Sequences & Series Questions and Answers

a) Write the line that goes through the two points: P₁(3,-2) and P₂(-1,1). Find the distance of the two points.

Given the function f(x, y) =2 x + 3 y on the convex region defined by R= {(x, y) : 6x + 2y ≤ 30,4x + 3y ≤ 30, x ≥ 0,y≥0} (a) Enter the maximum value of the function (b) Enter the coordinates (x, y) of a point in R where f(x, y) has that maximum value.

Let A = {0,-1,6);(-1,0,2); (2,1,0)). Then A is a basis for R² R³ the above vector space the above vector space

An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?

This question is about the ring Z11 of integers mod 11. (a) Is Z∈11 a field? (b) For which values of bZ11 does the equation x^2 + x = b have a solution?

Find the domain of the following function: f(x)= 1/ (-2x + 36) Select the correct answer below: A) All real numbers except 36 B) All real numbers except -36 C) All real numbers except -18 D)All real numbers except -2 E) All real numbers except 2 F)All real numbers except 18

You owe $302.87 on your credit card. The minimum payment is $28.00 and the interest rate on the credit card is 1.8%. What is the new balance? A) $309.22 B) $302.87 C) $317.28 D) $279.82

Which of the following sets is not a finite set? (A) { (x , y) : x^² + y^2 ≤ 1 ≤ x + y, x, y ∈ R } (B) { (x , y) : x^2 + y^2 ≤ 1 ≤ x + y, x, y ∈ Z } (C) { (x , y) : x^2 ≤ y ≤ |x|, x, y ∈ Z } (D) { (x , y) : x^2 + y^2 = 1, x, y ∈ Z}

The perimeter of the square below is 116m. What is the value of a? A print company will print business cards for $0.10 each plus a set up charge of $15.00. Another print company offers business cards for $0.15 each with a set up charge of $10.00. What number of business cards will cost the same amount from either printer?

Set up a Newton iteration to compute the square root of given positive number C and apply it to C=3.

A man gets a job with a salary of $31,200 a year. He is promised a $2,230 raise each subsequent year. What are his total earnings after 6 years?

Directions: Find the partial sum for each sequence. 15. {38, 31, 24, 17, ...};S₁₂ 16. (1, 8, 27, 64, 125,... };S₇

A compound has a generic formula A₃BC₄. What is the mass percent of A (29.98 g/mol) in A₃BC₄ (263.94 g/mol) ? (A) 11.36% (B) 45.53% (C) 34.08% (D) 41.35%

Armando invested a total of $111,000 in two accounts. The first account earned 9% after one year. However, the second account suffered a 6% loss in the same time. At the end of one year, the total amount of money gained was $1,890. $___at 9% $___at 6%

Find the factored form of 2x^3 - 12x^2 + 5x - 30. a)(X-6)(2X^2 + 5) b)(X-6)(2x^2 - 5) c)(x + 6)(2x^2 + 5)

True or False: If you owe $446 and make the minimum payment of $89, you still owe $357. True False

Look at your Pythagorean identities. What is sec^2θ - 1 going to be equal to? A) tan^2θ +1. B) tan^2θ. C) sec^2θ - tan^2θ. D) sec^2θ + 1.

Evaluate: 5 (2a + 7b) - 12 (b - 3a), when a = 2 and b= -1. A) 69 B) -69 C) -99

Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers? A) 35, 37 B) 45, 27 C) 27,54

Express $132 for 40 test tubes as a unit rate. (Answer as a fraction in lowest terms.)

You owe $561.54 on your credit card. The minimum payment is $45.00 and the interest rate on the credit card is 1.5%. What is the new balance ? 1. $509.89 2. $557.99 3. $524.29 4. $596.92

Joey and Andy go to a candy store to buy some candy. Joey eats 1/3 of the candy they bought. Andy ate 2/4 of the candy. How much candy is left?

Application Health care expenditures in the United States exceeded $1 trillion in the mid-1990s and exceeded $2 trillion in 2005. Many elderly and disabled persons rely on Medicare benefits to help cover health care costs. According to the Centers for Medicare and Medicaid 2005 Annual Report, Medicare expenditures were $7.1 billion in 1970. a) Assume Medicare spending has increased by 11.7% per year since 1970. Write a recursive rule to generate the sequence of increasing Medicare spending.

$890 is invested in an account earning 7.3% interest (APR), compounded quarterly. 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. Function: f(t) = _____ ( ______ ) ^ ____. Growth ____% increase per year.

Find an equation of a line perpendicular to the given in that contains the given point Write the equation in slope-intercept form. (If the equation is a vertical line, use the forma line 4x-3y=5. point (-3,2)

A set of data has a normal distribution with a mean of 100 and a standard deviation of 15. Find the percent of data from 85 to 130. (make sure to include % sign in answer.)

A new car is purchased for $30,000 and over time its value depreciates by one half every 6 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $3,500?

$4,300 is invested in an account earning 5.2% 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. Function: f(t)= Growth= ___ % increase per year

Find the slope of the equation -3x - 5y = 25 (A) -3/5 (B) -5/3 (C) 5/3

Musicians planed to organize a music party to raise fund for an orphanage. The admission fee is $20. Solve an inequality to determine how many tickets must be sold to raise at least $25,000. Write in set builder form. X/ X 2 25000) {X/X > 1250) (X/ x < 1250

Find the scalar equation for the plane passing through the point P(-1,5, 3) and containing the line L defined by X=-3-2t y = 3+3t z=1+t 0=0

What would cosθcscθtanθ be equal to? (A)0 (B)cos²θ (C)1 (D)sin²θ

What would secθ*cotθ*cscθ be equal to? 1. 1 + cot^2θ 2. sec^2θ 3. 1 4. tan^2θ + 1

Consider the generic chemical reaction: 3A + 2B --->5C Calculate the moles of A that are needed to completely react with 19.5 moles of B. O 3.00 moles O 19.5 moles O 29.3 moles O 20.3 moles

Question 7 Find the partial sum: -2+(-4) + (-8) +...+(-32)

The price of a widget was $362. Over nine years, the price dropped to $245. Assume a linear trend. (a) Find a linear model P = ax + b for this situation, where P is the price at time x. P = _______. (b) Use this model to predict the price in 23 years. $ ________.

Introduction Objective A Objective B Objective C Objective C: Rationalize Numerators Rationalize the numerator. √11/17

Consider the following differential equations: dy/dt = y^3(y-1) dy/dt = y^2 - 5y + 6 Analyze the differential equations using the qualitative-graphical approach: (a) Draw the phase line. (b) Identify the stationary point/s. (c) Analyze the dynamic stability of the stationary points.

Which of the following points lie on the f(x) = 3x² + 5 Select one: a. (0,5) b. (1,5) c. (2, 10) d. (3, 15)

Find each term described. 3rd term in expansion of (4y – 2x)⁴

Find the slope from the given equation: y = -4x + 21 (A) 21 (B) -4 (C) -1

Use the shaded region below to answer the questions that follow. The distance between each pair of neighboring gridlines is 8 yd. 8 yd 8 yd o Image Description What is the area of the shaded region? Give your answer as a decimal number with units. Answer: What is the perimeter of the shaded region? Give your answer as a decimal number with units. Answer:

Use the simplex method to solve the linear programming problem. Maximize z= 5x₁ + 2x₂ + x₃ subject to 3x₁ +9x₂ + x₃ ≤ 6 x₁ +5x₂ + 3x₃ ≤ 15 x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. ○ A. The maximum is ▢ when x₁ = ▢, x₂ = ▢, x₃ = ▢, s₁ = ▢ and s₂ = ▢ ○ B. There is no maximum.

Find an equation for the line perpendicular to 3x + 15y = 135 and goes through the point (-3,1). Write your answer in the form y = mx + b. y =

A linear function is given. Complete parts (a)-(d). h(x) = 1/3 x- 5 (a) Determine the slope and y-intercept of the function. The slope is (Type an integer or a simplified fraction.) The y-intercept is (Type an integer or a simplified fraction.) (b) Use the slope and y-intercept to graph the linear function. Use the graphing tool to graph the function. Use the slope and y-intercept when drawing the line. (c) Determine the average rate of change of the function. The average rate of change is . (Type an integer or a fraction.) (d) Determine whether the linear function is increasing, decreasing, or constant. Choose the correct answer below. O A. decreasing O B. constant

A magazine rotes different restaurants based on a five-star rating system. The following statements are true based on the analysis of the results, Twenty percent of the restaurants were rated from 1 to less than 2 stars. Seven of the restaurants received from 4 to less than 5 stars. .The number of restaurants that received a score of less than 2 was equal to the number that fell between 2 and less than 3. Fifty total restaurants were surveyed. • A total of 13 restaurants received a score of less than 2. 1. Unfortunately, the data was lost. Use the statements above and your understanding of frequency to complete the table and answer the

What is the molarity of 0.15 L MgCl2 solution that contains 0.033 moles of MgCl2? 1. 0.22 M 2. 4.5 M 3. 27 M 4. 0.0050 M

Darnell researched the public university he wants to attend to estimate the cost of attending. TUITION & FEES $8,000 ROOM & BOARD $9,100 BOOKS & SUPPLIES $950 TRANSPORTATION, ETC $650 What should Darnell estimate the total cost of one year to be? Darnell's family can contribute 60% of the total annual expenses (before financial aid), and Darnell does that leave for Darnell to cover for his first year of college? If Darnell has 18 months to save, how much should he save each month?

If the vector v can be written as a linear combination of V₁ and v₂ such that v=c₁ V₁ + c₂V₂: Which of the following is always false ? 1) None of them 2) If u is also a linear combination of v₁ and V₂, C₁ 3) C₁ can be as a multiple of c₂. 4) C₁C₂ should be positive. 5) v can be v= -5 V₂:

A magazine rates different restaurants based on a five-star rating system. The following statements are true based on the analysis of the results. Twenty percent of the restaurants were rated from 1 to less than 2 stars. • Seven of the restaurants received from 4 to less than 5 stars. The number of restaurants that received a score of less than 2 was equal to the number that fell between 2 and less than 3. • Fifty total restaurants were surveyed. • A total of 13 restaurants received a score of less than 2. 1. Unfortunately, the data was lost. Use the statements above and your understanding of relative frequency to complete the table and answer the questions. 2. What interval contains the most restaurants? 3. What percent of restaurants were rated two stars or more but less than three? 4. Describe the general shape of the relative frequency histogram. 5. Which two groups combined account for over half of the data?