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I need answers for items no. 18 and 19.
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- Consider the information in Exercise 2, but suppose you know that the area of the region defined by the intersection of the square and the circle measures 5. What is the area of the entire colored region? 2. The area of the square is 12, and the area of the circle is 30. Does the area of the entire shaded region equal 42? Why or why not?A circle K with a radius of R is given, along with a point A inside the circle, situated at a distance of a from the center of the circle. A point B is chosen randomly within the circle. Determine the probability that the circle with center A and radius ∣AB∣ will be completely within the circle K.Consider a segment AB of length l. point M and N are chosen randomly within this segment . what is the probability that point M is closer to point N than it is to point A ?
- Show that, If M and N are nbds. of a point p, then M∩N is also a nbd. of p. No type answerSuppose that an equilateral triangle with sides of length 9 ft contains 10 points randomly placed. Use the pigeonhole principle to prove that 2 of those points are at least 3 ft apart.An instructor has given a short quiz consisting of nvo parts. For a randomly selected student, let X= the number of points earned on the first part and Y= the number of points earned on the second part. Suppose that thejoint pmf of X and Yis given in the accompanying table. a. If the score recorded in the grade book is the total number of points earned on the nvo parts,what isthe expected recorded score E(X + Y)? b. If the maximum of the two scores is recorded,what isthe expected recorded score? A random variable is normally distributed with a mean of m =50 and a standard deviation of <T =5. Sketch a normal curve for the probability density Label the horizontal ax. is with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 35 and 65). What is the probability…
- Which of the following is always true about the lengths of the SHD and SD of skew lines? Choose the best answer. a. Shortest Horizontal Distance > Shortest Distance b. Shortest Horizontal Distance not equal to Shortest Distance c. Shortest Horizontal Distance >= Shortest Distance d. Shortest Horizontal Distance <= Shortest Distance e. Shortest Horizontal Distance < Shortest Distance f. Shortest Horizontal Distance = Shortest DistanceThe fireman of the project measures the interior angles of a pentagonal lot, and comes out with the following data on the lot. No. of Measurement∠A = 99°30' 3 times ∠B = 91°00' 4 times∠C = 101°20' 4 times∠D = 98°40' 5 times∠E = 150°30' 2 times Find the most probable value of the five(5) interior angles considering the no. of measurement made on each angles?A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1100 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. At least enter your response here% of adults in the country would travel into space on a commercial flight if they could afford it. B. 3030% of adults in the country would travel into space on a commercial flight if they could afford it. C. The percentage adults in the country who would travel into space on a commercial flight if they could…
- A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1100 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. At least enter your response here% of adults in the country would travel into space on a commercial flight if they could afford it. B. enter your response here% of adults in the country would travel into space on a commercial flight if they could afford it. C. The percentage adults in the country who would travel into space on a commercial…A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d belowA research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 30% say that they would travel into space on a commercial flight if they could afford it. At α=0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.