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A square is inscribed in a circle that is inscribed in a square. Find the ratio of the areas of the two squares.
The population of a city increases at a rate proportional to the present number. It has an initial population of 50000 that increases by 15% in 10 years. What will be the population in 30
years?
Mpohlo bought nine shirts at a total cost of R2 520,00. The large shirts costs R300,00 each and the small
shirts costs R240,00 each. Choose the correct statement.
[1] He bought twice as many small shirts as large shirts
[2] He bought three large shirts
[3] He paid R720 in total for the small shirts
[4] He paid double the amount for the large shirts as the amount that he paid for the small shirts
QUESTION 3 Let A = [ 4 0 1 −2 1 0 −2 0 1 ](its 3by3 matrix).
3.1. Find the eigenvalues of A.
3.2. For each eigenvalue of A find the corresponding eigenvectors.
3.3. Is A diagonalizable? Explain. If it is diagonalizable, then find P such that 𝐷 = 𝑃 −1𝐴𝑃 is a diagonal matrix. Do not compute 𝑃 −1(show all step!) .
When solving for x in the equation
((9x + 7)/2)-(x-(x-2))/7)=36
the equation that is NOT correct, is
[1] ((9x + 7)/2)-[(7x/7)-((x-2)/7)]=36
[2] ((9x + 7)/2)-((7x-x-2)/7)=36
[3] ((9x + 7)/2)-((6x+2)/7)=36
[4] 7(9x + 7) − 2(6x + 2) = 14 × 36.
For each of the linear operators below, determine whether it is normal, self adjoint, or neither
(a) T / (R ^ 2) -> R ^ 2 defined by T(x, y) = (2x - 2y, - 2x + 5y)
(b) T / (C ^ 2) -> C ^ 2 defined by T(x,y)=(2x+iu.x+2y)
Jemima has three boxes whose total weight is 51 1
5 kg. Box B weighs 5 1
2 kg more than box A and box C
weighs 3 1
5 kg more than box B. Choose the correct statement.
[1] Box A weighs 17 5
6 kg.
[2] Box C weighs 21 1
30 kg.
[3] Box A weighs 42 1
2 kg.
[4] Box B weighs 12 1
3 kg
8. Santa always leaves plans for his elves to determine the order in which the reindeer will pull his sleigh. This year, for the Asian leg of his journey, his elves are working on the following schedule that will form a single line of nine reindeers: "Comet behind Rudolph, Prancer and Cupid. Blitzen behind Cupid and in front of Donder, Vixen and Dancer. Cupid in front of Comet, Blitzen and Vixen. Donder behind Vixen, Dasher and Prancer. Rudolph behind Prancer and in front of Donder, Dancer and Dasher. Vixen front of Dancer and Comet. Dancer behind Donder, Rudolph and Blitzen. Prancer in front of Cupid, Donder and Blitzen. Dasher behind Prancer and front of Vixen, Dancer and Blitzen. Donder behind Comet and Cupid. Cupid in front of Rudolph and Dancer. Vixen behind Rudolph, Prancer and Dasher." What is the order in which the reindeer will pull Santa's sleigh?
if the samples are 16, 17, 15, 24, 20, 20, 20, 23, 18, and 19. what is the point estimate of the population standard deviation?
if the given samples are 45, 47, 48, 51, 50, 55, 49, 48, 55, and 54. compute the point estimate of the population variance.
