Sequences & Series Questions and Answers

Write the expression as a sum or difference of logarithms. Assume that variables represent positive numbers. log₆2/9z

Write the first term of the sequence an = 7ⁿ. The first term of the sequence a = 7ⁿ is a₁ =

Find a general term an for the sequence whose first four terms are given. 1/4,1/16,1/64,1/256

An auditorium has 53 seats in the first row, 59 seats in the second row, 65 seats in the third row, and so on. Find the general term of this arithmetic sequence and the number of seats in the twentieth row. The general term aₙ of this arithmetic sequence is _____ .

Solve the equation: √m + 3 = √(m + 12) Answer: m = Enter your answer as an integer or as a reduced fraction in the form A/B

Write an exponential function in the form y = ab^x that goes through points (0, 16) and (7,2048).

The first row of a conference hall has 11 chairs and 2 additional chairs in each subsequent row. How many chairs are in the 8th row? How many chairs in total are in the first 8 rows? 25, 144 25, 288 27, 304 27: 152

Find the sum of the terms of the infinite geometric sequence. 18, 6, 2, .... The sum of the terms of the infinite geometric sequence is.

Write the following in polar form (angles in degrees). 12.61 miles, 30° north of east. 1.66 miles, 40° west of south. 5.53 miles, in the direction opposite of 15° south of east.

A town has a population of 13000 and grows at 5% every year. What will be the population after 11 years, to the nearest whole number?

If C = s - 5 and D = s - 8, find an expression that equals C + 2D in standard form.

A building contractor is to dig a foundation 54 feet long, 24 feet wide, and 3 feet deep. The contractor pays $25 per load for trucks to remove the dirt. Each truck holds 9 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

Let P₂ denote the real vector space of polynomials in x with real coefficients and degree at most 2 with the basis B = {x+7x², 2+x, x²} Set p(x) = 3x and that suppose that coordinates of p with respect to B are given by

A pendulum swings a length of 22 inches on its first swing. Each successive swing is 9/10 of the preceding swing. Find the length of the fifth swing and the total length swung during the first five swings. The length of the fifth swing is

trivial solution then (x, y, z) = (a) (0, 1, 2) (b) (0, 0, 2) (c) (0,0,0) (d) (K,K,K)

The accompanying table shows the value of a car over time that was purchased for 19000 dollars, where x is years and y is the value of the car in dollars. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the value of the car, to the nearest cent, after 16 years.

A(n) sequence is a function whose domain is {1, 2, 3, ..., n}, where n is some natural number. Choose the correct answer below. A. general B. finite C. infinite

Use the Golden Search method to maximize the following unimodal function, ƒ(X) = −(x − 3)², 2≤ x ≤ 4 with ∆= 0.05.

Consider the following linear program. Does the linear program involve infeasibility, unbounded, and/or alternative optimal solutions? (Select all that apply.) infeasibility unbounded alternative optimal solutions Explain. (Select all that apply.) The regions defined by the constraints do not overlap. The second constraint allows the solution to be made infinitely large. There are more than one solution for A and B which produce the optimal value for 1A + 1B. The first constraint allows the solution to be made infinitely large.

Find the equation of the line that is parallel to 5x-2y-12=0 and passes through the point (-14,-4) Find the equation of the line that is perpendicular to 4x-7y-54= 0 and passes through the point (-44,-5)

Use the binomial formula to expand the binomial. (x + 4y)⁵ (x+4y)⁵ =

Find the seventh term of the arithmetic sequence whose first term is 14 and whose common difference is 4.

For what value of a is the following true? log(x + 8) = log x + log 8.

Answer the questions about the following polynomial. -x-7 The expression represents a ________ polynomial with _________ term . The constant term is _________ , the leading term is _________,and the leading coefficient is __________

Observers at points A and B, 60 km apart, sight an airplane at angles of elevation of 50° and 72", respectively. Use this information to determine how far the plane is from each observer if the plane is between them. (You'll use this same information in the next question.) What is the distance from point A to the plane? A. 67.288 B. 52.501 C.54.198 D. 66.423

A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts.

Answer the questions about the following polynomial. -(X^2/8) -1 The expression represents a_______ polynomial with______ terms. The constant term is_______ , the leading term is________ ,and the leading coefficient is ______

Gus analyzed data related to average salaries and years of working experience in five different industries. He performed a linear regression for each industry. The correlation coefficient, to the nearest hundredth, for each industry is given. Drag the correlation coefficients to the empty boxes in order from weakest to strongest correlation, with weakest to the left and strongest to the right.

If C = 1+p² + 3p and B = 2p + 6p², find an expression that equals 2C -B in standard form.

Write an exponential function in the form y=abˣ that goes through points (0,19) and (2, 1539).

Given the circle below with secants GHI and KJI. If JI = 30, KJ = 17 and HI = 31, find the length of GH. Round to the nearest tenth if necessary.

A newspaper is conducting a survey to find out people's favorite sport. The newspaper selects random people that walk into the Georgia Dome to watch the SEC Championship Football Game.

Given f(x) = 3x²-10x + k, and the remainder when f(x) is divided by x - 5 is 40, then what is the value of k?

The difference of the square of a number and 24 is equal to 5 times that number. Find the negative solution.

Among all three vectors u, v and w with lengths equal to 1,2, and 3,respectively, find those in which the box made out of them has the maximum volume. Justify your answer.

Find the center, vertices and foci of the hyperbola described by the following equation. (x + 3)² - [(y - 4)²]/4 = 1 Center: ___________ Vertices: __________ Foci: __________

Fill in the following table so that u is a function of v AND v is also a function of u u -8 0 ? 12 v ? 9 0 ?

A town has a population of 17000 and grows at 3% every year. What will be the population after 10 years, to the nearest whole number?

Given that f(x)=x-1 and g(x)=x²-x, find (f+g)(3), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (f+g)(3) = (Simplify your answer.) B. The value for (f+ g)(3) does not exist.

1).Suppose that p(x,y)-represents the production of a two-product firm. The company produces x units of the first product at a cost of c₁ each and y units of the second product at a cost of c₂ each. The budget constraint, B, is a constant given by the following formula. Use the method of Lagrange multipliers to find the value of λ in terms of Px. Py, C₁, and C₂. The resulting equation holds for any production function p and is called the Law of Equimarginal Productivity. B=C₁X+C₂Y Choose the correct answer below. a).λ ={Px /C1=Py\C2} b). λ=Px=C1=Py=C2 c).λ={Py/C1=Px/C2} d).λ={C1/Px=C2/Py}

Rhonda Brennan found her first job after graduating from college through the classifieds of the Miami Herald. She was delighted when the offer came through at $18.50 per hour. She completed her W-4 stating that she is married with a child and claims an allowance of 3. Her company will pay her biweekly for 80 hours (assume a tax rate of 6.2% on $128,400 for Social Security and 1.45% for Medicare). Calculate her take-home pay for her first check.(Round your answer to the nearest cent.)

Evaluate and simplify the expression when a = 2 and b = 4. 4a-2(a + b) + 1 = [?]

John paid $11.88 for a 2.38-pound bag of shrimp at one store. The following week, he paid $26.47 for a 5.08-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 2.38-pound bag: $ per pound Unit price for the 5.08-pound bag: $ per pound

Solve the equation. Give your simplified answer as an improper fraction. 4(x+5) = 6(2x - 1)

Use the distributive property. 6(3x - 4y +7z) = [?]x + []y +[]z

Use the properties of logarithms to simplify the expression so that the result does not contain logarithms of products, quotients, or powers. ln( x ( x + 1 ))

Determine the values. f(-2) = f(0) = f(1) = f(3) = (b) Determine the domain and range of the function. Domain: (A) [-4, 0) U (0, 3] (B) [-4, -0.5] U [0, 2.25] (C) [-5, 5] (D) [-3.5, 3] (E) (4, 2.25) Range: (A) [-3.5, 3] (B) (4, 2.25) (C) [-4, -0.5] U [0, 2.25] (D) [-5, 5] (E) [-4, 0) U (0, 3]

Evaluate and simplify the expression when x = 1 and y = 2. 3(x + 2y) - 2x + 10 = [?]

A football field is 360 feet long and 160 feet wide. 5 principals are making evacuation plans for their schools. How many more students can fit on all of the fields combined if each field is already 65% full? (Remember the expected floor space a standing person occupies is about 2.5 sq. feet) A. 8,064 B. 23,040 C. 40,320 D. 80,640

What satisfies sin (1/3) theta if cos theta is equal to 4/5, and the range is 360<theta<450?