Sequences & Series Questions and Answers

Solve the system of equations. Write your answer as an ordered pair. 3x+2y=8 2x-5y = 18

How many solutions does the following system have: 5x-4y=20 2x+1=3y Select one: a. 1 b. 0 c. none d. Infinitely many

The compound interest formula is in the next textbox, where R is the future value of the investment, r is the annual interest rate (as a decimal), n is the number of times interest is compounded each year, t is the number of years the principle is invested, and P is the principle which represents the original amount of money invested. Mary invested $1000 at 5% annual interest in an account that compounds interest 4 times per year. If she kept her money in the account for 5 years, how much will her future value be? P(1 + r/n)nt = R I don't know. $11,057.33 $1,250.00 $2413.16 $5,254.73 $1,525.47 $1,282.04

What is the "sub-reference" function, f'(x), for the function f(x) = -5(x+3)^2-4 (the function that handles the non-rigid transformation of the parabola, first)? f'(x) = -5x² f'(x) = x² f'(x) = 5(x+3)² f'(x) = -(x+3)²

An open-faced box is to be constructed by cutting squares out of the corners of a 12in by 12in sheet of tin and folding up the sides. Which of the following describes the volume of such a box? The volume of the box is given by h(12-2h)2 in³, where h is the side length of the cut out squares The volume of the box is given by h² (12-2h) in³, where h is the side length of the cut out squares The volume of the box is given by (12-2h)³ in³, where h is the side length of the cut out squares The volume of the box is given by h³ in³, where h is the side length of the cut out squares. I don't know.

USE THE SAVINGS PLAN FORMULA TOANSWER THE FOLLOWING QUESTION You put $350 per month in an investment plan that plays an APR of 4.5%. How much money will you have after 18 years? Compare this amount to the total deposits made over the time period. After 18 years the investment plan will contain $

The length of one leg of an isosceleſs right triangle is 3 ft. What is the perimeter of the triangle? 3+3√2 ft 3+3√3 ft 6+3√2 ft 6+3√3 ft

consider a student loan for $17,500 at a fixed APR of 9% for 15 years a. calculate the monthly payments b. determine the total amount paid over the term of the loan c. of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest

Write the given phrase as an algebraic expression. Use the variable x to represent each unknown number. A number divided by four. The answer is

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth. 0.4 radian 1.0 radian 2.7 radians 5.0 radians

Use the information given below to find tan (a-B). Cos α = 15/17 with a in quadrant IV tan B=5/12 with B in quadrant III Give the exact answer, not a decimal approximation. tan (a-B) =

Suppose I have $5000 to invest, and I am able to invest it at an 8% rate compounded quarterly. Which formula below shows the correct setup for calculating how much money will be in the account after 20 years? I will have A = 5000e0.08-20 dollars. I will have A = 5000(1+0.08/4)4.20 dollars. I will have A = 5000e0.08-4-20 dollars. I will have A = 5000(1+0.08\12)12.20 dollars.

For all positive values of s, t and h, which of the following is equivalent to s23t2t3/h-2? A. s5t6h2 B. s6t5h² C. s6t6h² D.s5t6/h2 E. s6t5/h2

The sum of three consecutive even integers is 162. Find the integers. The integers are (Use a comma to separate answers.)

Consider a home mortgage of 200,000 at a fixed APR of 4.5% for 25 years A. calculate the monthly payment B. Determine the total amount paid over the term of the loan C. of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest A. the monthly payment is $ B. The total amount paid over the term of the loan is $ C. of the total amount paid is paid toward the principal and is paid for interest

Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function T where T(d) = 800 (1/2)d is the amount of radioactive material remaining d days after the test. Write a log expression that represents the number of days until only 7 amounts of radioactive material remains?

Let z = [(a, b)] be an integer. Define [z] to be b-a if b>a, a-b if a> b, and 0 otherwise. Prove that this definition is unambiguous. Prove that if z and y are integers and z> [y] then there is no nonzero integer z such that x.z = y.

Compare and contrast the graphs of f(x) = (x - 1)(x + 5) / (x-1) and g(x) = x + 5

Consider the following functions. f = ((-3,-3), (1.-2)] and g= {(0, 2), (1,5). (5.2), (3, 2)) Step 3 of 4: Find (f g)(1).

«ƒ(2) = {3+ if " Evaluate f(5) if f x 2x x ≤2 3x-4 if2<x<54x-7 if x > 5

The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation. What is the minimum height of the flag? 3 feet 9 feet 12 feet 15 feet

If 'r' is the radius of the circle and 't' is the degree measure of a central angle that intercepts on the circle an arc of length 's' then s = rt. Select one: O True O False

Write the following sentence using mathematical symbols. Twice the difference of x and 2 is greater than the reciprocal of 10.

Plot the ordered pair (1.5,0). State in which quadrant or on which axis the point lies.

Solve the following inequality. Write the solution set using interval notation. -3x+1428 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) OB. The solution set is Ø.

Marsha and Jan both invested money on March 1, 2007. Marsha invested $10,000 at Bank A where the interest was compounded quarterly. Jan invested $9,000 at Bank B where the interest was compounded continuously. On March 1, 2013, Marsha had a balance of $14,077.60 while Jan had a balance of $12,416.88. What was the interest rate at each bank? (Round to the nearest tenth of a percent.) At Bank A, the interest rate is about 5.7%. (Round to one decimal place as needed.) At Bank B, the interest rate is about %. (Round to one decimal place as needed.) ***

Use mathematical induction to determine which formula is true for all natural numbers n. 01.3 +2.4+3.5 + ... + n(n + 2) = (n² + n)(2n + 7) 6 1 3+2 4+3.5+ O1 3+2 4+3 5+ *** *w* + n(n + 2) = + n(n + 2) = O1 3+2 4+3 5+ ... + n(n+ 2) = n(n + 2) 3 (n² + n)(n+7) 6 n(n + 2) 6 01.3+2 4+3.5+...+ n(n+ 2) = n(n + 1)(n + 2) 6

Let VR with Euclidean Inner Product, and let W = span{V1, V2, V3} where V₁ (1,0,-4, 0, 2), v2 = (0, 1, 3, 0, 7), v3 = (0, 0, 0, 1,-6). = State a basis for W, (the orthogonal complement of W.) NOTE: only the final answer will be graded, you do not need to show your work. You will need to do so using text to answer, however you do NOT need to use the math equation editor.

4. Decide whether the given statement is always, sometimes, or never true. Give a reason for your answer. a. Rational expressions contain exponents. b. Rational expressions are undefined for values of the variables that make the denominator 0. c. Restrictions on the variables change when a rational expression is simplified.

3. Divide. Show factoring to earn credit. 21x³ 8y a. b. C. 7x 4y³ ÷ x² x² + 2x + 1 6x² - 6x² XA +5 x3 ÷ = 3x x² - 1 3x²15x + 12 2x² + 2x - 40

1. Simplify each rational expression. State any restrictions on the variable. Show factoring to earn cr 5x³y 15xy³ a. b. C. x² + 8x + 16 x² - 2x - 24 2y² + 8y-24 2y²2²-8y + 8

7. Graph the pair of functions on a graphing calculator. Find the approximate point(s) of intersection. y = 1 X-3 - 6;y = 6.2

Corey spies a bald eagle in a tall tree. He estimates the height of the tree to be 80 feet and the angle of the elevation to the bird frim where he stands to be 68 degrees. The leaves on the tree make it difficult for Corey to watch the bird, so he takes several steps awag from the tree to get a better view. he now estimates his angle of elevation to be 41 degrees.

2 4. Write an equation for the translation of y = with asymptotes x = 4 and y = -8. X

The logistic growth model H(t) = 5,000 1+3e -0.72t what year did 4,808 families own a home? In what year did 4,808 families own a home? represents the number of families that own a home in a certain small (but growing) city t years after 1980. In

Find the domain, points of discontinuity, and x- and y- intercepts of the rational function. Determine whether the discontinuities are removable or non-removable. y = (12-3x) / (x² - 7x+12) B. There is no x-intercept. What is the y-intercept of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is 1. (Type an integer or a simplified fraction.) OB. There is no y-intercept. Determine whether the points of discontinuity are removable or nonremovable. Select all correct statements that apply. A. x=3 is a nonremovable discontinuity. C. y=4 is a removable discontinuity. E. x=3 is a removable discontinuity. G. y =3 is a nonremovable discontinuity. 1. x=4 is a removable discontinuity. K. y=3 is a removable discontinuity. M. There are no discontinuities in the given function. B. x = 0 is a removable discontinuity. D. y=0 is a removable discontinuity. ]F. y 4 is a nonremovable discontinuity. H. x=4 is a nonremovable discontinuity. y = 0 is a nonremovable discontinuity. 11 J. L. x = 0 is a nonremovable discontinuity.

2. The speeds of an airplane is given by s = d where d represents the distance and t is the time. A plane flies 700 miles from New York to t' Chicago at a speed of 360 mi/h. Find the time for the trip. Show your work.

6. CDs can be manufactured for $0.19 each. The development cost is $210,000. The first 500 discs are samples and will not be sold. a. Write function for the average cost of a disc that is not a sample. b. What is the average cost if 5000 discs are produced? Show work. c. How many discs must be produced to bring the average cost under $10? Show work.

Optional Extra Credit Challenge: What would it cost to send a rocket to Mars (7.9 x 107 km from the earth) if the average speed of the rocket is 1600 miles per minute and the fuel consumption averages 100 grams every 1.5 seconds and the cost of the fuel is $500.00 per pound. Use correct significant figures in your answer. Note: 1.6 km = 1 mi 2.2 lbs= 1 kg

Shureka Washburn has scores of 83, 64, 89, and 76 on her algebra tests. a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 78 or higher, given that the final exam counts es two tests. b. Explain the meaning of the answer to part (a).

4. Find the vertical and horizontal asymptotes of the graph of each rational function. Indicate if there are none. (x + 3)(x - 2) (x-2)(x + 1) a. y = b. y = x + 2 2x² - 8

How will the domain and range of the parent function y =1/x change after the translation of its graph by 3 units up and by 5 units left?

2 AI 7 5 35 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. The solution set is Ø.

Determine whether the equation is linear or not. Then graph the equation by y = 7x

k(x) = x² + 3x - 1 (x + 1)(x² + 2) Find the partial fraction decomposition for:

The grade point averages for 10 students are listed below. Find the range of the data. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system? O The system can be either inconsistent or consistent. O The system can be either independent or dependent. O The system can only be independent and consistent. O The system can only be dependent and inconsistent.

Every rational function has a vertical asymptote. Select one: O True O False

The graph of f(x) = Select one: True O False is contained within only two quadrants.

The graph of a rational function never crosses a vertical asymptote. Select one: O True O False