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Finite Mathematics For Business Economics Life Sciences And Social Sciences 14th Edition Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker - Solutions
Find(A) 9C2(B) 5C5
In Problem(A) Write Newton’s form for the interpolating polynomial.(B) Write the associated lower triangular system for the coefficients.(C) Use forward substitution to find the interpolating polynomial. X f(x) -1 1 1 3 2 7
Given the following polynomial and table,(A) Show that the graph of p(x) passes through each point in the table.(B) Is p(x) the interpolating polynomial for this table? If not, what is the interpolating polynomial for this table?(C) Discuss the relationship between the number of points in a table
Find the interpolating polynomial for the function defined by the following table: X f(x) -1 5 0 3 دیا 1 3 2 11
A manufacturing company has defined the revenue function for one of its products by examining past records and listing the revenue (in thousands of dollars) for certain levels of production (in thousands of units). Use the revenue function defined by Table 2 to estimate the revenue if 3,000 units
Evaluate.(A) 5!(B) 8!/7!(C) 10!/7!
In Problem(A) Write Newton’s form for the interpolating polynomial.(B) Write the associated lower triangular system for the coefficients.(C) Use forward substitution to find the interpolating polynomial. X f(x) 1 2 3 6 4 11
Consider the points in Table 1.(A) Let p1(x) = a0 + a1(x - 1). Determine a0 and a1 so that the graph of y = p1(x) passes through the first two points in Table 1.(B) Let p2(x) = a0 + a1(x – 1) + a2(x - 1)(x - 2). Determine a0, a1, and a2 so that the graph of y = p2(x) passes through the first
Refer to Example 1. Approximate the revenue if 2,000 units are produced and if 5,000 units are produced.Data from Example 1A manufacturing company has defined the revenue function for one of its products by examining past records and listing the revenue (in thousands of dollars) for certain levels
(A) Write each number in scientific notation: 47,100; 2,443,000,000; 1.45(B) Write each number in standard decimal form: 3.07 × 108; 5.98 × 10–6
Multiply, and express answers using positive exponents only.(A) 2c1/4(5c3 – c3/4)(B) (7x1/2 – y1/2)(2x1/2 + 3y1/2)
In Problem find the smallest integer k ≥ 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs. 이 [20] 0
Evaluate each of the following:(A) 161/2 (B) –√16 (C) 3√–27 (D) (–9)1/2 (E) (4√81)3
Write the first four terms of each sequence:(A) an = 3n - 2 (B) [(-1)"} n
Which of the following can be the first four terms of an arithmetic sequence? Of a geometric sequence?(A) 8, 2, 0.5, 0.125, . . .(B) -7, -2, 3, 8, . . . (C) 1, 5, 25, 100, . . .
Write the first four terms of each sequence:(A) an = –n + 3 (B) [(-1)") 2" n
Evaluate each of the following:(A) 41/2 and √4 (B) –41/2 and –√4 (C) (–4)1/2 and √–4(D) 81/3 and 3√8 (E) (–8)1/3 and 3√–8 (F) –81/3 and –3√8
Simplify, and express the answers using positive exponents only.(A) (2x3) (3x5)(B) x5x–9(C) x5/x7(D) x–3/y–4(E) (u–3v2)–2(F)(G) -2
Use the square-root property to solve each equation.(A) x2 – 7 = 0 (B) 2x2 – 10 = 0(C) 3x2 + 27 = 0 (D) (x – 8)2 = 9
Simplify, and express the answers using positive exponents only. (A) (3y4) (2y³) (D) -6-1 (B) m²m 6 (E) 8x2y-4 -5..2 6x-³y² (C) (u³v-²)-²
Use the square-root property to solve each equation.(A) x2 – 6 = 0 (B) 3x2 – 12 = 0(C) x2 + 4 = 0 (D) (x + 5)2 = 1
Which of the following can be the first four terms of an arithmetic sequence? Of a geometric sequence?(A) 1, 2, 3, 5, . . . . (B) –1, 3, –9, 27, . . . .(C) 3, 3, 3, 3, . . . . (D) 10, 8.5, 7, 5.5, . . . .
(A) If the 1st and 10th terms of an arithmetic sequence are 3 and 30, respectively, find the 40th term of the sequence.(B) If the 1st and 10th terms of a geometric sequence are 3 and 30, find the 40th term to three decimal places.
(A) If the 1st and 15th terms of an arithmetic sequence are –5 and 23, respectively, find the 73rd term of the sequence.(B) Find the 8th term of the geometric sequence -13 1-1 1 64' 32' 16'
Convert to radical form.(A) u1/5 (B) (6x2y5)2/9 (C) (3xy)–3/5Convert to rational exponent form.(D) 4√9u (E) –7√(2x)4 (F) 3√x3 + y3
Find the general term of a sequence whose first four terms are(A) 3, 4, 5, 6, . . . (B) 5, –25, 125, –625, . . .
Change rational exponent form to radical form.(A) x1/7(B) (3u2v3)3/5(C) y–2/3Change radical form to rational exponent form.(D) 5√6(E) –3√x2(F) √x2 + y2
Find the general term of a sequence whose first four terms are(A) 3, 6, 9, 12, . . . .(B) 1, -2, 4, -8, . . . .
Solve by factoring using integer coefficients, if possible.(A) 3x2 – 6x – 24 = 0 (B) 3y2 = 2y (C) x2 – 2x – 1 = 0
Solve by factoring using integer coefficients, if possible.(A) 2x2 + 4x – 30 = 0 (B) 2x2 = 3x (C) 2x2 – 8x + 3 = 0
Write 1 – x/x–1 – 1 as a simple fraction with positive exponents.
Write 1 + x–1/1 – x–2 as a simple fraction with positive exponents.
Find the sum of the first 40 terms in the arithmetic sequence:15, 13, 11, 9, . . . .
Find the sum of the first 40 terms in the arithmetic sequence:15, 13, 11, 9, . . .
Writewithout summation notation. Do not evaluate the sum. + 1 k
Solve x2 – 2x – 1 = 0 using the quadratic formula.
Simplify each and express answers using positive exponents only. If rational exponents appear in final answers, convert to radical form. (A) 93/2 (D) (2x-3/41/4) 4 (B) (-27)4/3 8x1/21/3 (E) x2/3 (C) (5y¹/4)(2y¹/3)
Writewithout summation notation. Do not evaluate the sum. 5 k k=1k² + 1
Simplify each and express answers using positive exponents only. If rational exponents appear in final answers, convert to radical form. (A) (3x¹/³)(2x¹/2) (B) (-8) 5/3 (C) (2x¹/³-2/3) 3 (D) 4x1/31/2 x¹/2
Solve 2x2 – 4x – 3 = 0 using the quadratic formula.
(A) Write each number in scientific notation:7,320,000 and 0.000 000 54(B) Write each number in standard decimal form:4.32 × 106 and 4.32 × 10–5
Find the sum of all the even numbers between 31 and 87.
Find the sum of all the odd numbers between 24 and 208.
Write the alternating seriesusing summation notation with(A) The summing index k starting at 1(B) The summing index j starting at 0 2 - 4 6 T 8 + 10 1 12
Write the alternating seriesusing summation notation with(A) The summing index k starting at 1(B) The summing index j starting at 0 1 3 + 1 9 27 + 1 81
Factor, if possible, using integer coefficients.(A) 4x2 – 65x + 264 (B) 2x2 – 33x – 306
Multiply, and express answers using positive exponents only.(A) 3y2/3(2y1/3 – y2)(B) (2u1/2 + v1/2)(u1/2 – 3v1/2)
Factor, if possible, using integer coefficients.(A) 3x2 – 28x – 464 (B) 9x2 + 320x – 144
Find the sum of the first eight terms of the geometric sequence: 100, 100 (1.08), 100(1.08) ²,
Find the sum (to 2 decimal places) of the first ten terms of the geometric sequence:1, 1.05, 1.052, . . . .
Write the following expression in the form axp + bxq, where a and b are real numbers and p and q are rational numbers: 5√x - 4√x 2√x3
Find the arithmetic mean of 3, 5, 4, 7, 4, 2, 3, and 6.
Find the arithmetic mean of 9, 3, 8, 4, 3, and 6.
Write the following expression in the form axp + bxq, where a and b are real numbers and p and q are rational numbers: 21 2√x - 3√x² 2√x
Find all real solutions to 6x4 – 486 = 0.
Find all real solutions to 6x5 + 192 = 0.
A person borrows $3,600 and agrees to repay the loan in monthly installments over 3 years. The agreement is to pay 1% of the unpaid balance each month for using the money and $100 each month to reduce the loan. What is the total cost of the loan over the 3 years?
Simplify using properties of radicals. (A) √(x³ + y³)7 (B) V8y3 (C) √16x¹y √2xy
Repeat Example 6 with a loan of $6,000 over 5 years.Data from Example 6A person borrows $3,600 and agrees to repay the loan in monthly installments over 3 years. The agreement is to pay 1% of the unpaid balance each month for using the money and $100 each month to reduce the loan. What is the total
At a large summer beach resort, the weekly supply-and demand equations for folding beach chairs areThe supply equation indicates that the supplier is willing to sell x units at a price of p dollars per unit. The demand equation indicates that consumers are willing to buy x units at a price of p
Simplify using properties of radicals. (A) √(3x²y³) 4 (B) 8 √/2 (C) xy 27
Repeat Example 6 if near the end of summer, the supply and- demand equations areData from Example 6At a large summer beach resort, the weekly supply-and demand equations for folding beach chairs areThe supply equation indicates that the supplier is willing to sell x units at a price of p dollars
The government has decided on a tax rebate program to stimulate the economy. Suppose that you receive $1,200 and you spend 80% of this, and each of the people who receive what you spend also spend 80% of what they receive, and this process continues without end. According to the multiplier
Rationalize each denominator. (A) 12ab² √3ab (B) 9 √6 + √3 (C) x² - y² √x - Vy
Repeat Example 7 with a tax rebate of $2,000.Data from Example 7The government has decided on a tax rebate program to stimulate the economy. Suppose that you receive $1,200 and you spend 80% of this, and each of the people who receive what you spend also spend 80% of what they receive, and this
Rationalize each denominator. (A) 6x √2x (B) 6 Vi - √5 (C) x - 4 √x + 2
Write the 10th term of the sequence in Problem 1.Data from Problem 1Write the first four terms for each sequence in Problem.an = 2n + 3
Rationalize each numerator. (A) V3 3√2 (B) 2 - Vn 4-n (C) √3+h V3 h -
Rationalize each numerator. (A) V2 2√3 (B) 3 + √m 9-m (C) √2+ h-√2 h
Write the 15th term of the sequence in Problem 2.Data from Problem 2Write the first four terms for each sequence in Problem.an = 4n – 3
Write the 99th term of the sequence in Problem 3.Data from Problem 3Write the first four terms for each sequence in Problem. an n + 2 n + 1
Write the 200th term of the sequence in Problem 4.Data from Problem 4Write the first four terms for each sequence in Problem. || 2n + 1 2n
In Problem write each series in expanded form without summation notation, and evaluate. 6 ΣΚ k=1
In Problem write each series in expanded form without summation notation, and evaluate. 5 Σκ k=1
In Problem write each series in expanded form without summation notation, and evaluate. 7 Σ (2k – 3) k=4
In Problem write each series in expanded form without summation notation, and evaluate. 4 Σ(-2)* k=0
In Problem write each series in expanded form without summation notation, and evaluate. 3 k=0 1 10%
In Problem write each series in expanded form without summation notation, and evaluate. 4 k=1 2k
Find the arithmetic mean of each list of numbers in Problems.5, 4, 2, 1, and 6
Find the arithmetic mean of each list of numbers in Problems.96, 65, 82, 74, 91, 88, 87, 91, 77, and 74
In Problem write each number in standard decimal notation.4 × 104
In Problem write each number in standard decimal notation.9 × 106
In Problem write each number in standard decimal notation.7 × 10–3
In Problem write each number in standard decimal notation.2 × 10–5
In Problem write each number in standard decimal notation.6.171 × 107
In Problem factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem.x2 + 40x – 84
In Problem factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theoremx2 – 32x + 144
In Problem factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem2x2 + 15x - 108
Consider the quadratic equation x2 + 4x + c = 0 where c is a real number. Discuss the relationship between the values of c and the three types of roots listed in Table 1. Table 1 b² - 4ac Positive Zero Negative ax²+bx+c = 0 Two real solutions One real solution No real solutions
In Problem factor, if possible, as the product of two first degree polynomials with integer coefficients. Use the quadratic formula and the factor theorem4x2 + 241x – 434
If n = 0, then property 1 in Theorem 1 implies that ama0 = am + 0 = am. Explain how this helps motivate the definition of a0.Data from Theorem 1 THEOREM 1 Exponent Properties For n and m integers and a and b real numbers, 1. ama" = am+n 2. (an) m = amn m 3. (ab) = ambm 4. m = am b b am 5. = am-n
If m = –n, then property 1 in Theorem 1 implies that a–nan = a0 = 1. Explain how this helps motivate the definition of a–n.Data from Theorem 1 THEOREM 1 Exponent Properties For n and m integers and a and b real numbers, 1. ama" = am+n 2. (an) m = amn m 3. (ab) = ambm 4. m = am b b am 5. =
Refer to Problem 51. What is the difference between 2(3)2 and (23)2? Which agrees with the value of 232 obtained with a calculator?Data from Problem 51What is the result of entering 232 on a calculator?
If A is a positive real number, the terms of the sequence defined bycan be used to approximate √A to any decimal place accuracy desired. In Problem compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of √A obtained from a
The sequence defined recursively by a1 = 1, a2 = 1, an = an – 1 + an – 2 for n ≥ 3 is called the Fibonacci sequence. Find the first ten terms of the Fibonacci sequence.
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.√x2 = x for all real numbers x
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.√x2 = |x|for all real numbers x
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.3√x3 = |x| for all real numbers x
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.3√x3 = x for all real numbers x
In Problem discuss the validity of each statement. If the statement is true, explain why. If not, give a counterexample.The fourth roots of 100 are √10 and –√10.
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