Sequences & Series Questions and Answers

Find the sum of the arithmetic series using a formula. 7+14+21+ ... +798

Consider the sequence 300, 360, 432,... (a) Find the fourth term of the sequence: 300, 360, 432, Number. ...... (b) Find a formula for the nth term of the sequence an The nth term of the sequence is an =___ (Your answer involves n and real numbers.) (c) Describe the sequence an O The sequence is arithmetic O The sequence is geometric O The sequence is neither arithmetic nor geometric

f(x) =-3/2*(3)^-x+3/2, for f (2) For the following exercises, evaluate each function. Round answers to four decimal places, if necessary.

(No Work = No Credit) Two polynomials P and D are given. Use Long Division to divide. P(x) = 6x^4-3x^3+29x², D(x)=3x^2+13

Which of the following is true about the graph of the polynomial p(x)= -2x³+4x²-3? A) p(x) → ∞ as x→-∞, p(x)→∞ as x→∞, y− int: (0, -3) B) p(x) → ∞ as x →-∞, p(x) →-∞ as x → ∞, y− int: (0, -3) C) p(x)→-∞ as x→-∞, p(x) →-∞ as x → ∞, y-int: (0, -3) D) p(x) →∞ as x→-∞, p(x) → −∞ as x → ∞, y-int: (0,−2)

The sum of three integers is 389. The sum of the first and second integers is 69 more than the third integer. The third integer is 60 less than the first integer. Let x represent the first integer, y represent the second, and z represent the third integer. Find the three integers. (We suggest that you set up a matrix and use the calculator to solve.)

Which could be the graph of f(x) = (x + a)^5?

Which is true about the minimum output value of the function. f(x) = mx² +nx + p? OA) minimum value is f(-n/2m) only when m is positive OB) minimum value is f(-n/2m) only when m is negative OC) minimum value is -n/2m only when m is positive OD) minimum value is -n/2m only when m is negative

show that distance between the points (t, 2) and (2,1) is equal to 2 if only t=0 or t= 4.

Draw an undirected graph represented by the given adjacency matrix. 1 2 0 1 2 0 3 0 0 3 1 1 1 0 1 0

Determine if the given expression is a polynomial. If it is, state the degree of the polynomial. -15x³ +7x⁴ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (A) The expression is a polynomial. The degree of the polynomial is ____. (B) The given expression is not a polynomial.

Smith's family, with total gross income of $144000 per year, wants to purchase a home. If %33 of their income goes to monthly payment and the interest rate is 3% compounded monthly, how much mortgage do they qualify for 30 years amortizations? a. $939269.95 b. $849212.78 c. $800300.69 d. $889260.55 e. $913591.26

Suppose that the number of crates an agricultural product is given by z =11xy-0.0002x² - 5y/0.03x + 4y where x is the number of hours of labor and y is the number of acres of the crop. Find the marginal productivity of the number of hours of labor (x) when x = 800 and y = 900. (Round your answer to two decimal places.)_____crates Interpret your answer. a) If 900 acres are planted and 800 hours are worked, this is the number of crates produced. b) If 900 acres are planted, the expected change in the productivity for the 801ˢᵗ hour labor is this many crates. c) If 800 acres are planted, the expected change in the productivity for the 901ˢᵗ hour of labor is this many crates. d) If 800 acres are planted and 900 hours are worked, this is the number of crates produced.

An auto dealer's sales numbers are shown in the table below. Find for each month the mean, median, and mode prices of the cars she sold. Round your answers to the nearest dollar Number sold Price May June July $20,000 22 25 24 $15,000 49 24 24 $13,500 25 49 49 May mean,median and mode ? June mean,median and mode? July mean,median and mode?

A bank charges an annual fee of $15 to have a checking account with them. The bank also charges $0.05 per check you write. Which function below models the total cost for the year to have a checking account with the bank if you write x checks throughout the year? A) f(x)= $0.05x + $15 B)f(x)= $0.03x + $15

Using the function you identified in the previous problem, what would you expect to be the total cost of the checking account if you write 58 checks during the year? f(x) = $0.05 (58) + 15 f(x) = $2.90 +15 f(x) = ? A)$17.90 B)$16.74

If $325,000 is invested in an account earning 6.5% annual interest compounded continuously, then how much interest is accrued in the first 3 years? Include a dollar sign in your answer and commas when appropriate. Round to the nearest cent.

Evaluate.i=4Σ7 (i-8) (Simplify your answer.)

The point (-12, 16) is on the graph of y = f(x). Find the corresponding point on the graph of y = g(x), where g(x) = (1/4)f(x). The corresponding point on the graph of y = g(x) is___.

the charges a fee of $125 to design an ad with an additional $5 per day the ad appears in the newspaper. Match each component of the slope-intercept form of a function, f(x)=mx+b, to its de- scription as it relates to this scenario. f(x) a. the number of days the ad ap- pears in the newspaper X b.the fee for designing an ad for the newspaper b c.the cost per day for an ad to ap- pear in the newspaper m d.the total cost of running an ad in the newspaper

Let f: Z -> Z be given by f(x) = x^2 + 1. Let P(S) denote the power set for a set S. Then, | P(f^(-1)(1) UNION f^(-1)(2) UNION f^(-1)(3)) | is equal to a. 2 b. 4 c. 8 d. 16 e. None of the Above

A town has a population of 4000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will reach 7500?

Given that sinθ = 15/17 and that angle terminates in quadrant I, then what is the value of cos θ?

Consider the functions defined by f(x)=6x-2, g(x)=-x²-4x+1, k(x)=\x-2| 8. f(x-2) 9. g(-3)+1 10. k(x-3)

.In Exercises 27-38, use the fundamental identities to simplify the expression. Use the table feature of a graphing utility to check your result numerically.

Solve for x to the nearest 10th. 1.4 = 250(0.5)ˣ/16

Determine whether each pair of functions are inverse functions. f(x)=2x+8 g(x)=1/2x-4

In AQRS, the measure of S=90°, RQ = 85, SR = 36, and QS = 77. What ratio represents the cosecant of Q?

Determine the amplitude and period of each graphed below. 5. cos 240= 120/x 6. sin 315=x/10 Consider the functions defined by f(x)=6x-2, g(x)=-x² - 4x+1, k(x)=x-2)

Answer the questions about the following function. f(x) =x+8/ X-2 (a) Is the point (3,13/3) on the graph of f? (b) If x= 1, what is f(x)? What point(s) are on the graph of f? (c) If f(x) = 2, what is x? What point is on the graph of f? (d) What is the domain of f? (e) List the x-intercept(s), if any, of the graph of f. (f) List the y-intercept, if any, of the graph of f.

Kaylee invested $830 in an account paying an interest rate of 6.6% compounded how long would it take, to monthly. Assuming no deposits or withdrawals are made, the nearest year, for the value of the account to reach $1,260?

Find the exact value of each trigonometric function without a calculator. (Use the Unit Circle) 1. sin 315° 2. tan(-π/6) 3. cos (2π/3)

Add the following terms if possible. 3√32 +5√50 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 3√32 +5√50= _____ (Type an exact answer, using radicals as needed.) B. The radicals cannot be combined.

Simplify the expression. √63 √63 = ____ (Type an exact answer, using radicals as needed.)

The average speed on Route 17 is 55 mph. Joe is traveling at 61 mph. What is Joe's deviation from the mean? (1) 104 (2) 6 (3) -6 (4) -7

A tree casts a shadow that is 38 feet long, with an angle of elevation of 32 degrees when the shadow meets the ground (As shown in the diagram below). Solve for the height of the tree and the distance from the end of the shadow to the top of the tree.

Evaluate the expression without using a calculator. 8^(4/3) Rewrite the expression using a radical. 8^(4/3) = ____ (Do not evaluate.)

Add the terms if possible. √32 +7√2 Select the correct choice below and fill in any answer boxes within your choice. A. √32 +7√2 = ____ B. The terms cannot be simplified.

You deposit $750 each month into an account earning 7.9% interest compounded monthly. a) How much will you have in the account in 17 years? b) How much total money will you deposit into the account, after 17 years of making monthly deposits? c) How much total interest will you earn after 17 years?

Use the product rule to simplify the following expression. Assume that variables represent nonnegative real numbers. √4x * √8x √4x * √8x = ____ (Type an exact answer using radicals as needed.)

Solve for x, rounding to the nearest hundredth. e³x = 5

Simplify by reducing the index of the radical. ⁶√x¹⁸

Graph the trigonometric function. y = 2 csc 3x Start by drawing three consecutive asymptotes. Then plot two points, one on each side of the second asymptote. Finally, click on the graph-a-function button.

Solve the equation: log₄(3x+5) = 1/2. Select all applicable answers. Select all that apply: -1 0 3 No Solution

Given two terms in a geometric sequence, write the explicit equation and determine the 8th term. t(0) = 229,376 and t(3) = 3,584 Explicit equation: _____________________ 8th term: _____________________

Let f(x) be a function, and f^(n) ~= 0 for n ≥ 3. Use a second order Taylor series expansion to show that if f(x) achieves a maximum at x = x*, then f" (x*) <0.

What are the roots of the function f(x) = (log(3^x) - 2 log(3)) (2^x -1) with xεR?

The information a₁ = 2 and an = 2an-1-7 defines a recursive sequence. Fill in the blanks below to find the first 5 terms of the sequence: a₁ = 2 a₂ = 2a₁ - 7 = 2(2)-7=__and a3 = 2a₂-7= 2(−3) - 7 = a4 = 2a3-7 = 2(____________) — 7 = a5 = 2a4 - 7 = 2(______)- 7 =

A circular flower bed is 24 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the area of the sidewalk in square meters. Use 3.14 for π. The area of the sidewalk is __ m². (Round to the nearest whole number as needed.)

A business has found that it can sell 670 items if it sets its price to $66.91. However, if it lowers its price to $43.71, it can sell 950 items. (a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places) p(x)=? It costs the business $11.86 per item to produce and they have $2,150 in overhead each month. (b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places) C (x)___x+ _____ R(x)=____x²+ _____x+______ P(x)=____x²+______x+______ (c) Consider the maximum profit the company can make: To maximize their profit, they should sell _______items at a price of $_______each and they will make $_____ in profit.