Sequences & Series Questions and Answers

. Given f(x) = 3x³ - 15x² + bx-3 has zero x = 2, and g(x)= x³ + cx²-3x + 10 has zero x = 2-i, find (f g) (-1)

Find the least and the greatest possible products for the expression using the digits 1 through 9. Each digit may be used only once in each case.

The sum of two numbers is 56. The larger number is 7 less than 3 times the smaller number. Find the smaller number.

Find an equation of the vertical line through 3 2 5'9

What is the difference between the "coefficient of determination" and the "correlation coefficient".

Etermine the half range Fourier cosine series in the range x=0 to x=7t for the following function: f(x)= X, 0 < x < 1/1 (x ( 1 (1-x), 81

In the answer box below, type an exact answer only (i.e. no decimals). You do not need to fully simplify/reduce fractions and radical expressions. 8 17 π 2 If sint = and <t<, then find tan (²)

Use the slope-intercept form to graph the equation y = 65 X-1.

Given the following table of values for f(x): Riemann Sum== x = f(x)= 5 8 -9 evaluate the Riemann sum for f(x), 1 ≤x≤7 with three equal sub-intervals and taking the sample points to be the left endpoints. 1 2 3 4 5 6 7 1 -1 -2 2 ⠀⠀ E

2. Given f(x) = 3x³ - 15x²+bx-3 has zero x = 2, and g(x)= x³ + cx²-3x + 10 has zero x=2-1. find (f g) (-1)

13.A sample space S is described. Would it be reasonable to make the equally likely assumption? A nickel and a dime are tossed, We are interested in the number of heads that appear, so an appropriate sample space is S = (0,1,2) No, we do not make the equally likely assumption Inconclusive None of the above @Yes, we can make the equally likely assumption

A diver records the depths, in feet, of her dives. They are: 60, 58, 53, 49, 60 The mean of the data set is 56. COMPLETE Use the equation for variance below, along with the given data set, to answer the following questions. 0² = (x₁ - 46)² + (x₂ − 46)² + ... + (x − µ)² N What does the numerator evaluate to? What does the denominator evaluate to? The variance equals: DONE

Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by 0.08t f(t) = 150e in thousands of dollars per year. Find the total income from the machines over the first 6 years. (Round your answer to the nearest thousand dollars.)

Find all complex cube roots of 1 + 4i. Steps: a) 1 + 4i = b) Let's find the primary cube root first, √/1 + 4i = = cis( c) The cube roots: r = cis( ) + 2kπ 1 3 +2km)) ³ 3 Round to 4 decimal places. d) Cube roots of 1 + 4i: and 0 = Give your answers in a + bi form, separated by commas. Round to 3 decimal places.

Find the slope of the line y = -7. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is (Simplify your answer. Type an integer or a fraction.) OB. The slope is undefined. EXIS

E Knowledge Check Suppose that an individual has a body fat percentage of 15.8% and weighs 132 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth. pounds ?

Find the slope of the line. 30x-5y=6.7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is OB. The slope is undefined. (Type an integer or a simplified fraction.)

Identify the next sequences and list the next three terms. Then, find the 100th term and the nth term. 30 193 +7.2³0, 193 + 8.2³0, 193 +9.23⁰

The duration t (in minutes) of customer service calls received by a certain company is given by the following probability density function. (Round your answers to four decimal places.) f(t) = 0.4e-0.4t t≥ 0 (a) Find the probability that a call selected at random lasts 2 minutes or less. (b) Find the probability that a call selected at random lasts between 6 and 11 minutes.

Let u, v, w be complex vectors such that <u,u>=4, <u,w>=2-2i, <v,w>=-11+6i, <u,v>=2+3i. Let c=4i, d=2i. Calculate <cu+dv,u+w>. 4-7i None of these 5+15i O-3-9i O-2-6i

Question 3: Please estimate the area under the curve c(x) = 1 - x³ for 0 ≤ x ≤ 1 using 4 1 rectangles with width Please show a sketch of the curve, the rectangles, and calculations. (A calculator is allowed.)

(graphing vertical and h Graph the linear equation. x=-2 CIE Use the graphing tool to graph the linear equation. Click to enlarge graph Question 5, 13.3.21 10. 10 8- 6- 4- 2 HW Score: 0%, 0 of 6 points O Points: 0 of 1 Ay A Q 5

Find an equation of the vertical line through (-1,2). The equation is (Type your answer in standard form.)

eval expressions w/expo Evaluate the expression with the given replacement value. 52² 9 52² 9 when z = -2 (Type an integer or a fraction.)

Add. 5 2 + x-3 x + 2 Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O A. OB. 5 2 X-3 x+2 5 x-3 + + 2 X+2 = x # no numbers must be excluded.

Algebra Given f(x)=1/x-4 and g(x)=/4x+2, find the domain of f(g(x)) Domain:

Graph the linear equation. y = -2 Use the graphing tool to graph the linear equation. * Click to enlarge graph

Plot the intercepts to graph the equation. 8x-4y=8 *** Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line. Click to enlarge graph

Write the following number in scientific notation. 0.00452 0.00452= (Use the multiplication symbol in the math palette as needed.)

Solve the system of linear equations by graphing y-4x = 4 -8x +2y = 8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice OA. The solution of the system is (Type an ordered pair.) OB. There are infinitely many solutions; ((x,y) y-4x=4) or ((x,y)-8x+2y=8) OC. There is no solution; or Ø. 4 48 880 Q

Graph the equation by plotting points. 2f(x) = -1

Graph the linear equation by plotting points. x+y=-4 For th

Let A, B, and C be sets such as #A=2, #B=#C=6 and #(B \cap C)=2. Find # (Ax(BUC).

Divide. 3 12p4 + 8p³ 2p 12p4 +8p³ 2p ||

Write the following number in standard notation. 7.815×10⁹ 7.815×10⁹ =

coord system) Plot the ordered pair (5,5). State in which quadrant or on which axis the point lies. Plot the ordered pair on the graph to the right. In which quadrant, or on which axis, does the point lie? O O O O O O || ... IV on the y-axis on the x-axis III ** -10 10 Ay O Q Q G

Find the x- and y-coordinates of the point C. The coordinates of Care (Type an ordered pair.) Question 1, 13.1.13 GECE 6 ← HW Score: 0%, 0 of 4 points O Points: 0 of 1 C Q

At a table factory two different machines can make tables. The older machine can make tables at a rate of 8 per minute and the newer machine can make tables at a rate of 14 per minute. If both machines operate at the same time, how long will it take the two machines to make 132 tables? Only provide the numerical solution for the minutes it will take to make the tables. Round to the nearest hundredth. No units are necessary.

Find the slope of the line. 10x+y=9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The slope is OB. The slope is undefined. (Simplify your answer. Type an integer or a fraction.) ***

Let y = 3². Find the change in y. Ay when I = 3 and Az = 0.2 3.72 Find the differential dy when I = 3 and dz = 0.2

A family stays at a hotel for $145 per night plus tax. They stayed two nights, ordered room service for a total of $65.38. Their total bill came to $380.03. What was the tax rate? Provide the numerical solution rounded to one decimal place for the percent. You do not need to include the % symbol. Example: If you get t = 0.032, submit 3.2

Angles A and B are complementary angles. Determine the measures of angles A and B if the measure of angle B is three less than half the measure of angle A. Measure of angle A = Measure of angle B = Only provide the numerical solution without any units.

Ryan pays a neighbor $8 each week to mow his entire yard. If a new lawn mower costs $259, how many weeks will it take for the weekly cost to be at least the cost of the mower. Only provide the numerical solution. No units are necessary.

Evaluate the expression using De Moivre's Theorem: √3 - i Steps: a) 3 − i = b) √√/3 − i = cis( ) So the root has r = cis Round to 4 decimal places. 12 2 and 0 = c) √√/3-i = Give your answer in a + bi form round to 3 decimal places. See Example 10 in textbook pages ».

Find the general solution of the system of differential equations da dt +12y = (6-n)ent, dy dt + 3x = 0.

Larry Mitchell invested part of his $13,000 advance at 6% annual simple interest and the rest at 4% annual simple interest. If his total yearly interest from both accounts was $560, find the amount invested at each rate. The amount invested at 6% is $ The amount invested at 4% is $

Let T: R² → R4 be the linear transformation defined by T(x, y) = (5x – 8y, −7x – 4y, 2y — 9x, 6x) for all (x, y) = R². - - - Find its associated A matrix A with respect to the standard bases of R2 and R4. www www www www www www HH www

2 Are functions ²1, X- x+1' from the vector space F ((2, ∞)) linearly independent?

Use intercepts to graph the equation. 5x + 6y + 30 = 0

As she plans for retirement, Audrey decides to invest $30,000. A portion of that money is invested at 2.5% and the remainder is invested at 1.5%. Find the amount deposited at each rate if the total amount of simple interest is $597.26. How much money was deposited at 2.5%? Only provide the numerical solution. Round to the nearest cent. No $ symbol is necessary. How much money was deposited at 1.5%? Only provide the numerical solution. Round to the nearest cent. No $ symbol is necessary.