Search & Filtering
Construct all random samples consisting two observations from the given data. You are asked to guess the average weight of the six watermelons by taking a random sample without replacement from the population.
Watermelon A B C D E F
Weight (in pounds) 19 14 15 9 10 17
- For what values of h the vectors
⟶ [ 1 ⟶ [ -1 ⟶ [ 5
u1 = -3 u2 = 9 u3 = -7
-2 ] -6 ] h ]
are linearly independent? (Show all working)
11•j=1(mod 4). Find j
(D^2-2D+5)y=x+5
Consider a population consisting of 4 members whose weights (in pounds) are 148, 156, 176 and 184.
i) Calculate the population mean and the population standard deviation (2marks)
ii) Draw all possible samples of size two, with replacement, from the population. Calculate the mean of each sample and obtain the distribution of the sample means .
The human resource management of an insurance company has organized a
recruitment process where all the applicants are MBA graduates. There are 10
applicants and the target for the firm is to recruit 2 MBA graduates. Assuming that the
applicants are independent and each applicant has the same probability of being a
perfect fit, what is the probability that the 5th individual interviewed will be the second
MBA graduate interviewed who is a perfect fit?
A sample of 40 children from Kafue state showed that the mean time they spend watching television is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 35 children from Chilanga showed that the mean time spent by them watching television is 23.5 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent watching television by children in Kafue state is greater than that for children in Chilanga? Assume that the standard deviations for the two populations are equal
Given the following points: 𝑃0 = (−1, −1,3),𝑃1 = (−1,3, −1),𝑃2 = (3,5,3)𝑃3 = (3,3,5), 𝑃4 = (− 1 2 , 3,3). a) Show that 𝑃0, 𝑃1,𝑃2, 𝑃3 lie on the same plane, H, and find the implicit equation of H. A pyramid is defined by the plane H and the following triangular faces: (𝑃0,𝑃2,𝑃4 ), (𝑃0, 𝑃1,𝑃4 ), (𝑃1,𝑃3,𝑃4 ), (𝑃2,𝑃3, 𝑃4 )
b) Determine the outwards facing unit normal vector of each triangular face. c) Calculate the implicit representation of the planes containing each face of the shape. d) For each of the following points determine if it is inside or outside the shape (hint: the point is inside the shape if it lies on the same side for all the planes) i) (− 1 2 , 1,2) ii) (1,0,1) iii) (3,2,4)
Let 𝑙1 be the line that passes through 𝑝1 = (2,9,8) and 𝑝2 = (1,9,9) and let 𝑙2 be the line that passes through 𝑝3 = (1,1,1) and 𝑝4 = (2,5,4) a) Find out if the two lines intersect and if so, find the intersection point of 𝑙1 and 𝑙2 b) Let 𝑆 be the sphere whose center is the intersection of 𝑙1 and 𝑙2 and whose radius is 𝑟 = 4. Write the implicit representation of the sphere. c) Find the implicit representation of the two planes 𝑃1 and 𝑃2 that are tangent to the sphere 𝑆 at the points of intersections of 𝑙1 towards 𝑝2 and 𝑙2 towards 𝑝4 , respectively.
A 2D light ray is sent from point 𝑃 = (1, −1). It is reflected off a surface (represented by a line) at 𝑅 = (6,11), and reaches a receiver point at 𝑄 = (25,13 2 17) . Note that light rays hitting a surface reflect in a direction which is symmetric according to the normal. a) Find the implicit representation of the surface such that its “up” is towards 𝑃 (i.e. it faces the incoming ray). b) Find the angle between the ray and the surface.
