Sequences & Series Questions and Answers

Find all solutions of the equation in the interval [0, 2x). 2 sin 6x cos2x-2 cos 6x sin 2x = √2 Write your answer in radians in terms of . If there is more than one solution, separate them with commas.

The function f is an even function whose graph contains the points (-2,5), (-1,3), (0, -2) The ordered pair (1, y) is also on the graph of y = f(x) for what value of Y? H Type your answer here

Select all of the statements below that are true. There is a set of 6 vectors in R8 that is linearly independent. There is a set of 4 vectors in R7 that spans R7. All sets of 8 vectors in R5 span R5 There is a set of 4 vectors in R9 that is linearly dependent. There is a set of 6 vectors in R5 that does not span IR5 There are infinitely many sets of 4 vectors in R5 that span R5.

The reference number of a is the distance from a to the nearest whole multiple of π . Now that you know that, compute the exact reference numbers of 19π/6, 17π/6

There are eight swimmers in a competition where the top three swimmers advance. In how many ways can three swimmers advance?

C and D are mutually exclusive events. Find P(C or D). P(C) = 3/7, P(D) = 4/7 P(C or D) = (Round to three decimal places as needed.)

When simplifying 2(8-7[25-(2+3)2]], we should be simplifying the inner- most parentheses first: (2 + 3) = 5. A True. B False. You need to simplify exponents first: 329. C) False. We should be subtracting in the brackets first: 8-7 = 1. D. False. We need to square both numbers inside the parentheses first: 22 +32 = 4+9

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability. Write the answer as a fraction in simplest terms in the form a/b. P(red or blue)

Solve the equation. (Enter your answers as a comma- separated list. If there is no solution, enter NO SOLUTION.) e x In 4 = 0.0625

About 30% of the U.S. population is under 20 years old. About 17% of the population is over 60. What is the probability that a person chosen at random is under 20 or over 60? Write your answer as a percent rounded to the nearest whole number. Do not include the percent symbol.

Danielle was charged interest of $64 for a loan amount of $2,800 that she borrowed for 120 days. What annual rate of simple interest was charged?

Find the solution of the quadratic equation x2-3 = 0 by using square roots method.

Solve the following system by of three equations. Write your solution as an ordered triple. 2x - 3y = -12 y = 2 -4x + 2y-3z = 1

Find the equations of the spheres passing through the circle x² + y² + z² - 6x - 2z + 5 = 0, y = 0 and touching the plane 3y + 4z + 5 = 0.

The annual interest rate on a credit card is 25% and interest is calculated by the average daily balance method of the billing cycle. The unpaid balance at the start of a 30-day billing cycle was $1672. A purchase of $265 was made on day 10 and a payment of $300 was credited to the account on day 20. Find the unpaid balance at the end of the billing cycle.

Find the slope of a line perpendicular to the following line. f(x) = 5x/9+2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A.The slope of a line perpendicular to f(x) is (Simplify your answer. Type an integer or a fraction.) B. The slope of a line perpendicular to f(x) is undefined.

Find the slope of a line parallel to the following line. f(x) = -4x/3-8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A.The slope of a line parallel to f(x) is. (Simplify your answer. Type an integer or a fraction.) B. The slope of a line parallel to f(x) is undefined.

In 2005, 11.8 out of every 50 employees at a company were women. If there are 46,392 total company employees, estimate the number of women.

Find the domain of the rational function. C(x) = X-2/ x²-1

Solve the following equation. z/3 - z/4= 48

Prove that with high probability, the binomial graph G(2n,1/2) has a perfect matching.

Suppose that 5 customers arrive, and each orders a different appetizer to share from a choice of 12 appetizers. In how many ways can this be done?

How does an earthquake of magnitude 7.9 compare in intensity with an earthquake of magnitude of 3.4 on the Richter scale?

Find the theoretical probability of the event when rolling a standard number cube. P(1)

v=-0.0098t + c In R v is the velocity of a rocket, t is the firing time, c is velocity of the exhaust, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel Find the velocity to the nearest hundredth of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.7 km/s, and a firing time of 30s.

Let f(x,y) = k(x² + y²)IA(x,y) where A is the region bounded by y = |x| and y = 2. Find k so that f is a genuine joint pdf.

The Fiore's wish to create a sinking fund to save for their children's education. a.) They estimate that they will need to save about $150,000 in 18 years. If the account returns 7.5%, how much are the monthly installments? b.) How much will The Fiore's deposit in the account? c.) Once in college, what are the monthly installments of the $150,000 pay out in 4 years? d.) What is the total amount the twins will receive from the $150,000 pay out during the 4 years they're in college

Find the reference angle of 15pi/8 Enter your answer in radians.

Find the x-intercept(s) algebraically. f(x) = 3x² + 4x-4 (Type an exact answer, using radicals needed. Use integers or fractions for any numbers in the expression. Type each solution only once. Use a comma to separate answers as needed.)

Given the sequence bn, defined recursively below, find b5. b₁ = 2 b₂ = 4 bn= -2bn-1-3bn-2

Which of the following statements describes the x-terms in the expression 8x8/x27 A. The larger exponent is on the x-term in the numerator. B. The larger exponent is on the x-term in the denominator. C. The exponents on the x-terms in the numerator and denominator are the same.

How many real and how many imaginary roots does the polynomial x² + 8x + 15 have? Select one: 2 real, 0 imaginary 1 real, 1 imaginary O real, 2 imaginary 3 real, 0 imaginary

Radium-226 has a half-life of 1660 years. How many years does it take a radium sample to decay to 55% of the original amount? Round your answer to the nearest year.

Graph 2 complete cycles of the function below. y = 4 sin(2x)

Find the inverse function, f-1(x) of the following f(x)=(3x-7)/(4x +3)

Describe in words the sequence of transformations that will take the graph of y = x² to the graph of y = -2(x+3)² - 8?

The point at which a company's profits equal zero is called the company's break-even point. Let R represent a company's revenue, let C represent the cor R(x) = 100x C(x) = 65.5x + 68,000 (a) Find the firm's break-even point; that is, find x so that R=C. (b) Find the values of x such that R(x) > C(x). This represents the number of units that the company must sell to eam a profit. (a) x= (Type a whole number.) (b) Solve the inequality for x. Type the correct inequality symbol in the first answer box below, and type an integer in the second answer box

Records over the past year show that 1 out of 355 loans made by Mammon Bank have defaulted. Find the probability that 5 or more out of 320 loans will default. Hint: Is it appropriate to use the Poisson approximation to the binomial distribution? (Round λ to 1 decimal place. Use 4 decimal places for your answer.)

Researchers want to determine which cold remedy is most effective at controlling cold symptoms. They are considering three methods of gathering data: Method A: Researchers give cold remedy A or cold remedy B to people with colds and then observe the duration of the cold symptoms exhibited by each group. Method B: Researchers observe the cold symptoms exhibited by people with colds who choose to take cold remedy A and people with colds who choose to take cold remedy B. Method C: Researchers ask people with colds if they feel better after taking cold remedy A or cold remedy B. Tell whether each method of gathering data is a survey, an observational study, or an experiment. Which option would give the most reliable results?

Karen uses a pedometer to track the number of steps she takes. On the average day, Karen takes about 2,075 steps, but this can vary by as many as 410 steps. On any given day, what are the maximum and minimum numbers of steps Karen can be expected to take?

The period of the sine and cosine curves is 360 degrees and the period of the tangent curve is 180 degrees. Select one: True False

Three of the vertices of quadrilateral ABCD are A(2, 8), B(0, 5), and C(2, 2). a. Suppose that ABCD is a rhombus. Find the coordinates of vertex D. Explain why there is only one possible location for D. b. Suppose that ABCD is a convex kite. Show that there is more than one possible set of coordinates for vertex D. Describe what all the possible sets of coordinates have in comm

The sum of the angles 41°42′36 and 20° 18'40" is 61º60′76". Select one: O True O False

The ground velocity of a jet is 410 km/h [S 30° E]. A 75 km/h wind is blowing from [N20°E]. Determine the air velocity of the jet. Include a proper fully sketched diagram, with the vectors arranged properly, and show all your steps.

Find the distance between the given points on a number line. - 4,0 The distance between - 4 and 0 on the number line is

Grab the point F₁, which represents a focus of an ellipse, and move the point F, to (-2.2) Grab the point F₂, which represents the other focus of an ellipse, and move the point F₂ to (6,4). What is the center of the ellipse? Confirm the center of the ellipse is at the midpoint of the two foci The center of the ellipse is (Type an ordered pair)

Rewrite cos 23° in terms of its cofunction cos 23⁰ °

Shawn purchases a retirement annuity that will pay him $1,000 at the end of every six months for the first nine years and $300 at the end of every month for the next six years. The annuity earns interest at a rate of 2.8% compounded quarterly. a. What was the purchase price of the annuity? b. How much interest did Shawn receive from the annuity?

Write the first four terms of the sequence. a =(-1)n(-9n) a₁ = a₂ = a3 = a4=

Check whether the sequence is arithmetic. If so, find the common difference d. 2, 11, 13, 22, 24... Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The common difference is B. The sequence is not arithmetic.