Homework Help for Mathematics

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Mathematics is an exact and deductive science that studies abstract entities such as numbers, geometrical figures, symbols ans their relation.

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10. If y = (c) satisfies y = cy, then when (a, y) = (2e, Ve), the derivative - - | వ

1. 18 marks) Factor the following invertible matrix A as a product of elementary matrices. Do not verify the result [ 1 2 01 AT 0 1 0 | 3 2 4

1. Evaluate the limit, or show that the limit does not exist: OR lim 3700 7x3 + use et

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. 3. What is the sampling distribution of the sample mean score for a random sample of 36 students? A) Approximately Normal, but the approximation is poor. B) Approximately Normal, and the approximation is good. C) Exactly Normal. D) Neither Normal nor non-Normal. It depends on the particular 36 students selected.

10. The graph of y = 373 + 13x² + 190 +3 has a slant asymptote which is the line (2 + 2)2 Ay= By= 30 - 1 y= 3x + 7 Dy= 32 Ey= 3x + 1

2. Find the value of lim 2-1 -2 -1

9. The Lemon brand cars have a transmission which fails with probability .6, and brakes which fail with probability .3; the two kinds of failures occur inde- pendently. What is the probability that exactly one of the failures occurs when you drive a Lemon? (a) .72 (b) .28 (c) .46 (d) .54 (e) .9 (f) none of the above

PROBLEM 03: Bob Loblaw drives past 4 stoplights on his way to work each morning. Each time he arrives at a stoplight, there is an 80% chance that the stoplight will be red. On a particular morning, what is the probability that exactly three of the four stoplights he passes will be red? A) 4.(-2):(.8)' B) 24.(.8)': (.2)' C) 4.(.8) (2) D) (.8) (-2)' E) (-2)(.8)' N) none of the above

8. (17 marksYou are operating a monopoly firm and consultants have told you that the demand q for your product as a function of the price p you choose is q(P) = 100 - VP a) (2 marks] Give ranges on p, q which would typically be imposed in considering alternate pricing strategies.

1 2 -1111 4. A linear system is represented by the following augmented coefficient matrix 1 5 47. 0 -4 41-8] This linear system has A) no solutions B) exactly one solution D) infinitely many solutions C) exactly two solutions E) none of these

PROBLEM 13: A fair coin is tossed until a total of two Tails land up, or until a total of three Heads land up, whichever comes first. Find the expected number of tails tossed. A) 4/3 B) 25/16 C) 1 D) 2 E) none of the above

A company makes two products, A and B, whose joint demand functions are 9. = 90 -4p. -2p. 9,- 50-2p. --2p. a) Determine whether products A and B are complimentary, competitive or neither Show your work here and put your concluding sentence in the box provided.

(d) Let f(0) = 1 + x 2 – 7x + 100. Find the point on the graph of f at which the tangent line has slope -8.

14. The solution to the separable differential equation 222, subject to y(-2)=1, y> 0 is ) = /431 c) v= f(x+3* +4 ) >= 3=42! D) Y= {+3+2 E) none of these

mark 18. Consider the linear system Ax = b where A is a 5 x 5 invertible matrix. Which one of the following statements is false? A: There is a row of five zeroes in the row-reduced echelon form of A. | B: The rank of A is 5. C: The rank of Ab] is 5. D: The system Ax = b has a unique solution. E: The system Ax = 0 has only the trivial solution.

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