Sequences & Series Questions and Answers

Consider to fit the data set {(xi, yi), i = 1,...,n} by the regression model yi = 3x² + €i, Find the least squares estimator of β.

Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form. P(-4,1); m=1

Which option choice Identify the Associative Law for AND and OR 1: AND: x + (yz) = (x + y)(x + z) and OR: x(y+z) = xy + xz 2: AND: (xy)' = x' + y' and OR: (x + y)' = x'y' 3: AND: x(x + y) = x and OR: x + xy = x 4: AND: (xy)z = x(yz) and OR: x + (y + z) = (x + y) + z

Cedar Hill State Park covers an area of 3,900 km² and each year this area decreases by 4.75%. At this rate, which measurement would best represent the area in square kilometers of Cedar Hill State Park in 15 years, rounded to the nearest whole number? Answer Record your answer in the boxes below. Be sure to use correct place value.

Neatly show all of your work as you find an expression for the exact value for sin 75° by using:- a)a sum or difference formula. b) a half-angle formula (note 75° is half of 150°).

Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a comma-separated list.) f(x) = (x²-3x-4)/(8x²+x-7)

There were 522 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 2.667% per month. At this rate of growth, which function can be used to determine s(m) the monthly cell phone sales. m months after January? A s(m) = 522(0.02667)m B) s(m) = 522(1.02667)m C) s (m) = 522(0.97333)m+1 D) s(m) = 522(0.2667)^(m+1)

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The function below can be used to model the number of bacteria in the colony after t minutes. b(t) = 12,000(0.851)^(t/10) Which value is closest to the amount of time in minutes needed for the population of the colony to drop to 8,000 bacteria? F) 11 minutes G) 25 minutes G) 25 minutes H) 8 minutes J) 42 minutes

What is the inverse of the equation below? h(x) = -1/2 log3(x) a) h-¹ (x)=3^(2x) b)h-¹(x) = 2(3)^x c)h-¹(x) = 2(logx 3) d)h-¹(x) = log3 (2x)

The corresponding system has no solution, {}. The corresponding system has one solution. The solution set is The corresponding system has infinitely many solutions. The solution set is {= is any real number}

Convert the rectangular equation to polar form and sketch its graph. 2x² - 8y² = 1

Let 8 be an angle in standard position. Name the quadrant in which 0 lies. sinθ > 0, cotθ < 0 The angle 8 lies in which quadrant? I IV II III

Use your graphing calculator to find all radian solutions in the interval 0≤x<2πr for each of the following equation cos x + 5 = 8 sin x x =_

Find the cos equation given amplitude: 1, period:(2π)/7, vertical shift: -2, and horizontal shift:π/14 A. y = cos((θ/7)+(π/14))-2 B.y = cos(7θ+(π/14))-2 C. y = cos((θ/7)+(π/2))-2 D. y = cos(7θ+(π/2))-2

After graduating from college, Carlos receives two different job offers. Both pay a starting salary of $49000 per year, but one job promises a $2450 raise per year, while the other guarantees a 4% raise each year. Complete the tables below to determine what his salary will be after t years. Round your answers to the nearest dollar.

Suppose is an angle such that cos(θ)=-1/3 If 0 < θ < π, then cos(θ/2)=_____ and sin(θ/2)=_____ If π < θ < 2π, then cos(θ/2)=_____ and sin(θ/2)=______ If 2π < θ < 3π, then cos(θ/2)=______ and sin(θ/2)=_____

Solve the following differential equations a. =x-xsquared b. =1-|x-1| c. = xt/1-x In each case also i) discuss the local existence and uniqueness; ii) discuss the maximum interval of existence of the solution(s); iii) draw the integral curves to show your findings

Use a half angle formula to find the exact value. Since 105° is in Quqadrant______, cos(105°) is _______ cos(105°) = cos(1/2____)

Assume that a surface S has the property that |k₁| ≤ 1,|k₂| ≤ 1 everywhere. Is it true that the curvature k of a curve on S also satisfies |k| ≤ 1?

Given log b a = c, which statement is true? (A). a = b^ c (B). c = a^ b (C). c = b^ a (D). a = c^ b

Which value of x makes the equation (x-3)/(x-8)=(x+3)/(x+6) true? A. 3/8 B. 1/2 C. -3/4 D. -4/3

Expand the logarithim: log₈5x² (a.) 5log₈x² (b.) 2log₈5 + 2log₈x (c.) Xlog₈5+ 2log₈5 (d.) log₈5 + 2log₈x

Let ABC be a triangle with legs a = 12, c = 18, and angle C = 40°. What is sin(A) ? (A) 2 sin (40⁰) /3 (B) 3 sin(40°) / 2 (C) 2 / 3 sin(40°) (D)3 / 2 sin (40⁰) (E) No such triangle can exists (F) There is not enough information to answer the question.

Select the correct answer. Which function is continuous across its domain? A. x + 4, -4 ≤ x < -2 f(x) = 0.5x², -2 ≤ x ≤ 4 25-3x, 4 ≤ x ≤ 8 B. x + 4, -4 ≤ x < -2 f(x) = 0.5x², -2 ≤ x < 4 20-3x, 4 ≤ x ≤ 8 C. x - 2, -4 ≤ x < -2 f(x) = 0.5x², -2 ≤ x < 4 25-3x, 4 ≤ x ≤ 8 D. x + 6, -4 ≤ x < -2 f(x) = 0.5x², -2 ≤ x < 4 20-3x, 4 ≤ x ≤ 8

The functions f and g are defined by f(x)=(16-x²)² and g(x)=(x²-1)² respectively. Suppose the symbols Df and Dg denote the domains of f and g respectively. Determine and simplify the equation that defines a)f+g and give the set Df+g b)f-g and give the set Df-g c)f.g and give the set Df.g d)f/g and give the set D f/g.

For the geometric sequence -2, 6, -18, .., 486 find the specific formula of the terms. Write the sum-2+ 6-18 +.. + 486 using the summation notation and find the sum.

Question 4 Find the slope of a line passing through the pair of points: (-7, 0) and (-7, 6)

How long do you need to invest your money in an account earning an annual interest rate of 3.359% compounded daily so that your investment grows from $1,185.79 to $10,448.00 over that period of time? ________________days (Note: Your answer should be an integer)

Solve the following equation and check graphically. |x-6/7|=7 Select the correct choice below and, if necessary, fill-in the answer box to complete the choice. (A.) The solution(s) is/are x = (Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.). (B.) There is no solution.

In each part of this problem, information about a sequence or series is given. Use the given information to determine the requested information. a) sequence is arithmetic, with a3 = −8 and a = −26; find a10 b) series is arithmetic, with S21 = -1764 and a₁ = 1; find d c) series is geometric, with a2 = -8/3 and a5 = 64/81; find S6 d) series is geometric, with r = -2 and S5 = 33; find a3

How much time will be needed for $35,000 to grow to $38,657.01 if deposited at 5% compounded quarterly? The amount $35,000 will grow to $38,657.01 in ____ year(s). (Do not round until the final answer. Then round to the nearest tenth as needed.)

Express using rational exponents. 1/∜(5³) Sorry, that's incorrect. Try again?

Fill in the blanks: a. A sphere is the set of points in _________________. b. A circle is the set of points in __________________.

7. What can AC be called? 8. What can you conclude about ∠ADC and ∠ABC?

Solve the following equation. Determine whether the equation is an identity, conditional equation, or an inconsistent equation: 7x + 13 =2(2x - 5) + 3x + 23 Ø; conditional equation Ø; Inconsistent equation Ø; identity equation {-1}; Inconsistent equation

If the expression 10x+11/2x+1 was placed in the form 5+a/2x+1, then which of the following would be the value of a? (1) 6 (2) -7 (3) 3 (4) -5

If C = x+8 and D = 2x + 10, which expression equals 2C + 3D? A. 8x + 18 B. 8x + 46 C. 3x + 18 D. 3x + 46

Find the horizontal asymptote as x --> 8 and then describe what this means in practical terms. F(x) = 150x + 120/0.05x + 1; the number of bass, f(x), after x months in a lake that was stocked with 120 bass. the number of bass, f(x), after y months in a lake that was stocked with 130 bass the number of bass, f(x), after x months in a lake that was stocked with 120 bass the number of bass, f(x), after x months in a lake that was stocked with 140 bass the number of bass, f(x), after x months in a lake that was stocked with 150 bass

A group of 40 trees in a forest are not growing properly. A botanist determines that 34 of the trees have a disease or are being damaged by insects, with 18 trees having a disease and 20 being damaged by insects. What is the probability that a randomly selected tree has both a disease and is being damaged by insects? The probability is [?]%.

The table gives the crude oil production of a certain country, in billions of barrels, for the years from 2010 projected to 2030. Complete parts (a) through (f).

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another triangle, then the triangles are congruent. A. Side-Side-Angle (SSA) Congruence B. Angle-Side-Angle (ASA) Congruence C. Hypotenuse-Leg (HL) Congruence D. Side-Side-Side (SSS) Congruence

Find the solutions of the following difference equations with the given values of xo: a) X(t+1) = 2x(t) + 4, Xo = 1 b) 2x(t+1) + 3x(t) + 2 = 0, Xo = -1 c) 3X(t+1) = x(t) + 2 = 0, Xo = 2 d) X(t+1)-x(t) + 3 = 0, Xo = 3

Solve. 5-4∛(2x+1) = 0. Do not include = in your answer. Provide your answer below:

There are two right triangles, Triangle A and Triangle B. In Triangle A, besides the right angle, one more angle is given and one side length is given. In Triangle B, besides the right angle, no other angles are given and two sides length are given. In your opinion, which would be the easier problem to start solving? Please explain your reasoning with mathematically relevant details and principles.

Precalculus show that f'(x) = 2/4x-x^2 when g(f(x)) = x-2 and g'(x) = 2 -[f(x)]^2

Let A = {1,2,3} and R and S be two relations defined on A as follows: R = {(1,3), (3,2), (2,3), (3,3), (1,2)} S = {(1,1), (2,2), (1,3), (2,1), (3,1), (1,2)} Which of the following statements are correct? I. R is transitive but S is not transitive. II. R is not symmetric but S is symmetric. III. Neither R nor S is antisymmetric. IV. R U S is reflexive. V. S - R is antisymmetric. (A) II, III, IV and V (B) I, II, III, IV and V (C) I and III (D) IV and V

Use polynomial long division to simplify each of the following ratios. There should be a zero remainder. (a) x² +5x-24 / x-3 (b) 6x² +11x-10 / 3x-2

1. Find it DNF 2. find its dual function(using two methods the definition and the theorem) ƒ( x, y, z)= x ⇔ (ȳ+z)

e^(5x-3)-2 =10,476 Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution: (a){ In 10, 478 + 3/5};~ 2.45 (b){ In 10, 376 + 3/5}; ~ 1.78 (c){ In 12, 402 + 2/5};~2.16 (d){ In 10, 277 + 3/8}; ~ 1.57

Find the indicated term of each geometric sequence. 4) a₉ for 3, 6, 12, 24, ... 5) a₈ for 1/8, 1/4, 1/2 ....