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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Complete the following for the given system of linear equations. (a) Write the system in the form AX = B. (b) Solve the linear system by computing X = A-1B with a calculator. Approximate the solution to the nearest hundredth when appropriate. -231x + 178y = -439 525x329y= 2282
Shade the region of feasible solutions for the following constraints. x+y=4 x+y=1 x = 0, y = 0
The following matrix represents a simple social network.Row 2 in the matrix contains only 0's. What does this tell us about Person 2? 0 0 1 1 0 0000 1100 10 10.
Write a system of linear inequalities that describes the shaded region. 5 2 (0.2.5) 12 (3, 1) 45 X
Complete the following. (a) Design a matrix A with dimension 4 X 4 that represents a digital image of the given letter. Assume that there are four gray levels from 0 to 3. (b) Find a matrix B such that B- A represents the negative image of the picture represented by matrix A from part
Does the number represent a probability? 품
Find an equation of the hyperbola centered at (1, 3) with a horizontal transverse axis of length 6 and a conjugate axis of length 4. Identify the foci.
Count the number of ways that the questions on an exam could be answered.Ten true-false questions
Sketch a graph of each equation. Label any foci. (a) y² = 2x (c) 9x² 18x + 4y² + 16y + 25 = 36 (x - c + 1)? _ (v - 2)? (d) 16 9 (b) 1 9 + 25 1
Find the probability of tossing a coin four times and obtaining a head every time.
How many distinct license plates could be made using a letter followed by five digits or letters?
Count the number of possible license plates with the given constraints.Three digits followed by three letters
Count the number of possible license plates with the given constraints.Two letters followed by four digits
Write each rational number in the form of an infinite geometric series.2/3
Find the average rate of change of f(x) = x3 - 4 from x = -2 to x = -1.
Count the number of possible license plates with the given constraints.Three letters followed by three digits or letters
Find a general term an for the arithmetic sequence. a₂ = 5, a6 = 13 96
Count the number of possible license plates with the given constraints.Two letters followed by either three or four digits
Find the probability of the compound event.Rolling a die four times and obtaining at least one 6
How many ways can four people stand in a line?
A combination lock consists of four numbers from 0 to 49. If a number may be repeated, find the number of possible combinations.
Count the different license plates having four numeric digits followed by two letters.
A jar contains 13 red, 27 blue, and 20 green marbles. If a marble is drawn from the jar at random, find the probability that the marble is the following. (a) Blue (b) Not blue (c) Red
Find a general term an for the arithmetic sequence. a3 = 22, a₁7 = -20 917
Two dice are rolled. Find the probabil- ity that the dice show a sum other than 7 or 11.
A softball team has 10 players. How many batting orders are possible?
How many ways can seven people sit at a round table?
Find the probability of drawing a 2, 3, or 4 from a standard deck of 52 playing cards.
In how many ways can nine players be assigned to the nine positions on a baseball team, assuming that any player can play any position?
Find the probability of drawing 2 diamonds from a standard deck of 52 cards without replacing the first card.
Suppose a coin is not fair, but instead the probability of obtaining a head (H) is 3/4 and a tail (T) is 1/4. What is the probability of each event? (a) HT (c) HHT (b) HH (d) THT
Suppose a die is not fair, but instead the probability P of each number n is as listed in the table. Find the probability of each event.(a) Rolling a number that is 4 or higher (b) Rolling a 6 twice on consecutive rolls P 1 0.1 2 3 0.1 0.1 4 0.2 5 6 0.2 0.3
Find a general term an for the arithmetic sequence. a₁ = 8, a₁ = 17
The monthly density of an insect population, measured in thousands per acre, is described by the recursive sequenceUse your calculator to graph the sequence in the window [0, 16, 1] by [0, 5000, 1000]. Include the first 15 terms and discuss any trends illustrated by the graph. a₁ 100; an = 2a-1 1
Find a general term an for the arithmetic sequence. a₁ = -2, as = 8
Find a general term an for the arithmetic sequence. as = -4, ag = -2.5
Write each rational number in the form of an infinite geometric series.1/9
Find a general term an for the arithmetic sequence. a3 = 10, a = -4
Plate glass sales G can be affected by the number of new building contracts B issued and the number of automobiles A produced, since plate glass is used in buildings and cars. To forecast sales, a plate glass company in California collected data for three consecutive years, shown in the table. All
In how many ways can five people have different birthdays?
Write each rational number in the form of an infinite geometric series.9/11
Suppose there are two dice, one red and one blue, having the probabilities shown in the table in Exercise 53. If both dice are rolled, find the probability of the given sum. (a) 12 (b) 11
Write the sum of each geometric series as a rational number. 0.8+ 0.08 +0.008 + 0.0008 +
A scheduling committee has one room in which to offer five mathematics courses. In how many ways can the committee arrange the five courses over the day?
Explain how to find the numbers in Pascal's triangle.
Find a general term a, for the geometric sequence. a₁ = 2₁ r = 1 2,
Write the sum of each geometric series as a rational number. 0.9 +0.09 + 0.009 + 0.0009 +
Write each rational number in the form of an infinite geometric series.14/33
Write the sum of each geometric series as a rational number. 0.36 + 0.0036 + 0.000036 +
Find a general term a, for the geometric sequence. a₁ = 0.8, r = -3
Write the sum of each geometric series as a rational number. 0.45 + 0.0045 + 0.000045 +
How many 10-digit telephone numbers are there if the first digit and the fourth digit cannot be a 0 or a 1?
Compare the expansion of (a + b)n with the expansion of (a - b)n. Give an example.
Write each rational number in the form of an infinite geometric series.1/7
Find a general term a, for the geometric sequence. = = ㅎ 43 = 이 32
The code for some garage door openers consists of 12 electrical switches that can be set to either 0 or 1 by the owner. Each setting represents a different code. What is the probability of guessing some- one's code at random?
A refinery produces both gaso- line and fuel oil, and sells gasoline for $4.00 per gallon and fuel oil for $3.60 per gallon. The refinery can produce at most 600,000 gallons a day but must produce at least 2 gallons of fuel oil for every gallon of gasoline. At least 150,000 gallons of fuel oil must
A jar contains 22 red marbles, 18 blue marbles, and 10 green marbles. If a marble is drawn from the jar at random, find the probability that the color is the following.(a) Red (b) Not red (c) Blue or green
There are 10 basic colors available for a new car, along with 5 basic styles of trim. In how many ways can a person pick the color and trim?
Find a general term a, for the geometric sequence. a₁ = -3, r = 2
Find a general term a, for the geometric sequence. a4 = 3, r = 3
Write each rational number in the form of an infinite geometric series.23/99
A jar contains 55 red marbles and 45 blue marbles. If 2 marbles are drawn from the jar at random without replacement, find the probability that the marbles satisfy the following. (a) Both are blue (b) Neither is blue (c) The first marble is red and the second marble is blue
To win a lottery, a person must pick three numbers from 0 to 9 in the correct order. If a number may be repeated, what is the probability of winning this game with one play?
Write out the terms of the series and then evaluate it. Σ« (k + 1)
Find a general term a, for the geometric sequence. t= = 1²7 = 1
To win the jackpot in a lottery, a person must pick five numbers from 1 to 59 and then pick the powerball, which has a number from 1 to 35. If the numbers are picked at random, what is the probability of winning this game with one play?
Write out the terms of the series and then evaluate it. WI (3k - 1)
Find a general term a, for the geometric sequence. a₂ = 10, r = 5 a2
(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 Student 3 College A College B College A 10 9 11 College B 5 8 3 Cost per Credit $60 $70
(a) Find a matrix A and a column matrix B that describe the following tables. (b) Find the matrix product AB, and interpret the result. Student 1 Student 2 Student 3 College A College B College C College A 6 11 0 College B 0 3 12 Cost per Credit $50 $65 $60 College C 3 0 3
The area of a rectangle with length 1 and width w is computed by A(1, w) = Iw, and its perimeter is calculated by P(1, w) = 21+ 2w. Assume that I > w and use the method of substitution to solve the system of equations for I and w. A(1, w) = 35 P(1, w) = 24
Suppose that a closed economic region has three industries: service, electrical power, and tourism. The service industry uses 20% of its own production, 40% of the electrical power, and 80% of the tourism. The power company uses 40% of the service industry, 20% of the electrical power, and 10% of
Use Gauss-Jordan elimination to solve the system of equations. x = y + 2z = 7 2x + y4z = -27 0 =x + y = z = -x
A store owner makes two separate orders for three types of auto parts: I, II, and III. The numbers of parts ordered are represented by the matrix A.For example, Order I called for 4 parts of type II. The cost in dollars of each part can be represented by the matrix B.Find AB and interpret the
Find the probability of drawing a queen from a standard deck of cards given that one card, a queen, has already been drawn and not replaced.
Find the probability of drawing a king from a standard deck of cards given that two cards, both kings, have already been drawn and not replaced.
Use Gauss-Jordan elimination to solve the system of equations. 2x - 4y - 62 = 2 x - 3y + z = 12 2x + y + 3z = 5
A card is drawn from a standard deck of 52 cards. Given that the card is a face card, what is the probability that the card is a king?
Find the probability of drawing a heart or an ace from a standard deck of 52 cards.
A breeder is mixing Brand A and Brand B. Each serving should contain at least 60 grams of protein and 30 grams of fat. Brand A costs 80 cents per unit, and Brand B costs 50 cents per unit. Each unit of Brand A contains 15 grams of protein and 10 grams of fat, whereas each unit of Brand B contains
Two car dealers buy four different makes of cars: I, II, III, and IV. The number of each make of automobile bought by each dealer is represented by the matrix A.For example, Dealer 2 bought 7 cars of type III. The cost in thousands of dollars for each type of car can be represented by the matrix
Use Gauss-Jordan elimination to solve the system of equations. 2x + y x - 2y + x + 3y - z = 2 z = 0 2z = 4
Use Gauss-Jordan elimination to solve the system of equations. -2x = - y + z = 3 32 = 1 4z = 2 x + y = x - 2y =
Use technology to find the solution. Approximate values to the nearest thousandth. 5x - 7y + 9z = 40 -7x + 3y = 72 = 20 5x8y- 5z = 15
The following graph shows web page links.Create a matrix A that represents this situation. Page 1 Page 3 Page 2 Page 4
The following graph shows web page links.Compute A2. Page 1 Page 3 Page 2 Page 4
Use technology to find the solution. Approximate values to the nearest thousandth. 2.1x + 0.5y + 1.7z = 4.9 -2x + 1.5y-1.7z = 3.1 5.8x4.6y + 0.8= = 9.3
Use technology to find the solution. Approximate values to the nearest thousandth. 12x - 4y = 72 = 8 - -8x - бу + 92 = 7 9z 34x + бу - 2z = 5 =
Two substances, X and Y. are found in pet food. Each substance contains the ingredients A and B. Substance X is 20% ingredient A and 50% ingredient B. Substance Y is 50% ingredient A and 30% ingredient B. The cost of substance X is $2 per pound, and the cost of substance Y is $3 per pound. The pet
A pet owner is buying two brands of food, X and Y, for his animals. Each serving of the mixture of the two foods should contain at least 60 grams of protein and 40 grams of fat. Brand X costs 75 cents per unit, and Brand Y costs 50 cents per unit. Each unit of Brand X contains 20 grams of protein
A manager wants to buy filing cabinets. Cabinet X costs $100, requires 6 square feet of floor space, and holds 8 cubic feet. Cabinet Y costs $200, requires 8 square feet of floor space, and holds 12 cubic feet. No more than $1400 can be spent, and the office has room for no more than 72 square feet
The following graph shows web page links.Which page can be reached in a single click from every other page in the network? Page 1 Page 3 Page 2 Page 4
The following graph shows web page links.Which two pages cannot be reached using a 2-click path from any other page in the network? Page 1 Page 3 Page 2 Page 4
A breeder can raise no more than 50 hamsters and mice and no more than 20 hamsters. If she sells the hamsters for $15 each and the mice for $10 each, find the maximum revenue produced.
Discuss how to solve the matrix equation AX = B if A-1 exists.
A business manufactures two parts, X and Y. Machines A and B are needed to make each part. To make part X, machine A is needed for 4 hours and machine B is needed for 2 hours. To make part Y, machine A is needed for 1 hour and machine B is needed for 3 hours. Machine A is available for 40 hours
Give an example of a 2 x 2 matrix A with only nonzero elements that does not have an inverse. Explain what happens if one attempts to find A-1 symbolically.
For three food shelters, monthly food costs F in dollars, number of people served per month N, and monthly charitable receipts R in dollars are as shown in the table.(a) Model these data using F = aN + bR + c, where a, b, and care constants. (b) Predict the food costs for a shelter that serves
Use technology to find the solution. Approximate values to the nearest thousandth. 103x886y + 4312 = 1200 -55x + 981y = 1108 99 -327x + 421y + 337z =
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