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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Find the sum of the first 20 terms of the arithmetic sequence:4, 10, 16, 22, . . . .
In Exercises 37–44, find the sum of each infinite geometric series. 1 + + + -18 27 +
Use the Fundamental Counting Principle to solve Exercises 29–40.In the original plan for area codes in 1945, the first digit could be any number from 2 through 9, the second digit was either 0 or 1, and the third digit could be any number except 0. With this plan, how many different area codes
Consider the statement Sn given by n2 - n + 41 is prime. Although S1, S2, . . . , S40 are true, S41 is false. Verify that S41 is false. Then describe how this is illustrated by the dominoes in the figure. What does this tell you about a pattern, or formula, that seems to work for several values of
In Exercises 35–37, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a7 when a1 = 2, r = 3.
In Exercises 29–42, find each indicated sum. 9 Σ11 i=5
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x2 + 1)16
Find the sum of the first 25 terms of the arithmetic sequence:7, 19, 31, 43, . . . .
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
In Exercises 36–37, write the linear function in slope intercept form satisfying the given conditions.Graph of f passes through (6, 3) and (-2, 1).
In Exercises 37–44, find the sum of each infinite geometric series. 1 1 + + 4 1 1 + 16 64
In Exercises 35–37, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a6 when a1 = 16, r = 1/2.
Use the Fundamental Counting Principle to solve Exercises 29–40.How many different four-letter radio station call letters can be formed if the first letter must be W or K?
In Exercises 29–42, find each indicated sum. 7 Σ 12 =3
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(x2 + 1)17
The table shows the educational attainment of the U.S. population, ages 25 and over. Use the data in the table, expressed in millions, to solve Exercises 33–38.Find the probability, expressed as a simplified fraction, that a randomly selected American, age 25 or over, has not completed four years
Find the sum of the first 50 terms of the arithmetic sequence:-10, -6, -2, 2, . . . .
In Exercises 36–37, write the linear function in slope intercept form satisfying the given conditions.Graph of g passes through (0, -2) and is perpendicular to the line whose equation is x - 5y - 20 = 0.
Use the Fundamental Counting Principle to solve Exercises 29–40.Six performers are to present their comedy acts on a weekend evening at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer’s request is granted, how many different ways
In Exercises 35–37, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence.Find a5 when a1 = -3, r = 2.
In Exercises 29–42, find each indicated sum. 4 i=0 (-1)
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(y3 - 1)20
In Exercises 37–44, find the sum of each infinite geometric series. 3+ + ترا در + 3
Find the sum of the first 50 terms of the arithmetic sequence:-15, -9, -3, 3, . . . .
In Exercises 29–42, find each indicated sum. 4 (-1)²+1 =0 (i+1)!
In Exercises 37–40, determine whether each statement makes sense or does not make sense, and explain your reasoning.I use mathematical induction to prove that statements are true for all real numbers n.
In Exercises 38–40, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8, the eighth term of the sequence.1, 2, 4, 8, . . .
In Exercises 37–44, find the sum of each infinite geometric series. 5+ 9 5 + 6² + 5 +
Use the Fundamental Counting Principle to solve Exercises 29–40.Five singers are to perform at a night club. One of the singers insists on being the last performer of the evening. If this singer’s request is granted, how many different ways are there to schedule the appearances?
In Exercises 31–38, write the first three terms in each binomial expansion, expressing the result in simplified form.(y3 - 1)21
Find 1 + 2 + 3 + 4 + g + 100, the sum of the first 100 natural numbers.
In Exercises 37–40, determine whether each statement makes sense or does not make sense, and explain your reasoning.I begin proofs by mathematical induction by writing Sk and Sk+1, both of which I assume to be true.
The perimeter of a soccer field is 300 yards. If the length is 50 yards longer than the width, what are the field’s dimensions?
In Exercises 37–40, determine whether each statement makes sense or does not make sense, and explain your reasoning.This triangular arrangement of 36 circles illustrates that 1+2+3+... + n = is true for n = 8. 888 50 388 388 n(n + 1) 2
In Exercises 38–40, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8, the eighth term of the sequence.100, 10, 1, 1/10, . . .
Use the Fundamental Counting Principle to solve Exercises 29–40.In the Cambridge Encyclopedia of Language (Cambridge University Press, 1987), author David Crystal presents five sentences that make a reasonable paragraph regardless of their order. The sentences are as follows:• Mark had told him
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.
In Exercises 39–48, find the term indicated in each expansion.2x + y)6; third term
Find 2 + 4 + 6 + 8 + g + 200, the sum of the first 100 positive even integers.
In Exercises 37–40, determine whether each statement makes sense or does not make sense, and explain your reasoning.When a line of falling dominoes is used to illustrate the principle of mathematical induction, it is not necessary for all the dominoes to topple.
If 10 pens and 12 pads cost $42, and 5 of the same pens and 10 of the same pads cost $29, find the cost of a pen and a pad.
Use the Fundamental Counting Principle to solve Exercises 29–40.A television programmer is arranging the order that five movies will be seen between the hours of 6 p.m. and 4 a.m. Two of the movies have a G rating and they are to be shown in the first two time blocks. One of the movies is rated
In Exercises 38–40, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for an to find a8, the eighth term of the sequence.12, -4, 4/3, - 4/9, . . .
In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.
In Exercises 39–48, find the term indicated in each expansion.(x + 2y)6; third term
Use the formula for nPr to solve Exercises 41–48.A club with ten members is to choose three officers—president, vice president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
Find the sum of the first 60 positive even integers.
In Exercises 29–42, find each indicated sum. 5 i! { (i-1)! i=1
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. x + y + z = 2x + 3y - 2= x + y + 2z = 10 6 3
Colors for computer monitors are often described using ordered triples. One model, called the RGB system, uses red, green, and blue to generate all colors. The figure describes the relationships of these colors in this system. Red is (1, 0, 0), green is (0, 1, 0), and blue is (0, 0, 1). Since equal
Graph the solution set to the system of inequalities. Use the graph to identify one solution. x² + y > 2 x² + y² ≤ 9
If possible, graphically approximate the solution of each system of equations to the nearest thousandth. Identify each system as consistent or inconsistent. If the system is consistent, determine if the equations are dependent or independent. (a) 3.1x + 4.2y = 6.4 1.7x9.1y = 1.6 (b) 6.3x5.1y =
The boundedness theorem shows how the bottom row of a synthetic division is used to place upper and lower bounds on possible real zeros of a polynomial function. Let P(x) define a polynomial function of degree n ≥ 1 with real coefficients and with a positive leading coefficient. If P(x) is
If a line passes through the points (x1, y1) and (x2, y2), then an equation of this line can be found by calculating the determinant.Find the standard form ax + by = c of the line passing through the given points. 1 det | x y 1 | - . ܐܐ ܕ 1
Solve the system using technology. 12x + 7y 3z = 14.6 8x11y+13= = -60.4 +9z = -14.6 -23x
Write the system of linear equations that the augmented matrix represents. 3 1 05 0 0 4 8 -7 0 -1
Let A be the given matrix. Find det A by using the method of cofactors. 0 0 -83-9 15 5 0 9
If possible, solve the system. a-2b + c = -1 a + 5b = -3 2a + 3b + c = -2
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. 3 3 x + 2y + z = x + y = = = -x-2y+z=-5
Graph the solution set to the system of inequalities. 2x² + y ≤0 x²-y≤ 3
The graph shows the distance that the driver of a car on a straight highway is from home. Find the slope of each line segment and interpret each slope. Distance (miles) 12 3 4 5 Time (hours)
If a line passes through the points (x1, y1) and (x2, y2), then an equation of this line can be found by calculating the determinant.Find the standard form ax + by = c of the line passing through the given points. 1 det | x y 1 | - . ܐܐ ܕ 1
Represent the system of linear equations in the form AX = B. -1.1x + 3.2y = -2.7 5.6x3.8y=-3.0
Explain the type of growth that each salary offer is exhibiting. Write an equation that calculates each salary after x weeks.
If possible, find AB and BA. 4=[4] 2 -4 -[- 10-2 -4 8 1 B =
Graph the solution set to the system of inequalities. x² + 2y = 4 x²-y≤0
If possible, find AB and BA. 와 61 0 51 4 -7 10 10 B = 20 30
The largest angle in a triangle is 25° more than the smallest angle. The sum of the measures of the two smaller angles is 30° more than the measure of the largest angle.(a) Let x, y, and z be the measures of the three angles from largest to smallest. Write a system of three linear equations whose
Give an example of data that could be modeled by a logistic function and explain why.
Represent the system of linear equations in the form AX = B. z = 5 2 = 6 x - 2y + зу - 5x - 4y - 7z = 0
Let A be the given matrix. Find det A by using the method of cofactors. 2 1 3 034 05 10
The perimeter of a triangle is 105 inches. The longest side is 22 inches longer than the shortest side. The sum of the lengths of the two shorter sides is 15 inches more than the length of the longest side. Find the lengths of the sides of the triangle.
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. x + 2y = 2 = -1 2x = y + z = 0 7 -x = y + 2z =
If a line passes through the points (x1, y1) and (x2, y2), then an equation of this line can be found by calculating the determinant.Find the standard form ax + by = c of the line passing through the given points. 1 det | x y 1 | - . ܐܐ ܕ 1
Graph the solution set to the system of inequalities. +5₂ + 2x x² + 2y = 2
If possible, find AB and BA. 0 3-4 2 0 1 5 B = 1 3
The total distance D in feet that an object has fallen after 1 seconds is given by D(t)= 16t2 for 0 ≤ 1 ≤ 3. (a) Find the average rate of change of D from 0 to 1 and from 1 to 2. (b) Interpret these average rates of change. (c) Find the difference quotient of D.
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. x + 3y - 2z = -4 2x + 6y + z = -3 x + y = 4z = -2
Prices of homes can depend on several factors such as size and age. The table shows the selling prices for three homes. In this table, price Pis given in thousands of dollars, age A in years, and home size S in thousands of square feet. These data may be modeled by P = a + bA + cS.(a) Write a
A sum of $20,000 is invested in three mutual funds. In one year the first fund grew by 5%, the second by 7%, and the third by 10%. Total earnings for the year were $1650. The amount invested in the third fund was four times the amount invested in the first fund. Find the amount invested in each
Graph the solution set to the system of inequalities. 2x + 3y = 6 x²-y≤2
Suppose one person can mow a large lawn in 4 hours and another person can mow the same lawn in 6 hours. How long will it take to mow the lawn if they work together?
Represent the system of linear equations in the form AX = B. 4x = y + 3z = x + 2y + 5z = 2x - 3y -2 11 = -1
Choose two matrices A and B with dimension 2 x 2. Calculate det A, det B, and det (AB). Repeat this process until you are able to discover how these three determinants are related. Summarize your results.
A company is selling a product at market price that has a daily cost function C(x) = 10x + 300 in dollars and a daily revenue function R(x) = 13x in dollars, where x is units sold. (a) Determine the coordinates of the break-even point and interpret its meaning. (b) Graph the cost and
Write out the terms of the series and then evaluate it. S (k’ – k) -
Represent the system of linear equations in the form AX = B. 4x - 3y + 2z = 8 -x + 4y + 3z = 2 -2x 5z = 2 I
Represent the system of linear equations in the form AX = B. x - 2y + z = 12 4y+32 13 = -2 -2x + 7y
If one student is selected at random, use TABLE 8.10 to calculate each of the following. (a) The probability that the student is male (b) The probability that the student is taking French, given that the student is male (c) The probability that the student is male and taking French
Let A be the given matrix. Find det A by using the method of cofactors. 302 135 -5 2 0
If possible, find AB and BA. A 1-1 3-2 1 03 4 2-20 8 B = 1 0 2 -5 5 534 3 4
Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or an ordered triple whenever possible. 3x + x+ -2x - 14 6 y + 3z = z= y+ у+ 2y + 3z = -7 то
Use the given A and B to evaluate each expression.AB 3-2 4 2-3 5 4 A = 5 7 B = 11 -1 0-7 -6 4 3
Use a graphing calculator to evaluate the expression with the given matrices A, B, and C. Compare your answers for parts (a) and (b). Then interpret the results. 414-643 3-5 B = 3 -4 -5 7 [14 -3 0-2 C = 81 46
Let A be the given matrix. Use technology to find det A. State whether A is invertible. 13 22 55 -57
Find the minimum value of C = 3x + y subject to the following constraints. x + yz 1 2x + 3y ≤ 6 x ≥ 0, y = 0
SolveFor t. nt A = P(1 + # ) ²¹
The following matrix represents a simple social network.Draw a graph of this network. 0 0 1 1 0 0000 1100 10 10.
The force of gravity F varies inversely with the square of the distance d from the center of Earth. If a person weighs 150 pounds on the surface of Earth (d = 4000 miles), how much would this person weigh 10,000 miles from the center of Earth?
Find a general term a, for the geometric sequence. a₂= 6, a4 = 24, r> 0
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