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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

If the population of the United States is approximately 3.0 × 108 and each person produces about 4.6 pounds of garbage per day, express the total number of pounds of garbage produced in the United
In Exercises 15–58, find each product.(8x3 + 3)(x2 - 5)
Simplify each exponential expression in Exercises 28–31.(-5x3y2)(-2x-11y-2)
Express in scientific notation: 0.00076.
In Exercises 29–34, find the union of the sets.{1, 2, 3, 4} ∪ {2, 4, 5}
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime.4x2 + 16x + 15
A human brain contains 3 × 1010 neurons and a gorilla brain contains 7.5 × 109 neurons. How many times as many neurons are in the brain of a human as in the brain of a gorilla?
Evaluate: 27-5/3.
How can you distinguish parabolas from other conic sections by looking at their equations?
Write an equation for the path of each of the following elliptical orbits. Then use a graphing utility to graph the two ellipses in the same viewing rectangle. Can you see why early astronomers had
In Exercises 81–84, determine whether each statement makes sense or does not make sense, and explain your reasoning.I changed the addition in an ellipse’s equation to subtraction and this changed
Look at the satellite dish shown in Exercise 71. Why must the receiver for a shallow dish be farther from the base of the dish than for a deeper dish of the same diameter?Data from Exercise 71A
In Exercises 81–84, determine whether each statement makes sense or does not make sense, and explain your reasoning.I noticed that the definition of a hyperbola closely resembles that of an ellipse
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed an ellipse with a horizontal major axis and foci on the y-axis.
Explain how to identify the graph of Ax2 + Cy2 + Dx + Ey + F = 0.
In Exercises 81–84, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed a hyperbola centered at the origin that had y-intercepts but no
In Exercises 90–93, determine whether each statement makes sense or does not make sense, and explain your reasoning.I graphed a parabola that opened to the right and contained a maximum point.
Explain how to use mathematical induction to prove that a statement is true for every positive integer n.
Use the formula for nPr to solve Exercises 41–48.In a production of West Side Story, eight actors are considered for the male roles of Tony, Riff, and Bernardo. In how many ways can the director
What is a combination?
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.At age 25, to save for retirement, you decide to deposit $50 at the end of each month in an
In Exercises 76–82, solve by the method of your choice.How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?
What is the meaning of the symbol Σ? Give an example with your description.
In Exercises 78–81, determine whether each statement makes sense or does not make sense, and explain your reasoning.I was able to find the sum of the first 50 terms of an arithmetic sequence even
In Exercises 77–80, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.To find the fifth term in the expansion of
Explain how to distinguish between permutation and combination problems.
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.At age 25, to save for retirement, you decide to deposit $75 at the end of each month in an
In Exercises 76–82, solve by the method of your choice.From the 20 CDs that you’ve bought during the past year, you plan to take 3 with you on vacation. How many different sets of three CDs can
You buy a new car for $24,000. At the end of n years, the value of your car is given by the sequenceFind a5 and write a sentence explaining what this value represents. Describe the nth term of the
In Exercises 77–80, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.There are no values of a and b such that
In Exercises 78–81, determine whether each statement makes sense or does not make sense, and explain your reasoning.The sequence for the number of seats per row in our movie theater as the rows
Write a word problem that can be solved by evaluating 7C3.
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.To offer scholarship funds to children of employees, a company invests $10,000 at the end
In Exercises 76–82, solve by the method of your choice.How many different ways can a director select from 20 male actors and cast the roles of Mark, Roger, Angel, and Collins in the musical Rent?
In Exercises 81–85, use a calculator’s factorial key to evaluate each expression. 200! 198!
Use the Binomial Theorem to expand and then simplify the result: (x2 + x + 1)3.
In Exercises 78–81, determine whether each statement makes sense or does not make sense, and explain your reasoning.Beginning at 6:45 a.m., a bus stops on my block every 23 minutes, so I used the
In Exercises 81–85, use a calculator’s factorial key to evaluate each expression. 300 20
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.To offer scholarship funds to children of employees, a company invests $15,000 at the end
In Exercises 76–82, solve by the method of your choice.In how many ways can five airplanes line up for departure on a runway?
Find the term in the expansion of (x2 + y2)5 containing x4 as a factor.
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.Here are two ways of investing $30,000 for 20 years.After 20 years, how much more will you
Suppose that a survey of 350 college students is taken. Each student is asked the type of college attended (public or private) and the family’s income level (low, middle, high). Use the data in the
In Exercises 81–85, use a calculator’s factorial key to evaluate each expression. 20! 300
Prove that n ("') = (₂,²,). n
A degree-day is a unit used to measure the fuel requirements of buildings. By definition, each degree that the average daily temperature is below 65°F is 1 degree-day. For example, an average daily
Use the formula for the value of an annuity to solve Exercises 77–84. Round answers to the nearest dollar.Here are two ways of investing $40,000 for 25 years.After 25 years, how much more will you
Suppose that a survey of 350 college students is taken. Each student is asked the type of college attended (public or private) and the family’s income level (low, middle, high). Use the data in the
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the Fundamental Counting Principle to determine the number of five-digit
In Exercises 81–85, use a calculator’s factorial key to evaluate each expression. 20! (20 - 3)!
Show that n r n n+ + · ( ₁ ² ₁ ) = (^² + 1).
Show that the sum of the first n positive odd integers, 1 + 3 + 5 + g+ (2n - 1), is n2.
Follow the outline below and use mathematical induction to prove the Binomial Theorem:a. Verify the formula for n = 1.b. Replace n with k and write the statement that is assumed true. Replace n with
In Exercises 83–86, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used the permutations formula to determine the number of ways the manager of a
Suppose that a survey of 350 college students is taken. Each student is asked the type of college attended (public or private) and the family’s income level (low, middle, high). Use the data in the
Use the formula for the sum of an infinite geometric series to solve Exercises 85–87.A new factory in a small town has an annual payroll of $6 million. It is expected that 60% of this money will be
In Exercises 81–85, use a calculator’s factorial key to evaluate each expression. 54! (54 - 3)!3!
Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x - 3y + 9 = 0.
Use the formula for the sum of an infinite geometric series to solve Exercises 85–87.How much additional spending will be generated by a $10 billion tax rebate if 60% of all income is spent?
Graph: f(x) = -2(x - 1)2(x + 3).
A mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must be shown. If an examinee must answer 8 of the multiple-choice questions and 3 of the
What is the probability of a family having five boys born in a row?
Convert the equation 4x2 + y2 - 24x + 6y + 9 = 0 to standard form by completing the square on x and y. Then graph the ellipse and give the location of the foci.
Fill in each blank so that the resulting statement is true.A combination of numbers, variables, and operation symbols is called an algebraic________ .
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. -√25
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s).8x - y, for x = 3 and y = 4
Fill in each blank so that the resulting statement is true.The negative-exponent rule states that b-n =______ , b ≠ 0.
Evaluate each exponential expression in Exercises 1–22. (-2)4
In Exercises 1–10, factor out the greatest common factor.4x2 - 8x
Fill in each blank so that the resulting statement is true.The set of elements common to both set A and set B is called the______ of sets A and B, and is symbolized by________ .
Fill in each blank so that the resulting statement is true.A simplified polynomial that has two terms is called a/an ________.
Fill in each blank so that the resulting statement is true. ______ , x ≠ 0 x || X | در 3 ·|· 3/10
In Exercises 1–25, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate. 7x + 3[9 (2x - 6)]
In Exercises 1–18, simplify the given expression or perform the indicated operation (and simplify, if possible), whichever is appropriate.(2x2y3 - xy + y2) - (-4x2y3 - 5xy - y2)
In Exercises 5–8, find the degree of the polynomial.3x2 - 5x + 4
In Exercises 4–7, let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set.A ∪ B
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. V24x4 √3x
Simplify each exponential expression in Exercises 28–31.(2x3)-4
College students are graduating with the highest debt burden in history. The bar graph shows the mean, or average, student-loan debt in the United States for five selected graduating years from 2001
In Exercises 29–34, find the union of the sets.{1, 3, 7, 8} Φ {2, 3, 8}
Simplify each exponential expression in Exercises 23–64. x-6.x12
In Exercises 15–32, multiply or divide as indicated. x² r+ x − 12 rẻ +5x+6 x² + x 30 x² - 2x 2x - 3 x + 3 x² + 7x + 6
Big (Lack of) Men on Campus In 2007, 135 women received bachelor’s degrees for every 100 men. According to the U.S. Department of Education, that gender imbalance has widened, as shown by the bar
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime.8x2 + 33x + 4
Simplify each exponential expression in Exercises 28–31. 7x5y6 28x¹5y-2
In 2007, world population was approximately 6.6 × 109. By some projections, world population will double by 2040. Express the population at that time in scientific notation.
Simplify each exponential expression in Exercises 23–64. (x3)7
In Exercises 15–32, multiply or divide as indicated. x3 - 25x 4x2 *2 2x²2 6x + 5 x2 + 5x 7x + 7
In Exercises 15–58, find each product.(x + 5)(x - 5)
In Exercises 29–34, find the union of the sets.{0, 1, 3, 5} ∪ {2, 4, 6}
In Exercises 32–33, write each number in decimal notation.3.74 × 104
In Exercises 15–32, multiply or divide as indicated. x² - 4 x² + 3x - 10 x+5x+6 x² + 8x + 15
In Exercises 15–58, find each product.(7x3 + 5)(x2 - 2)
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime.9x2 + 5x - 4
Simplify each exponential expression in Exercises 23–64. (x11)5
In Exercises 33–58, add or subtract as indicated. 4x + 1 6x + 5 + 8x + 9 6x + 5
In Exercises 32–33, write each number in decimal notation.7.45 × 10-5
Simplify each exponential expression in Exercises 23–64. (x-5)³
In Exercises 29–34, find the union of the sets.{a, e, i, o, u} ∪ Φ
In Exercises 17–38, factor each trinomial, or state that the trinomial is prime.20x2 + 27x - 8

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