Sequences & Series Questions and Answers

The count in a bacteria culture was 400 after 15 minutes and 1400 after 30 minutes. Assuming the count grows exponentially, What was the initial size of the culture? 114.2857 Find the doubling period. 8.3011 Find the population after 100 minutes. 2517 When will the population reach 11000. 45.669098 X You may enter the exact value or round to 2 decimal places.

John takes out a loan of $11600 that charges 10% interest compounded monthly. If John makes $130 monthly payments, determine how long it will take him to pay off the loan. Round your answer up. John will pay off the $11600 loan after months.

The radius of the wheel on a car is 32 inches. If the wheel is revolving at 454 revolutions per minute, what is the linear speed of the car in miles per hour? Round your answer to the nearest tenth.

Prove that if F is a field, K is a finite extension of F and E is a finite extension of K, [E: K[K: F] = [E: F].

In a classroom of children, do the following assignments give functions? Explain why or why not. To each child, assign his or her first name. From a list of the last names of children in the class, assign the child.

Write the sum as a rational number 0.45 +0.0045 + 0.000045 +...

Let t(n) be the function that assigns the nth term of a sequence to n the number of the term. a. If t(n)=4n - 3, determine which of the following are output values of the function: i. 1 ii. 385 iii. 389 iv. 392 b. If t(n) = n², determine which of the following are output values of the function. i. O ii. 25 iii. 625 iv. 1000 v. 90 c. If t(n) = n(n-1), determine which of the following are in the range of the function. ii. 2 i. 0 iii. 20 iv. 999

Consider the exponential function g(x)= 36(1.07)^7x a. As an increases throughout the function's domain, g(z) sometimes increases and sometimes decreases. b. Whenever a increases by 1, the value of g(x) is multiplied by c. The 1-unit growth factor for g is d. The 1-unit percent change for g is e. The unit growth factor for g is

Consider the sequence -11,-5, 1,7,... (a) What is the general term of this sequence? (b) What is the 100th term in this sequence? (c) What is the sum of the first 100 terms in this sequence?

For the following function defined that is one-to-one, write an equation for the inverse function in the form y=f(x), and then graph fan one-to-one, say so. f(x)=√√4+x.x2-4 The domain of fis (Type your answer in interval notation.) The range of fis (Type your answer in interval notation.) If the function is one-to-one, find the domain of f OA. The domain off OB. The function is not one-to-one If the function is one-to-one, find the range of f Select the correct choice below, and fill in the answer box if necessary. is(Type your answer in interval notation) Select the correct choice below, and fill in the answer box if necessary

An initial sample of 428 g of a radioactive substance decays according to the function A(t) = 428e-0.038t where t is given in years. (a) How many grams of the substance will remain after 124 years? Round your answer to one decimal place. (b) What is the half-life of the substance? Round your answer to one decimal place.

Consider the differential equation x2y"-7xy' + 15y = 0; x³, x5, (0, ∞). Verify that the given functions form a fundamental set of solutions of the differential equation on Form the general solution.

A number is 12 more than another number. Twice the sum of the two numbers is 20. Find the two numbers.

Let b be a positive constant. Select all of the following statements that apply to the exponential function f(x) = b. Decreases when 0 < b < 1 and increases when b > 1. Increases when 0 < b < 1 and decreases when b > 1. Horizontal asymptote at y = 0. Vertical asymptote at x = 0. Has domain (0, ∞). Has domain (-∞, ∞0). Has range (0, ∞). Has range (-∞, ∞). a-intercept at (1,0). y-intercept at (0, 1).

Find the centroid of the region bounded by the curves. Y = Sin x Y=0 O≤x≤4

How do I Find the center and the radius of the circle represented by the equation 2x 2 + 4x + 2y 2 - y = 3

A speed trap on the highway set by the O.P.P. shows that the mean speed of cars is 105 km/h with a standard deviation of 7 km/h. The posted speed limit on the highway is 100 km/h. Drivers who are going 20 km/hour over the limit get demerit points? What percentage of drivers should get demerit points?

Algebra Jeremy wants to set up a fund for his son's education such that he could withdraw $1,596.00 at the beginning of every 3 months for the next 4 years. If the fund can earn 3.30% compounded semi-annually, what amount could he deposit today to provide the payment? Round your answer to the nearest cent

Consider the function f(x) = x + b, where b is a constant, and find the following. a. f(f(0)) b. f(f(2)) C. All inputs x for which the final output is x, that is, f(f(x)) = x.

Algebra Assume that 11% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below. a. The first lefty is the fifth person chosen. b. There are some lefties among the 5 people. c. The first lefty is the second or third person. d. There are exactly 3 lefties in the group. e. There are at least 3 lefties in the group. f. There are no more than 3 lefties in the group.

Find the area of a parallelogram bounded by the y-axis, the line x = 2, the line f(x) = 6 + 2x, and the line parallel to f(x) passing through (4, 12). square units

Which of the following is true? Enter a, b, c, d, or e. a. Irrationals = {|p, qe all INT} b. 2.59 is irrational c. 1.2345678... is rational d. {(Natural Numbers) n (Whole Numbers)} {Natural Numbers} = e. 16 is irrational

if sin(x) + cos(x) = √(2) calculate the value of H = tan (x) + cot (x)

1-1 0 -1- -1 5-2 0-2 4 find an interval of length 1 that contains A2, the second eigenvalue of A. A=

Which of the following terms describes the shape of the following data set? 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 20, 21, 22 A Symmetric D Uniform Bimodal Skewed right

Find an for the arithmetic sequence. ag = 10, a10 = 22 an=n-C

Discuss the continuity of function f(x,y)=(y² - x²/y² + x²)2 Be sure to state any type of discontinuity.

2. With what tire pressure would his car start hydroplaning at 45 miles per hour? 3. At 55 miles per hour? 4. At 65 miles per hour?

Let C be the function whose graph is given to the right. This graph represents the cost C of using m anytime cell phone minutes in a month for a five-person family plan.

What is the annual growth rate of P(t) = 50(1.62) where t is given in years) as a percent? Be sure to show all your work

Solve the following inequality for y: -9x - y < 10 y<10-9x y> 10-9x y≤ 10+ 9x y<-10-9x y≤ -10 + 9x y>-10-9x

Considering the inequality 5x - 4y < 12, the shaded area of its graph is described by shaded above a dashed line shaded below a dashed line shaded above a solid line shaded below a solid line

Solve the systems of linear equations using a graphing method. 4x + y = 29 x + 4y = 26 (6,5) (5,6) (5,5) no solution, parallel lines

How many of the eleven integers greater than 10^7 and less than 10^7+12 are divisible by 11? (solve without calculator)

Use Substitution to solve: 2x-3y=-19 11xy=-27

Solve the systems of linear equations using the substitution method. y = 3x 8 5x + 5y = -36

William has sold 89, 48, 76 and 63 appliances in the last four months, respectively. How many appliances will he need to sell this month to maintain an average of at least 71 sales per month?

The fraction that is found halfway between 8/9 and 1/10is: 89/180 162/180 71/180

Given a line whose slope, m, is - 2 and passes through point (3, 0), the graph will go up to the left and cross the y-axis at (0,

Given two circles whose radii are 9" and 3", the ratio of their areas is what? Mark all correct answers, more than one answer may be correct. 9/1 3/1 9:1 3:1 3 to 1 9 to 1

Your boss asks you to package toy blocks into a box so he can deliver them to the toy store to sell. Each block is a cube with one inch side lengths. The interior of the box measures 10 x 10 x 5 in inches. What are the upper and lower limitations for how many toys fit into the box? upper limitation: 500; lower limitation: 250 upper limitation: 250; lower limitation: 0 upper limitation: 500; lower limitation: - 500 upper limitation: 500; lower limitation: 0 There are no parameters in this situation.

Use the addition property and/or the multiplication properties to find a and b. If -5<x<4 then a <2x+2<b. a= b = (Type an integer or a simplified fraction.)

solve the following equation on the interval 0<theta<2pie. show work. should be four solutions 2 sin2θ = sin θ

The function A Age 23st models the amount an individual owes a credit company t years after some initial debt. If a person currently owes $1,900 and makes no payments, how much time will pass before that person owes $15,0007 Round to 3 decimal places. After about years.

Jan and Jim started hiking from the same location at the same time. Jan hiked at 5 mph with a bearing of N32 E, and Jim hiked at 3 mph with a bearing of N38 W. How far apart were they after 2 hours? After 2 hours of hiking, they were

If f(x) = int(3x), find: (a) f(1.5) (b) f(3.9) (c) f(-2.4) (a) f(1.5)= (Simplify your answer.)

You are the sales manager for your school's drama production. From what you've noticed in the past, you will likely sell 450 tickets at $11 each. You reason, however, that each time you drop the price by $1, you can expect 50 more sales. Graphically determine the ticket price that will maximum revenue for the school.

The displacement d (in meters) of an object at time t (in seconds) is given by the equation: d = r sin(2 t). What is the time required for one oscillation?

A man improvises a temporary shield from the sun using a rectangular piece of wood with dimensions of 1.4m, 1.5m, and 1.3m. With the longest side lying horizontally on the ground, he props up the corner above the ground with a vertical pole 0.9m long. What would be the area in sq.m. of the shadow on the ground when the sun is vertically overhead? 0.95 0.84 O 0.75 1 pts O 0.5

A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as shown in the figure. The height of the satellite above the earth varies between 110 mi and 440 mi. Assume that the earth is a sphere with radius 3960 mi. Find an equation for the path of the satellite with the origin at the center of the earth. (Assume the elliptical orbit of the satellite lies in the xy coordinate plane with a focus at the origin and the other focus lying on the negative x axis.)