Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Chapter 7, Problem 11T
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1. Find the solution set of In(x) sin(x) ≤ 0, for x = [0,14].
Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6.
a. Use simulation to generate 1,000 plays from this strategy. Each play should indicate the net amount won or lost. Then, based on these outcomes, calculate a 95% confidence interval for the total net amount won or lost from 1,000 plays of the game. (Round your answers to two decimal places and if your answer is negative value, enter "minus" sign.) I worked out the Upper Limit, but I can't seem to arrive at the correct answer for the Lower Limit. What is the Lower Limit?…
4. Consider Chebychev's equation
(1 - x²)y" - xy + λy = 0
with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant.
(a) Show that Chebychev's equation can be expressed in Sturm-Liouville form
d
· (py') + qy + Ary = 0,
dx
y(1) = 0, y(-1) = 0,
where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2
(b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the
functional A[y], where
A[y]
=
I[y]
J[y]'
and I[y] and [y] are defined by
-
I [y] = √, (my² — qy²) dx
and
J[y] = [[", ry² dx.
Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1.
1
(c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable
4
trial functions for estimating the smallest eigenvalue. Show that the value of A[y]
for these trial functions is
4k2
A[y] =
=
4k - 1'
and use this to estimate the smallest eigenvalue \1.
Hint:
L₁ x²(1 − ²)³¹ dr =
1
(1 - x²)³ dx
(ẞ > 0).
2ẞ
Chapter 7 Solutions
Prealgebra (6th Edition)
Ch. 7.1 - Fill in the blanks. To solve the equation y+8=17,...Ch. 7.1 - Fill in the blanks. To solve the equation a1=7, we...Ch. 7.1 - Fill in the blanks. To solve the equation x15=82,...Ch. 7.1 - Fill in the blanks. To solve the equation x+15=22,...Ch. 7.1 - Fill in the blanks. Before we solve the equation...Ch. 7.1 - Fill in the blanks. Before we solve the equation...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...Ch. 7.1 - Fill in each blank with the missing phrase. To...
Ch. 7.1 - Fill in each blank with the missing phrase. We...Ch. 7.1 - Fill in each blank with the missing phrase. We...Ch. 7.1 - Solve and check your answer. a6=19Ch. 7.1 - Solve and check your answer. y4=11Ch. 7.1 - Solve and check your answer. a+9=1Ch. 7.1 - Solve and check your answer. x+13=1Ch. 7.1 - Solve and check your answer. 5=x+5Ch. 7.1 - Solve and check your answer. 7=y+6Ch. 7.1 - Solve and check your answer. 79=y4Ch. 7.1 - Solve and check your answer. 811=x4Ch. 7.1 - Solve and check your answer. 712=x6+32Ch. 7.1 - Solve and check your answer. 813=x2+32Ch. 7.1 - Solve and check your answer. 8+42=a+64Ch. 7.1 - Solve and check your answer. 5+32=a+57Ch. 7.1 - Solve and check your answer. 12x111x1=5Ch. 7.1 - Solve and check your answer. 8x+77x+2=3Ch. 7.1 - Solve and check your answer. 1216=4y+83yCh. 7.1 - Solve and check your answer. 89=3x42xCh. 7.1 - Solve and check your answer. 6x65x+1=2+4Ch. 7.1 - Solve and check your answer. 11x+1210x1=4+11Ch. 7.1 - Solve and check your solution. 16=x3Ch. 7.1 - Solve and check your solution. 3=x2Ch. 7.1 - Solve and check your solution. 14=y2Ch. 7.1 - Solve and check your solution. 4=a6Ch. 7.1 - Solve and check your solution. a4=6+9Ch. 7.1 - Solve and check your solution. y3=911Ch. 7.1 - Solve and check your solution. x4=8+6Ch. 7.1 - Solve and check your solution. x5=6+2Ch. 7.1 - Solve and check your solution. y2=4+22Ch. 7.1 - Solve and check your solution. x1=5+42Ch. 7.1 - Solve and check your solution. 3x5=9Ch. 7.1 - Solve and check your solution. 57x=15Ch. 7.1 - Solve and check your solution. 23a=18Ch. 7.1 - Solve and check your solution. 58a=15Ch. 7.1 - Solve and check your solution. 76y=42+5Ch. 7.1 - Solve and check your solution. 37y=524Ch. 7.1 - Solve and check your solution. 3(2x)=24Ch. 7.1 - Solve and check your solution. 4(6x)=48Ch. 7.1 - Solve and check your solution. 6=2(5x)Ch. 7.1 - Solve and check your solution. 2=6(4x)Ch. 7.1 - Solve and check your solution. 8x+4(4x)=48Ch. 7.1 - Solve and check your solution. 6x+3(3x)=45Ch. 7.1 - Solve and check your solution. 6(2x)3x=30Ch. 7.1 - Solve and check your solution. 5(5x)4x=29Ch. 7.1 - Solve and check your solution. 102=3(4x)+2xCh. 7.1 - Solve and check your solution. 63=2(3x)+3xCh. 7.1 - Solve and check your solution. 213=5x+3(4x)Ch. 7.1 - Solve and check your solution. 328=8x+2(2x)Ch. 7.1 - Solve and check your solution. x=9Ch. 7.1 - Solve and check your solution. x=16Ch. 7.1 - Solve and check your solution. x=4Ch. 7.1 - Solve and check your solution. x=6Ch. 7.1 - Solve. a. 2x=12 b. x2=12 c. x2=12 d. x+2=12Ch. 7.1 - Solve. a. 5y=20 b. y5=20 c. x5=20 d. x+5=20Ch. 7.1 - Solve. a. y10=9 b. y+10=9 c. y10=9 d. 10y=9Ch. 7.1 - Solve. a. x6=11 b. x+6=11 c. x6=11 d. 6x=11Ch. 7.1 - Solve. 15=a+5Ch. 7.1 - Solve. 2=y+7Ch. 7.1 - Solve. 5x+24x=4Ch. 7.1 - Solve. 7x+36x=4Ch. 7.1 - Solve. x7=2+32Ch. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - The sum of each row, each column, and each...Ch. 7.1 - Prob. 82ECh. 7.1 - Prob. 83ECh. 7.1 - Prob. 84ECh. 7.1 - Prob. 85ECh. 7.1 - Prob. 86ECh. 7.1 - Prob. 87ECh. 7.1 - Prob. 88ECh. 7.1 - Prob. 89ECh. 7.1 - Prob. 1QQCh. 7.1 - Prob. 2QQCh. 7.1 - Prob. 3QQCh. 7.1 - Prob. 4QQCh. 7.2 - Write in words the question asked by each...Ch. 7.2 - Write in words the question asked by each...Ch. 7.2 - Prob. 3ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 5ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 7ECh. 7.2 - Fill in the boxes in each step with the values...Ch. 7.2 - Prob. 9ECh. 7.2 - Solve and check your solution. 3y9=12Ch. 7.2 - Prob. 11ECh. 7.2 - Solve and check your solution. 7x10=18Ch. 7.2 - Prob. 13ECh. 7.2 - Solve and check your solution. 15=6y3Ch. 7.2 - Prob. 15ECh. 7.2 - Solve and check your solution. 3x2=12Ch. 7.2 - Prob. 17ECh. 7.2 - Solve and check your solution. 6w+7=67Ch. 7.2 - Prob. 19ECh. 7.2 - Solve and check your solution. 5y9=74Ch. 7.2 - Prob. 21ECh. 7.2 - Solve and check your solution. 36=4x8Ch. 7.2 - Solve and check your solution. 1=75yCh. 7.2 - Solve and check your solution. 2=94xCh. 7.2 - Prob. 25ECh. 7.2 - Solve and check your solution. 10=46xCh. 7.2 - Prob. 27ECh. 7.2 - Solve and check your solution. 3=92yCh. 7.2 - Prob. 29ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 31ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 33ECh. 7.2 - Simplify the left side of the equation by...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Solve and check your solution. 2y+6=12Ch. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Solve and check your solution. 13x=8x+20Ch. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Prob. 1QQCh. 7.2 - Prob. 2QQCh. 7.2 - Prob. 3QQCh. 7.2 - Prob. 4QQCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Solve and check your solution. 4(2x+1)=53xCh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Solve and check your solution. 4(x2)=2(x+6)+31Ch. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Solve and check your solution. 3(5x+1)4x=16Ch. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Solve and check your solution. (x2+3x1)(2x+1)=x25Ch. 7.3 - Prob. 38ECh. 7.3 - Is x=19 a solution to (2x+9)+(3x2)(5x+1)=2(x6)(x1)...Ch. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 1QQCh. 7.3 - Prob. 2QQCh. 7.3 - Prob. 3QQCh. 7.3 - Prob. 4QQCh. 7.4 - Fill in the blanks. To solve x3+x5=10 we multiply...Ch. 7.4 - Prob. 2ECh. 7.4 - Fill in each box with the correct number to...Ch. 7.4 - Prob. 4ECh. 7.4 - Solve and check your solution. x8+x4=3Ch. 7.4 - Prob. 6ECh. 7.4 - Solve and check your solution. x6+x4=5Ch. 7.4 - Prob. 8ECh. 7.4 - Solve and check your solution. x2x5=6Ch. 7.4 - Prob. 10ECh. 7.4 - Solve and check your solution. 3x+23=92Ch. 7.4 - Prob. 12ECh. 7.4 - Solve and check your solution. 5x+18=34Ch. 7.4 - Prob. 14ECh. 7.4 - Solve and check your solution. 5x12=18Ch. 7.4 - Prob. 16ECh. 7.4 - Solve and check your solution. 2x+12=37Ch. 7.4 - Prob. 18ECh. 7.4 - Solve and check your solution. 4x+23=16Ch. 7.4 - Prob. 20ECh. 7.4 - Solve and check your solution. x3+x=8Ch. 7.4 - Prob. 22ECh. 7.4 - Solve and check your solution. x3+x=6Ch. 7.4 - Prob. 24ECh. 7.4 - Solve and check your solution. x2+x=6Ch. 7.4 - Prob. 26ECh. 7.4 - Solve and check your solution. x42x=3Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Solve and check your solution. 59+x6=23Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Translate using symbols. [1.3.2] Twelve less than...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 1QQCh. 7.4 - Prob. 2QQCh. 7.4 - Prob. 3QQCh. 7.4 - Prob. 4QQCh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Salary Comparison Mark is a teaching assistant at...Ch. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Geometry A triangle has a perimeter of 24 inches....Ch. 7.5 - Prob. 25ECh. 7.5 - Geometry The perimeter of a rectangle is 74 feet....Ch. 7.5 - Price of College Books Jacob bought 2 books for...Ch. 7.5 - Number of Skiers On Monday the total number of...Ch. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Geometry A triangle with all sides of equal length...Ch. 7.5 - a. Find the missing numbers for sequence x, then...Ch. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - a. Find the missing numbers for sequence x, then...Ch. 7.5 - [5.6.1]Checker Board The dimensions of an opened...Ch. 7.5 - Use the following information for problems 13. The...Ch. 7.5 - Prob. 2QQCh. 7.5 - Use the following information for problems 13. The...Ch. 7.5 - Concept Check The high school marching band...Ch. 7 - Prob. 1RPCh. 7 - Prob. 2RPCh. 7 - Prob. 3RPCh. 7 - Prob. 4RPCh. 7 - Solve and check your solution. 5+22=x5Ch. 7 - Solve and check your solution. 67a=221Ch. 7 - Solve and check your solution. 3x+2(4x)=182Ch. 7 - Solve and check your solution. x=18Ch. 7 - Prob. 9RPCh. 7 - Solve and check your solution. 6x8=34Ch. 7 - Solve and check your solution. 2y+16=58Ch. 7 - Solve and check your solution. 20=87yCh. 7 - Prob. 13RPCh. 7 - Solve and check your solution. 14y=19Ch. 7 - Solve and check your solution. 8x75x=15Ch. 7 - Solve and check your solution. 6x=9x+36Ch. 7 - Solve and check your solution. 5x=2x+30Ch. 7 - Solve and check your solution. 3x85x=6Ch. 7 - Prob. 19RPCh. 7 - Prob. 20RPCh. 7 - Solve and check your solution. 8x95x+18=3x2+2xCh. 7 - Prob. 22RPCh. 7 - Prob. 23RPCh. 7 - Solve and check your solution. 4(2x+9)+5x=3Ch. 7 - Prob. 25RPCh. 7 - Prob. 26RPCh. 7 - Prob. 27RPCh. 7 - Solve and check your solution. (5x2+x2)(5x25)=6x+9Ch. 7 - Prob. 29RPCh. 7 - Solve and check your solution. x5x2=6Ch. 7 - Solve and check your solution. y+y5=12Ch. 7 - Prob. 32RPCh. 7 - Solve and check your solution. 2x34=13Ch. 7 - Prob. 34RPCh. 7 - Solve and check your solution. 13=3y+12Ch. 7 - Prob. 36RPCh. 7 - For exercises 36 and 37: Write an equation. Solve...Ch. 7 - Prob. 38RPCh. 7 - For each of the following problems: a. Define the...Ch. 7 - For each of the following problems: a. Define the...Ch. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Solve and check. 3=74yCh. 7 - Solve and check. 6x+49x=15Ch. 7 - Solve and check. 14x=2x+16Ch. 7 - Solve and check. 2x+4(3x6)=4(6x+2)Ch. 7 - Solve and check. 3(2x+6)+3x=27Ch. 7 - Solve and check. 4(x1)=6(x+2)+48Ch. 7 - Solve and check. (3x22x+1)+(3x210)=5x+5Ch. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - Prob. 18TCh. 7 - Write the answers. Use the following information...Ch. 7 - Prob. 20TCh. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...Ch. 7 - Write the answers. Use the following information...
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