Sequences & Series Questions and Answers

Graph the following system of linear inequalities to find the solution set. x + 4y ≥ - 8 - 3x +y ≥ -3

The mean number of songs downloaded by a group of teens last month was 28 with a standard deviation of 3. If the number of songs that Jack downloaded was one standard deviation below the mean, how many did he download?

Solve the following system of linear equations using Gauss-Jacob iterative method. Perform only three iterations. 5x - 7y + 3z = 15 x-5x - 2z = 4 3x + 2y +z = 2 Take initial estimates as x = 0, y = 0 and z = 0.

Let E be the solid that lies under the plane z = 3x + y and above the region in the xy-plane enclosed by y=2/x ,x = 2, and y = 2x. Then, the volume of the solid E is equal to 35/3 Select one: True False

$650 is invested in an account earning 8.7% interest (APR), compounded continuously. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Simplify the following product. x8x2x10 Select the correct answer below: x18 x20 x22 x19 x28

Simplify y3 . y4. Select the correct answer below: y7 y8 y9 y12

How many terms are in the geometric series whose first term is 3, last term is 768, with a common ratio of 2? 5 6 7 8 9 10

A company that sells canned vegetables buys 50-lb pallets of tomatoes from two area farmers. For Farmer 1, the standard deviation is 2.1 pounds. For Farmer 2, the standard deviation is 1.5 pounds. A sample of 30 pallets from Farmer 1 had a mean of 48.3. A sample of 40 pallets from Farmer 2 had a mean of 47.9. Find the probability of observing these sample means if the two population means are equal using a z-test. If your alpha is 0.1, what will you conclude? A. Fail to reject the null hypothesis, which states that the population means are equal. B. Reject the null hypothesis, which states that the population means are equal. C. You do not know enough to accept or reject the null hypothesis. D. In this situation, an ethical researcher will change the alpha so that the null hypothesis can be rejected.

Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates. slope: 1, ordered pair: (3,-5) Choose the correct answer from the options below. y = 2x - 8 y = - 8x + 1 y = x -8 y = x - 1/8

Overall, around 50% of people have brown eyes. You randomly choose 30 locations in your town and noted the eye color of the first person you saw. The first time you did this, you saw 25 people with brown eyes. The second time you did this, you saw 16 people with brown eyes. Which statement below is correct? Select all that apply. A. You cannot use a z-test to compare proportions since your samples are not random. B. The two samples have proportions that are statistically significantly different at the 90% confidence level. C. The proportions do not have a statistically significant difference at the 90% confidence level. D. You can use a z-test to compare proportions since your samples are random.

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling? 1 mile = 5,280 feet 45 miles per hour 46 miles per hour 47 miles per hour 48 miles per hour

Determine the number of triangles with the given parts, and solve the triangle. y = 45°, b=22, c=11√2

Consider the ellipse: 4(x - 1)^2 + 16(y + 3)^2 = 64 • How do you know this is an ellipse? • Write in standard form. • Identify the major axis and its length and the minor axis and its length. • Graph and label the center. • Plot the foci and explicitly write the points. • Write the domain and range.

The radius of a circle is 3.5 inches. What is the area of the circle? Use pi = 3.14. (A) 3.5 sq.Inches (B) 38.47 sq.Inches (C) 21 sq.Inches

Directions: Find the first five terms of each sequence. 7) an = -2(n-7) 8) an = (1/2)^(n+3) 9) an = 4n^2 10) an = (n+1)^3

An orange has a diameter of 3 1/2 inches. What is the approximate volume of the orange? Use 3.14 as an approximation for pi . 12.62 cubic inches 12.82 cubic inches 21.98 cubic inches 22.44 cubic inches

Using Gauss- Seidel method and the first iteration as (0, 0, 0), calculate the next three iterations for the solution of the system of equations : 5x - y + z = 10 2x + 8y - z = 11 -x + y + 4z = 3.

Simplify the following product. (t^9)(t^6) Select the correct answer below: (A) t^16 (B) t^15 (C) t^22 (D) t^17 (E) t^14

Evaluate the expression below for m =2/3 and n =1/3: 4 (m – n) - 5 (n – m)

Simplify the following expression. (x^13)/(x^11) Select the correct answer below: (A) x (B) x^4 (c) x^2 (D) x^3

Find the perimeter of a rectangle if its length is 14 in, and its width is 10 in. (A) 24 in. (B) 48 in. (C) 32 in.

Simplify: (x^2y^5z)^3 Select the correct answer below: (A) x^6y^15z^3 (B) x^6y^5z^3 (C) x^6y^8z^3 (D) x^6y^15z (E) x^5y^8z^3

What is the area of the circle if the circumference of the circle is 25.12 cm? Use pi = 3.14 (A) 25.12 cm^2 (B) 12.56 cm^2 (C) 50.24 cm^2

Find the binomial expansion of the following: 7 ( ) 5 Select the best answer from the choices provided. A) 21 B) 35 C)14 D) 7

(2) Let f(x) = {-1/(x-2)} +3, g(x) = 3^(x-1) - 2, and h(x) = log2(x+3)+1. (a) Find (f - g)(3), (f * h)(-1), and (goh)(5). (b) Graph g(x). Find the range and the horizontal asymptote. (c) Graph h(x). Find the domain and the vertical asymptote. (d) Find h^(-1)(x). Graph h^(-1)(x) on the same coordinate plane.

Find the area of the circle if the circumference is 6π inches. (A) 9π ln.^2 (B) 6π ln.^2 (C) 4π ln.^2

Suppose the intergenerational curve for the white and black families are as follows, respectively: ―― ――― yw,t = 25 + 0.5 * yw,t-1 ―― ――― yb,t = 21 + 0.3 * yb,t-1 Please calculate the steady state income rank for both groups. Please also calculate the racial gap in income rank in the seady state.

A new compound is discovered on Mars . It has the formula X₂(YZ₃)₃ . Calculate the molar mass of this compound . X = 13.953 g/mol Y = 17.458 g/mol Z = 7.149 g/mol (A) 243.174 g/mol (B) 74.124 g/mol (C) 281.313 g/mol (D) 324.621 g/mol

Determine whether the equality is always true 4 (x-3) 4 1 (y+3) 4 ∫ ∫ ∫ f(x, y, z)dz dy dx = ∫ ∫ ∫ f(x, y, z)dz dx dy. 3 (x-3) -4 0 (y^2 +3) -4 Select one: True False

Simplify the expression 3x+27/3 1) x-9 2) x+9/3 3) x+9

given the vectors from R2. v1=( 1 0 ) and v2 = (0 1). a) (-3 1) can not be written as a linear combination of v1 and v2. Select one: A) True B) False b) Given the following set of the vectors from M22 S = 1 1 + 0 0 + 0 1 0 0 0 0 1 1 S is the spanning set. Select one: A) True B) False

One-fourth times a number is 100. Find the number. 1) 400 2) 25 3) 200

A set of date has a normal distribution with a mean of 100 and a standard deviation of 15. Find the percent of data to the right of 55. (make sure to include % sign in answer.)

Consider the series Sn = Σ e^(-k). Which of the following is true? k-1 A) Sn is divergent. B) lim Sn = e/(e-1). n⟶∞ C) Sn is a telescoping series. D) Sn is not a geometric series. E) lim Sn = 1/(e-1). n⟶∞ F) None of the options. G) Sn =( e^(n+1) - 1 )/ (e-1).

You owe $644.90 on your credit card. The minimum payment is $68.00 and the interest rate on the credit card is 1.9%. What is the interest charged? 1. $10.96 2. $9.61 3. $12.99 4. $11.66

Find the center and radius of the circle whose equation is x² – 14x + y² + 20y – 20 = 0 = center = radius

$780 is invested in an account earning 2% interest (APR), compounded monthly. Write a function showing the value of the account after t years, where the annual a growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

The following sum is a partial sum of an arithmetic sequence; use either formula to determine its value. Reduce your answer to lowest terms. -5+ (-9/2)+ ... + 29

Suppose that the temperature Tat every point (x,y) in the cartesian plane is given by the formula T=1−x^2+2y^2. The correct statement about the maximum and minimum temperature along the line x + y = 1 is : (a) minimum is - 1, there is no maximum. (b) maximum is -1, there is no minimum. (c) maximum is 0, minimum is - 1. (d) there is neither a maximum nor a minimum along the line.

Pearl's Candles sold the following number of candles over the last 6 days: 35, 49, 24, 36, 78, 60. Find the average number of candles sold each day. (A) 43.5 (B) 47 (C) 96.5

Graph xy = -12. Be sure to include the table of values used to make the graph.

Jesse is a member of the Ecology Club. The club is sponsoring a school drive to collect items for recycling. The members plan to place recycling boxes around the school to encourage the collection. For the drive, a local packing company has donated sheets of box cardboard to the club to make the collection boxes. The club members must now make boxes from the cardboard. Jesse is in charge of designing the boxes. Each sheet of cardboard is a 6-foot square. What does Jesse know about each sheet of cardboard? Fill in the statement with the appropriate terms. Since each side of the square sheet of cardboard measures__ feet, the area of the cardboard sheet is__ square feet The area of a square is found using the formula A=s².where s is the length of the square and is measured in units squared.

Find the surface area of the rectangular prism with side lengths listed below. Show your work. Include units (in^2) with your answer. 4in. ,7 in., and 1.5 in.

Directions: Determine whether the sequence is arithmetic. If yes, identify the common difference and give the next three terms. 1.(-3, -12, -48, -192, ... 2.{-18, -27, -36, -45, ...} 3.{4, 11, 18, 25,... } 4.{16, 8, 4,1, ...) 5.{-9, -33, -57,-81, ...} 6. [1 5 7 3 2 6 6 2]

Given that f(x) = a(x^3) - 8(x^2) - 9x + b is exactly divisible by (3x – 2) and leaves a remainder of 6 when divided by x, find the values of a and b. Determine m and n so that 3x^3 + mx^2 – 5x +n is divisible by Both (x - 2) and (x + 1). factorize the resulting polynomial completely.

Solve the initial value problem y" + 6y' + 13y = 0; y(0) = 2, y' (0) = 0

Find the requested function and state the domain. Find fog, for f(x) = 1/(x-5) and g(x) = 7/x. Select a single answer A) (fog)(x) = x/(7 - 5x); domain: (-∞, 0) ∪ [0, 7/5] ∪ [7/5, ∞] B) (fog)(x) = x/(7+5x); domain: (-∞, 5) ∪ (0, ∞) C) (fog)(x) = x/(7+5x); domain: [0, 7/5] ∪ [7/5, ∞] D) (fog)(x) = x/(7 - 5x); domain: (-∞, 5) ∪ (0, ∞)

Which statement is not correct for x > 0, y> 0? A) log x + log y = log xy B) 2 + log x = log (x + 2) C) 3 log x = log x^3 D) log x - log 4 = log(1/4*x)

The half-life of radium is 1690 years. If 40 grams are present now, how much will be present in 190 years? (Do not round until the final answer. Then round to the nearest thousandth as needed.)