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Questions and Answers of Mathematics Economics Business

If r = 1, neither the first form nor the second form for the sum of a finite geometric series is valid. Find a formula for the sum of a finite geometric series if r = 1.
The number N of registered voters in a precinct over a 10-year period is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the interpolating polynomial to approximate
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) -2 2 0 0 2 2
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) 6 0 2 1 0 2 -6 3 2 نرا
Find the indicated term in each expansion in Problem.(2x + y)12; 11th term
In Problems use the quartic regression routine on a graphing calculator to fit a fourth degree polynomial to the tables in the indicated problems. Compare this polynomial with the interpolating
The number N of registered voters in a precinct over a 30-year period is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the interpolating polynomial to approximate
Physiologists use a machine called a pneumotachograph to produce a graph of the rate of flow R on air into the lungs (inspiration) and out (expiration). The figure gives the graph of the inspiration
A lake that is used for recreational swimming is treated periodically to control harmful bacteria growth. The concentration C (in bacteria per cubic centimeter) t days after a treatment is given in
If $1,000 is invested at 5% compounded annually, the amount A present after n years forms a geometric sequence with common ratio 1 + 0.05 = 1.05. Use a geometric sequence formula to find the amount A
The concentration C (in milligrams per cubic centimeter) of a particular drug in a patient’s bloodstream t hours after the drug is taken is given in the table.(A) Find the interpolating polynomial
The temperature C (in degrees celsius) in an artificial habitat after t hours is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the interpolating polynomial to
The cost C (in thousands of dollars) of producing x thousand microwave ovens is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the interpolating polynomial to
The revenue R (in thousands of dollars) from the sale of x thousand table lamps is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the interpolating polynomial to
If you borrow $4,800 and repay the loan by paying $200 per month to reduce the loan and 1% of the unpaid balance each month for the use of the money, what is the total cost of the loan over 24 months?
Refer to Problem 43. After making a series of adjustments for things like taxes, fringe benefits, and returns on home equity, the income distribution for the United States in 1999 is represented by
Find the equation of the parabola whose graph passes through the points (–x1, y1), (0, y2), and (x1, y1), where x1 > 0 and y1 ≠ y2.
The income distribution for the United States in 1999 is represented by the Lorenz curve y = f(x), where f(x) is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the
A hardware store orders 147 lawn mowers. The inventory I of lawn mowers on hand t months after the order arrived is given in the table.(A) Find the interpolating polynomial for this table.(B) Use the
Does there exist a finite arithmetic series with a1 = 1 and an = 1.1 that has sum equal to 105? Explain.
Suppose the cash reserves C (in thousands of dollars) for a small business are given by the following table, where t is the number of months after the first of the year.(A) Find the interpolating
Does there exist a finite arithmetic series with a1 = 1 and an = 1.1 that has sum equal to 100? Explain.
Find the equation of the parabola whose graph passes through the points (0, 0), (x1, y1), and (2x1, 0), where x1 > 0 and y1 ≠ 0.
Show that nCr – 1 + n Cr = n + 1Cr for n ≥ r ≥ 1.
The following table was obtained from the function f(x) = (9 – x2) / (1 + x2):Find the interpolating polynomial p(x) for this table. Graph p(x) and f(x) on the same set of axes.
Show that nCr = "7+¹n Cr-1 for n ≥r≥ 1.
The following table was obtained from the function f(x) = 10x/(1 + x2):Find the interpolating polynomial p(x) for this table. Graph p(x) and f(x) on the same set of axes.
Explain why the alternating sum of the entries in each row of Pascal’s triangle (e.g., 1 - 4 + 6 - 4 + 1) is equal to 0.
The following table was obtained from the function f(x) = 6/√x:Find the interpolating polynomial for this table. Compare the values of the interpolating polynomial p(x) and the original function
The following table was obtained from the function f(x) = 2x:Find the interpolating polynomial for this table. Compare the values of the interpolating polynomial p(x) and the original function f(x) =
Find f(1) + f(2) + · · · + f(10) if f(x) = (1/2)x.
In Problems use the quartic regression routine on a graphing calculator to fit a fourth degree polynomial to the tables in the indicated problems. Compare this polynomial with the interpolating
Show that nCr = nCn – r for n ≥ r ≥ 0.
Find f(1) + f(2) + f(3) + · · · + f(50) if f(x) = 2x – 3.
In Problems use the quartic regression routine on a graphing calculator to fit a fourth degree polynomial to the tables in the indicated problems. Compare this polynomial with the interpolating
In Problems use the quartic regression routine on a graphing calculator to fit a fourth degree polynomial to the tables in the indicated problems. Compare this polynomial with the interpolating
Show that nC0 = nCn for n ≥ 0.
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) -2 -1 -3 0 0 5 1 0 2 -3
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. -2 -1 0 X f(x) -8 0 2 1 4 2 12
Find the indicated quantities. Sg 8 · Στ k=1 = = ?
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. x f(x) -2 1 -1 5 0 3 1 1 2 5
Find the indicated quantities. 8 S = Σ ( −2)−1 = ? -2)*- k=1
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) -3 0 -1 4 0 3 1 0
Find the indicated quantities. 50 Sso = Σ (2k – 3) = ? k=1
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) 0 0 2 2 0 3 -4
Find the indicated quantities. S41 41 = = Σ (3k + 3) = ? k=1
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) 0 -4 1 -3 2 0
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) 0 -4 1 -2 2 0
Expand each expression in Problem using the binomial theorem.(x – 1)6Data from binomial theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = „Coa" + ₂C₁a"-¹b +
In Problem find the interpolating polynomial. Graph the interpolating polynomial and the points in the given table on the same set of axes. X f(x) -2 2 0 0 2 -2
Use the binomial theorem to find the sixth term in the expansion of (x – 1)18.Data from Binomial Theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = „Coa" + nC₁a"-¹b +
Expand each expression in Problem using the binomial theorem.(a + b)4Data from binomial theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = "Coa" + nc₁a"-¹b + С₂an-²b² +
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. -3 -2 f(x) 40 0 ? X (A) f(-2.5) + (B) f(1.5)
In Problem evaluate each expression.18C3
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. -3 f(x) -24 X -2 -6 0 1 0 2 (A) f(-0.5) ? (B) f(2.5)
In Problem evaluate each expression.18C15
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. -6 f(x) 19 (A) f(1) ~ ? X 0 2 10 3 (B) f(5) ? -2 3 نیا 6 19
In Problem evaluate each expression.5C5
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. -2 f(x) 0 (A) f(1) ~ ? X 6 1% -96 (B) f(4) ≈ ? 0 0 2 0
In Problem evaluate each expression.5C0
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. -2 f(x) 0 (A) f(1) ~ ? X 6 1% -96 (B) f(4) ≈ ? 0 0 2 0
In Problem evaluate each expression.7C4
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. X -1 f(x) 0 (A) f(2)= ? 0 1 0 4 15 (B) f(3) = ? 0
In Problem evaluate each expression.6C5
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. X -5 f(x) 250 (A) f(-3) 0 50 5 100 10 -350 ? (B) f(8) = ?
In Problem evaluate each expression.7C3
In Problem use the interpolating polynomial to approximate the value of the function defined by the table at the indicated values of x. X -4 -64 0 32 4 0 f(x) (A) f(2)? (B) f(6) = ? 8 224
In Problem evaluate each expression.5C3
Can a table with four points have a linear interpolating polynomial? A quadratic interpolating polynomial? A cubic interpolating polynomial? A quartic interpolating polynomial? Explain.
In Problem evaluate each expression.52!/50!2!
Can a table with three points have a linear interpolating polynomial? A quadratic interpolating polynomial? A cubic interpolating polynomial? Explain.
In Problem evaluate each expression.20!/3!17!
In Problem find the divided difference table and then find the interpolating polynomial. X f(x) 17 0 10 3 25 5 5
In Problem evaluate each expression.7!/4!(7 - 4)!
In Problem find the divided difference table and then find the interpolating polynomial. X f(x) -2 25 1 10 2 17 4 13
In Problem evaluate each expression.6!/5!(6 – 5)!
In Problem find the divided difference table and then find the interpolating polynomial. f(x) -1 5 0 6 1 3 2 2
In Problem evaluate each expression.7!/3!4!
In Problem find the divided difference table and then find the interpolating polynomial. X f(x) -3 0 1 1 3 2 9
In Problem evaluate each expression.5!/2!3!
In Problem find the divided difference table and then find the interpolating polynomial. X f(x) 1 1 2 3 3 1
In Problem evaluate each expression.10!/6!
In Problem find the divided difference table and then find the interpolating polynomial. f(x) 1 4 2 8 3 14
In Problem evaluate each expression.12!/9!
A store orders 8,000 units of a new product. The inventory I on hand t weeks after the order arrived is given in the following table:Use the interpolating polynomial to approximate the inventory
Find(A) 5C2 (B) 6C0
Use the binomial theorem to expand (u + v)6.Data from Binomial Theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = „Coa" + C₁a"-¹b + C₂an-²b² + ₁С3a"-³b³ + +nCnb ...
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
In Problem evaluate each expression.20!/19!
Refer to Example 4. Approximate the inventory after 7 weeks and the average inventory during the first 7 weeks.Data from Example 4A store orders 8,000 units of a new product. The inventory I on hand
Use the binomial theorem to find the fourth term in the expansion of (x – 2)20.Data from Binomial Theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = „Coa" + nC₁a"-¹b +
(A) Find the divided difference table for the points in Table 7.(B) Use the divided difference table to find the interpolating polynomial. Table 7 X f(x) 0 35 1 25 2 19 3 -7 4 -29
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
A graphing calculator can be used to calculate a divided difference table. Figure 5A shows a program on a TI-84 Plus CE that calculates divided difference tables and Figure 5B shows the input and
In Problem evaluate each expression.10!/9!
(A) Find the divided difference table for the points in Table 8.(B) Use the divided difference table to find the interpolating polynomial. Table 8 X f(x) 0 5 1 1 2 -1 3 -7 نیا 4 1
Use the binomial theorem to expand (x + 2)5.Data from Binomial Theorem THEOREM 2 Binomial Theorem For all natural numbers n, (a + b)" = „Coa" + nC₁a"-¹b + C₂an-²b² + ₁С3a"-³b³ +
Find the interpolating polynomial for the function defined by the following table: 0 f(x) 5 x 1 4 2 -3 3 -4
In Problem evaluate each expression.7!
Evaluate.(A) 4! (B) 7!/6!(C) 8!/5!

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