Path To College Mathematics
1st Edition
ISBN: 9780134654409
Author: Martin-Gay, K. Elayn, 1955-
Publisher: Pearson,
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Chapter 8.1, Problem 54ES
To determine
To find the empirical probability that number belongs to class 70-79
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Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.Student AStep 1:1/Cos x * 1/sin x = cot x + tan xStep 2: 1/cos x sin x = cot x + tan xStep 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan xStep 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan xStep 5: cos x/sin x + sin x/cos x = cot x + tan xStep 6: cot x + tan x = cot x + tan xStudent BStep 1: sec x csc x = cos x/ sin xStep 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin xStep 3: sec x csc x = cos^2x + sin^2x/cos x sin xStep 4: sec x csc x = 1/cos x sin xStep 5: sec x csc x = (1/cos x), (1/sin x)Step 6: sec x csc x = sec x csc xPart A: Did either student verify the identity properly? Explain why or why not. Part B: Name two identities that were used in Student A's verification and the steps they appear in.
2. [15] Let X and Y be two discrete RVs whose joint PMF is given by the following table:
y
Px,y(x, y)
-1
1
3
0
0.1
0.04
0.02
I
2
0.08
0.2
0.06
4
0.06
0.14
0.30
(a) Find P(X ≥ 2, Y < 1).
(b) Find P(X ≤Y - 1).
(c) Find the marginal PMFs of X and Y.
(d) Are X and Y independent? Explain
(e) Find E(XY) and Cov(X, Y).
Let sinθ = 2√2/5 and π/2 < θ < πPart A: Determine the exact value of cos 2θ.Part B: Determine the exact value of sin(θ/2)
Chapter 8 Solutions
Path To College Mathematics
Ch. 8.1 - Prob. 1ESCh. 8.1 - Prob. 2ESCh. 8.1 - For each set of numbers, find the mean, median,...Ch. 8.1 - Prob. 4ESCh. 8.1 - Prob. 5ESCh. 8.1 - Prob. 6ESCh. 8.1 - Prob. 7ESCh. 8.1 - For each set of numbers, find the mean, median,...Ch. 8.1 - Prob. 9ESCh. 8.1 - Prob. 10ES
Ch. 8.1 - Prob. 11ESCh. 8.1 - Prob. 12ESCh. 8.1 - Prob. 13ESCh. 8.1 - The ten tallest buildings in the world, completed...Ch. 8.1 - Prob. 15ESCh. 8.1 - Prob. 16ESCh. 8.1 - Prob. 17ESCh. 8.1 - Prob. 18ESCh. 8.1 - Prob. 19ESCh. 8.1 - During an experiment, the following times (in...Ch. 8.1 - Prob. 21ESCh. 8.1 - Prob. 22ESCh. 8.1 - Prob. 23ESCh. 8.1 - Prob. 24ESCh. 8.1 - Prob. 25ESCh. 8.1 - Prob. 26ESCh. 8.1 - Prob. 27ESCh. 8.1 - Prob. 28ESCh. 8.1 - Prob. 29ESCh. 8.1 - Prob. 30ESCh. 8.1 - Below are lengths for the six longest rivers in...Ch. 8.1 - Prob. 32ESCh. 8.1 - Prob. 33ESCh. 8.1 - Prob. 34ESCh. 8.1 - Prob. 35ESCh. 8.1 - Prob. 36ESCh. 8.1 - Prob. 37ESCh. 8.1 - Prob. 38ESCh. 8.1 - Prob. 39ESCh. 8.1 - Prob. 40ESCh. 8.1 - Prob. 41ESCh. 8.1 - Prob. 42ESCh. 8.1 - Prob. 43ESCh. 8.1 - Prob. 44ESCh. 8.1 - Prob. 45ESCh. 8.1 - Prob. 46ESCh. 8.1 - Prob. 47ESCh. 8.1 - Prob. 48ESCh. 8.1 - Prob. 49ESCh. 8.1 - Prob. 50ESCh. 8.1 - Prob. 51ESCh. 8.1 - Prob. 52ESCh. 8.1 - Prob. 53ESCh. 8.1 - Prob. 54ESCh. 8.1 - Prob. 55ESCh. 8.1 - Prob. 56ESCh. 8.1 - Prob. 57ESCh. 8.1 - Prob. 58ESCh. 8.1 - Prob. 59ESCh. 8.1 - Prob. 60ESCh. 8.1 - Prob. 61ESCh. 8.1 - Prob. 62ESCh. 8.2 - Prob. 1ESCh. 8.2 - Prob. 2ESCh. 8.2 - Find the range for each data set. See Example 1....Ch. 8.2 - Prob. 4ESCh. 8.2 - Prob. 5ESCh. 8.2 - Prob. 6ESCh. 8.2 - Prob. 7ESCh. 8.2 - Prob. 8ESCh. 8.2 - Prob. 9ESCh. 8.2 - Prob. 10ESCh. 8.2 - Prob. 11ESCh. 8.2 - Prob. 12ESCh. 8.2 - Prob. 13ESCh. 8.2 - Prob. 14ESCh. 8.2 - Prob. 15ESCh. 8.2 - Prob. 16ESCh. 8.2 - Prob. 17ESCh. 8.2 - Prob. 18ESCh. 8.2 - Prob. 19ESCh. 8.2 - Prob. 20ESCh. 8.2 - Prob. 21ESCh. 8.2 - Prob. 22ESCh. 8.2 - Prob. 23ESCh. 8.2 - Prob. 24ESCh. 8.2 - Prob. 25ESCh. 8.2 - Prob. 26ESCh. 8.2 - Prob. 27ESCh. 8.2 - Prob. 28ESCh. 8.2 - Prob. 29ESCh. 8.2 - Prob. 30ESCh. 8.2 - Prob. 31ESCh. 8.2 - Prob. 32ESCh. 8.2 - Prob. 33ESCh. 8.2 - Prob. 34ESCh. 8.2 - Prob. 35ESCh. 8.2 - Prob. 36ESCh. 8.2 - Prob. 37ESCh. 8.2 - Prob. 38ESCh. 8.2 - Prob. 39ESCh. 8.2 - Prob. 40ESCh. 8.2 - Prob. 41ESCh. 8.2 - Prob. 42ESCh. 8.3 - Prob. 1ESCh. 8.3 - Prob. 2ESCh. 8.3 - Prob. 3ESCh. 8.3 - Prob. 4ESCh. 8.3 - Prob. 5ESCh. 8.3 - Prob. 6ESCh. 8.3 - Prob. 7ESCh. 8.3 - Prob. 8ESCh. 8.3 - Prob. 9ESCh. 8.3 - Prob. 10ESCh. 8.3 - Prob. 11ESCh. 8.3 - Prob. 12ESCh. 8.3 - Prob. 13ESCh. 8.3 - Prob. 14ESCh. 8.3 - Prob. 15ESCh. 8.3 - Prob. 16ESCh. 8.3 - Prob. 17ESCh. 8.3 - Prob. 18ESCh. 8.3 - Prob. 19ESCh. 8.3 - Prob. 20ESCh. 8.3 - Prob. 21ESCh. 8.3 - Prob. 22ESCh. 8.3 - Prob. 23ESCh. 8.3 - Prob. 24ESCh. 8.3 - Prob. 25ESCh. 8.3 - Prob. 26ESCh. 8.3 - Prob. 27ESCh. 8.3 - Prob. 28ESCh. 8.3 - Prob. 29ESCh. 8.3 - Prob. 30ESCh. 8.3 - Prob. 31ESCh. 8.3 - Prob. 32ESCh. 8.3 - Prob. 33ESCh. 8.3 - Prob. 34ESCh. 8.3 - Prob. 35ESCh. 8.3 - Prob. 36ESCh. 8.3 - Prob. 37ESCh. 8.3 - Prob. 38ESCh. 8.3 - Prob. 39ESCh. 8.3 - Prob. 40ESCh. 8.3 - Prob. 41ESCh. 8.3 - Prob. 42ESCh. 8.3 - Prob. 43ESCh. 8.3 - Prob. 44ESCh. 8.3 - Prob. 45ESCh. 8.3 - Prob. 46ESCh. 8.3 - Prob. 47ESCh. 8.3 - Prob. 48ESCh. 8.3 - Prob. 49ESCh. 8.3 - Prob. 50ESCh. 8.3 - Prob. 51ESCh. 8.3 - Prob. 52ESCh. 8.3 - Prob. 53ESCh. 8.3 - Prob. 54ESCh. 8.3 - Prob. 55ESCh. 8.3 - Prob. 56ESCh. 8.3 - Prob. 57ESCh. 8.3 - Prob. 58ESCh. 8.3 - Prob. 59ESCh. 8.3 - Prob. 60ESCh. 8.3 - Prob. 61ESCh. 8.3 - Prob. 62ESCh. 8.3 - Prob. 63ESCh. 8.3 - Prob. 64ESCh. 8.3 - Prob. 65ESCh. 8.3 - Prob. 66ESCh. 8.3 - Prob. 67ESCh. 8.3 - Prob. 68ESCh. 8.3 - Prob. 69ESCh. 8.3 - Prob. 70ESCh. 8.3 - Prob. 71ESCh. 8.3 - Prob. 72ESCh. 8.3 - Prob. 73ESCh. 8.3 - Prob. 74ESCh. 8.3 - Prob. 75ESCh. 8.3 - Prob. 76ESCh. 8.3 - Prob. 77ESCh. 8.3 - Prob. 78ESCh. 8.3 - Prob. 79ESCh. 8 - Prob. 1VCCh. 8 - Prob. 2VCCh. 8 - Prob. 3VCCh. 8 - Prob. 4VCCh. 8 - Prob. 5VCCh. 8 - Prob. 6VCCh. 8 - Prob. 7VCCh. 8 - Prob. 8VCCh. 8 - Prob. 9VCCh. 8 - Prob. 10VCCh. 8 - Prob. 11VCCh. 8 - Prob. 12VCCh. 8 - Prob. 13VCCh. 8 - Prob. 14VCCh. 8 - Prob. 15VCCh. 8 - Prob. 16VCCh. 8 - Prob. 1RCh. 8 - Prob. 2RCh. 8 - Prob. 3RCh. 8 - Prob. 4RCh. 8 - Prob. 5RCh. 8 - Prob. 6RCh. 8 - Prob. 7RCh. 8 - Prob. 8RCh. 8 - Prob. 9RCh. 8 - Prob. 10RCh. 8 - Prob. 11RCh. 8 - Prob. 12RCh. 8 - Prob. 13RCh. 8 - Prob. 14RCh. 8 - Prob. 15RCh. 8 - Prob. 16RCh. 8 - Prob. 17RCh. 8 - Prob. 18RCh. 8 - Prob. 19RCh. 8 - Prob. 20RCh. 8 - Prob. 21RCh. 8 - Prob. 22RCh. 8 - Prob. 23RCh. 8 - Prob. 24RCh. 8 - Prob. 25RCh. 8 - Prob. 26RCh. 8 - Prob. 27RCh. 8 - Prob. 28RCh. 8 - Prob. 29RCh. 8 - Prob. 30RCh. 8 - Prob. 31RCh. 8 - Prob. 32RCh. 8 - Prob. 33RCh. 8 - Prob. 34RCh. 8 - Prob. 35RCh. 8 - Prob. 36RCh. 8 - Prob. 37RCh. 8 - Prob. 38RCh. 8 - Prob. 39RCh. 8 - Prob. 40RCh. 8 - Prob. 41RCh. 8 - Prob. 42RCh. 8 - Prob. 43RCh. 8 - Prob. 44RCh. 8 - Prob. 1GRFTCh. 8 - Prob. 2GRFTCh. 8 - Prob. 3GRFTCh. 8 - Prob. 4GRFTCh. 8 - Prob. 5GRFTCh. 8 - Prob. 6GRFTCh. 8 - Prob. 7GRFTCh. 8 - Prob. 8GRFTCh. 8 - Prob. 9GRFTCh. 8 - Prob. 10GRFTCh. 8 - Prob. 11GRFTCh. 8 - Prob. 12GRFTCh. 8 - Prob. 1TCh. 8 - Prob. 2TCh. 8 - Prob. 3TCh. 8 - Prob. 4TCh. 8 - Prob. 5TCh. 8 - Prob. 6TCh. 8 - Prob. 7TCh. 8 - Prob. 8TCh. 8 - Prob. 9TCh. 8 - Prob. 10TCh. 8 - Prob. 11TCh. 8 - Prob. 12TCh. 8 - Prob. 13TCh. 8 - Prob. 14TCh. 8 - Prob. 15TCh. 8 - Prob. 16TCh. 8 - Prob. 17TCh. 8 - Prob. 18TCh. 8 - Prob. 19TCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 14CRCh. 8 - Prob. 15CRCh. 8 - Prob. 16CRCh. 8 - Prob. 17CRCh. 8 - Prob. 18CRCh. 8 - Prob. 19CRCh. 8 - Prob. 20CRCh. 8 - Solve: (5x1)(2x2+15x+18)=0.Ch. 8 - Prob. 22CRCh. 8 - Prob. 23CRCh. 8 - Prob. 24CRCh. 8 - Prob. 25CRCh. 8 - Prob. 26CRCh. 8 - Prob. 27CRCh. 8 - Prob. 28CRCh. 8 - Prob. 29CRCh. 8 - Prob. 30CRCh. 8 - Prob. 31CRCh. 8 - Prob. 32CRCh. 8 - Prob. 33CRCh. 8 - Prob. 34CRCh. 8 - Prob. 35CRCh. 8 - Prob. 36CRCh. 8 - Prob. 37CRCh. 8 - Prob. 38CRCh. 8 - Prob. 39CRCh. 8 - Prob. 40CRCh. 8 - Prob. 41CRCh. 8 - Prob. 42CRCh. 8 - Prob. 43CRCh. 8 - Prob. 44CR
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