. One group was given a candle, a book of matches, and a box of tacks. A second group was given the same items, except that the tacks and the box were presented separately as two distinct items. The solution to this problem involves using the tacks to mount the box on the wall, creating a shelf for the candle. Duncker reasoned that the first group of participants would have trouble seeing a new function for the box (a shelf) because it was already serving a function (holding tacks). For each participant, the amount of time to solve the problem was recorded. Data similar to Duncker’s are as follows. Time to Solve Problem (in sec.) Box of Tacks Tacks and Box Separate 128 42 160…Research has shown that losing even one night's sleep can have a significant effect on performance of complex tasks, such as problem solving (Linde& Bergstroem,1992). To demonstrate this phenomenon, a sample of n : 25 college students was given a problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep inbetween the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students averaged M, : 4.7 points better on the first test with a variance of s2 : 64 for the difference scores. a. Do the data indicate a signficant change in problem-solving ability? Use a two-tained test with a: .05"
- 2/3(6+d) -2d= -3/4(d-8) Pls expain veryyy simply,I'm only in seventh grade!nternet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 44 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year? MicrosoftTime WarnerYahooGoogleVx (-y +2,22 +323, 2233) =? 0 (3y -3222, 223, -2 + 2) 0 (-3y +3X372, -332, 1 + 2x) 0 (2y +2224-423,1 + 22) 0 (-34-3222, 42,1 +22) 0 (-3y +322y2, -3'2, 1 + 2)
- if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y -5=0A commuter owns 2 cars, 1 compact and 1 standard model. About ¾ of the time he uses the compact to travel to work, and about ¼ of the time the larger car is used. When he uses the compact car, he usually gets home by 5:30 p.m. about 75% of the time; if he uses the standard-sized car, he gets home by 5:30 p.m. about 25% of the time (but he enjoys the air conditioner in the larger car). a) If he gets home at 5:35 p.m., what is the probability that he used the compact car? b) If he gets home at 5:30 p.m., what is the probability that he used the standard model?
