Sequences & Series Questions and Answers

How can knowing the mathematics of ratios and percents be used to help make decisions when shopping?

The monomials that make up a polynomial are called which of the given choices below? Choose the correct answer below. (A) coefficients (B) variables (C) factors (D) terms

Taylor is running a 26.2-mile marathon. Let x represent the number of miles Taylor has run since he started the race. a. Write an expression (in terms of x) that represents Taylor's distance (in miles) from the finish line ._________ b. Write a formula to represent Taylor's distance (in miles) from the finish line, d, in terms of x _____

Find the domain of the function. f(x)={(X+5) / (2-X)} The domain of the function is ____ (Type your answer in interval notation.)

What number should not be included in the domain of the rational expression {(x+2)/(x-6)} ? In the rational expression {(x + 2 )/ (X-6)} the domain cannot include the number ___

Solve (y-7)⁴/³ = 4 where y is a real number. Simplify your answer as much as possible.

You invested $3000 between two accounts paying 2% and 9% annual interest, respectively. If the total interest earned for the year was $200, how much was invested at each rate? $____ was invested at 2% and $______ was invested at 9%.

Use the formula E = t (s/√n) to find the value of E given the values of s, n, and α². (Hint: The value of t is determined from the table in the Written Example using the given value of α² and the formula d.f. = n - 1.) Round the result to the nearest ten-thousandth. S= 19.5 ,n = 9, α²= 0.02 E= ___________

Use the table in the Written Example to find A for the given values of x² and d.f. x² = 0.211 and d.f. = 2 A =?

Express the interval [5,7) as an inequality.

For the following vector field, compute (a) the circulation on and (b) the outward flux across the boundary of the given region. Assume the boundary curve is oriented counterclockwise. F = {x,y}; R is the half annulus {(r.θ):2 ≤r≤7.0≤θ≤π) The circulation on the boundary is __? (Type an exact answer, using π as needed.)

Write the first five terms of the geometric sequence whose first term is 81, and whose common ratio is 1/3 a₁=? a₂=? a₃ = a₄ = a₅=

A culture of fungus starts with 5 units and grows according to the sequence defined by aₙ= 5.2ⁿ⁻¹, where n is the number of fungus units at the end of the day. Find the total number of fungus units there will be at the end of the sixth day. The total number of fungus units on the sixth day is____ units.

The bat population in a certain Midwestern county was 340,000 in 2021, and the observed doubling time for the population is 28 years. a). Find a function n(1) = n₀2 ᵗ/a that models the population t years after 2021. b). Find a function (1)=neʳᵗ that models the population t years after 2021. You may round r to 4 decimal places. c). What is the relative growth rate of the population per year, to the nearest tenth of a percent? d). To the nearest tenth of a year, how long does it take the population to reach 2 million?

A couple wants to buy a $30,000 car and can borrow the money for the purchase at 5%, paying it off in 3, 4, or 5 years. The table to the right gives the monthly payment and total cost of the purchase (including the loan) for each of the payment plans. Suppose that when the payment is over t years, P(t) represents the monthly payment and C(t) represents the total cost for the car loan. Use this information to answer parts (a) through (d). t Monthly Total (years) Payment $ Cost $ Cost $ 3 899.13 32368.68 4 690.88 33162.24 5 566.14 33968.40 (a) Find (4) and write a sentence that explains its meaning. Select the correct choice below and fill in the answer box to complete your answer. (A) If the car is financed over 4 years, the payment is P(4) = $____ (b) What is the total cost of the purchase if it is financed over 5 years? Write the answer using function notation. Select the correct choice below and fill in the answer box to complete your choice. (A) C(5) = $______ (B) P(5) = $____ (c) What is t if C(t) = $33,162.24? t = _____ (d) How much will the couple save if they finance the car for 3 years rather than 5 years? $______

Given the functions defined by f(x) =(4x - 1) and g(x) = 3x, find (f o g)(x).

A person starts walking from home and walks: 4 miles East, 7 miles Southeast, 3 miles South,1 miles Southwest and 2 miles East. This person has walked a total of ____ miles. Find the total displacement vector for this walk:<__>Put your answer in angle brackets in the form < x,y>. If this person walked straight home, they'd have to walk_____miles. Give answers rounded to at least 2 decimals.

(f) The equation 3x = 7 in Z₁₁ has a unique solution. True False Justification: (g) The equation 2x = 7 in Z₁₀ has a unique solution. True False Justification:

Find the LCD for the list of rational expressions. 9x+1/x²+5x-6, 5x/x²+4x-5 The LCD is____.(simplify your answer. Type your answer in either fully expanded or completely factored form.)

Simplity the expression below 1.){ √45x³ - √20x³}

A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need to be repaired twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need a) no repairs? b) no more than one repair? c) some repairs?

Find the inverse: f(x)= log₂ (x+3) . Present the answer using function notation, Select the correct answer below: O f-¹(x) = 2x - 3 O f(x)=2x-3 O f-¹(x) = 2ˣ - 3 O f(x)=2ˣ-3

[(-3)(-4)-(-5)(-2)]/((-2)(11)) a). -11 b). -1/11 C).1/11 d). -1

Write the series with summation notation. 1+8+27 +64 + 125+ 216 1+8+27 +64 +125+216 =i=1Σ? (Simplify your answer.)

A room is half as long again as it is broad. The cost of carpeting the room at Rs. 5 per sq. m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m² is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.

Which of the numbers cannot be represented by a repeating decimal? 11/9 23/7 Square Root of 3 4 1/3

Write the arithmetic sequence 24,17,10,3,...24,17,10,3,... in the standard form: an=

Let {x, y, z, w} be an independent set in R". Is the following set independent? Support your answer. (x-y, y-z z-x}

The tax rate is 6.8%. How much in dollars is the tax on $9.95? Enter only the tax amount, not the total amount of the purchase. Round to the nearest hundredth.

A truck can be rented from Company A for $120 a day plus $0.20 per mile. Company B charges $40 a day plus $0.60 per mile to rent the same truck. How many mile For Company A to have a better deal, the truck must be driven more than __ miles per day.

Gaby's piggy bank contains quarters and dimes worth $10.20. If she has 54 coins in all, how many of each does she have? Gaby has quarters and dimes in her piggy bank.

Dujuan bought a car for $17000, and ever since the car's value has decreased exponentially by 19% per year. How long will it take for the car's value to be $6500? a. The answer to this question is the solution to what equation? [Lett be the number of year since bought the car b. What is the solution?

If possible, sketch a graph of a degree 4 polynomial with 3 turning points that's an even function. If it's not possible, explain why.

Find the LCM of 12 and 30.

-Prove the statement by induction. 1+4+4² +4³ +...+4^n-1 = 4^n - 1 / 3

Solve the following equation if 0 ≤ x ≤ 2π. (Write your final answer(s) here and include your work in your File Upload for full credit.) cos 2x = - √2/2

Consider the function f(x) = |sin(x/2| (a) Compute the Fourier coefficient a0 for this function. (b) Explain (without making any computation) why by must be zero for all k.

You have 180 ft of fencing to construct the boundary of a rectangle. The rectangle has length I and width w. • Write the perimeter P and area A of the rectangle in terms of I and w. • Write A in terms of w only. Hint: use substitution. • Find w that maximizes the area. • What is the corresponding / that maximizes the area? • What is the maximum area?

Solve the equation log 2(x+3)+ log2 (x+2) = 1

You deposit $4000 in an account earning 2% interest compounded continuously. The amount of money in the account after t years is given by A(t) = 4000e0.02t How much will you have in the account in 6 years? $ _____ Round your answer to decimal places. How long will it be until you have $19700 in the account? answer to 2 decimal places.How long does it take for the money in the account to double? ---------- years round your answer to 2 decimal places.

Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. R = 500; 6.2% interest compounded semiannually for 7 years.

Write this number in standard form. Two million four hundred sixty-nine thousand five hundred fifty-two

Is the number 56,240 evenly divisible by the number 10? Yes No

Is the number 996 evenly divisible by the number 2? Yes No

For a given arithmetic sequence, the first term, a₁, is equal to -18, and the 40th term, 40, is equal to -174. Find the value of the 10th term, a10.

Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given. a=7; r = -3 a. Find the 5th term of the sequence b. Find the formula for the nth term of the sequence

Find the sum of the arithmetic sequence. 1+3+5+ ... +1823

Find the open interval of convergence of the power series Σm=1 (x − 8)^m /(m²+8)7^m Your answer should be an interval of the form (a, b). Enter the values of a and b below. a = b=

R= 4 2 2 4 R is the matrix of a linear transformation consisting of a rotation with angle θ and a scaling. Determine θ and r.

Find the sum of the first n terms of the following arithmetic sequence. a1 = 13, d = 75; n = 10