Sequences & Series Questions and Answers

Solve (a) f(x)=0. (b) f(x) > 0, and (c) f(x) <0 over the interval [0,2π). f(x)=2 sin2xcos x-2 cos x

A man gets a job with a salary of 38900 dollars a year. He is promised a 2870 dollars raise each subsequent year. His total earning for a 8-year period is

Given that cos(x) = -0.27, what is cos(-x)?

If the half-life of an element is 87.7 yr and the initial quantity is 2.5 kg, we can write a function of the form A(t) = Aoekt to model the quantity of the element left after t years. Find the values of Ao and k. Round k to four decimal places.

The graph of the function g(x)=√x-1+2 is the graph of f(x) = √x A)... shifted to the left 1 unit and up 2 units B)... shifted to the right 1 unit and up 2 units C)... shifted to the left 2 units and down 1 unit D)...shifted to the right 2 units and down 1 unit

A. Find the time required for an investiment of $14,000 to grow $18,000 at an annual interest rate of 5% if the interest is compunded yearly.

The population of a country on January 1, 2000, is 11.3 million and on January 1, 2010, it has risen to 12.5 million. Write a function of the form P(t) = Poert to model the population P(t) (in millions) ₺ years after January 1, 2000. Then use the model to predict the population of the country on January 1, 2014. Round the value of r to five decimal places. P(t) = 11.3e0.0100⁹t; 13 million P(t) = 12.5e0.01009t; 53. 7 million P(t) = 12.5e0.01009t; 14. 4 million P(t) = 11.3e0.01009t; 48.6 million

Write the equation in exponential form. log729 9 = 1/3

Find the exact value of sin 105° by using a sum or difference formula.

Use a system of equations to solve the following problem The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine, Main floor tickets are $52, balcony tickets are $36, and mezzanine tickets are $33. One particular night, sales totaled $75,220. There were 209 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 494 more than 2 times the number of mezzanine tickets sold. How many of each type of ticket were sold? Answer How to enter your answer (opens in new window) main floor tickets w balcony tickets mezzanine tickets= Keypad Keyboard Shortcuts

Use a calculator to find the value in radians of the following expression rounded to two decimal places. sin ¹0.2 **** sin ¹0.2= radian(s) (Type your answer in radians. Round to the nearest hundredth as needed.).

The monthly sales volume y (in thousands of dollars) is related to monthly advertising expenditures x (in thousands of dollars) according to the following equation. y =300x/X + 10 Spending how much money on advertising will result in sales of at least $150,000 per month? At least $ must be spent on advertising so that the sales is at least $150,000 per month.

$6300 is invested part of it at 12% and part of it at 7% for a certain year the total yield is $ 596.00 How much was invested at each rate $___was invested at 12%

Suppose the correlation coefficient between a baby's weight and the price a computer is 0.87. Which statement must be true? A. As the baby gains weight, computer prices tend to decrease. B. Increased computer prices cause the baby to gain weight. C. As the baby gains weight, computer prices tend to increase. D. The baby's weight gain causes the price of a computer to increas

The number of bank debit cards issued (in millions) if given by the function C(x)=-0.31x³+5.8x2-15x +9, where 'x' is the number of years since 1990. How many debit cards were issued in the year 1993? 0.51 million debit cards 9 million debit cards 7.83 million debit cards 2431 million debit cards 24.57 million debit cards

For problems 16 - 18: Chris has $ 3500 that is to be invested in an account with 6% interest compounded monthly. Write the formula to calculate the account balance. A =3500e0.005t A =1.06(3500) ¹2t ○ A = 3500(1.005) ¹2t A = 3500(1.06)¹2t A = 3500e1.06t

Find the x-value(s) that solve(s) the system of nonlinear equations: 2x+y=-6 y=x²+6x+7 x= -2.3, -5.7 x= -1.5, -2.3 x= -1.5, 5.5 No solution x= -5.7, 5.5

Which of the following statements is accurate about the average score as the time increases? The average score will decrease for a period of time and then increase. The average score will decrease but level off at 65 percent. The average score will be constant for the entire time period. The average score will increase for a period of time and then decrease. The average score will always decrease.

Marisa is organizing an event at a mystery room to celebrate the birthdays of three of her friends, The cost to rent the venue for the event is $200. She doesn't know how many total people will be going, but she does know that the 3 birthday girls are not paying. Write a function that could be used to find C. the cost per person paying, if there are n people going to event in total. C=200/n C=200/(n-3) C=n/(n-3) C=200/(n-3)

Factor the polynomial 10ab( 3a - b) - 15b( 3a − b ) Select one: a. 15b(3a - b)(a-3) b. b(a-3b) (10a -3) c. 10b(a - b)(2a-3) d. 5b(3a-b) (2a-3)

The growth of outpatient surgeries as a percent of total surgeries at hospitals is approximated by f(x)=-1316+304 In x where x is the number of years since 1900. (a) What does this function predict for the percent of outpatient surgeries in 1997? (b) When did outpatient surgeries reach 30%? (a) What does this function predict for the percent of outpatient surgeries in 1997? % (Round to the nearest percent as needed.) (b) When did outpatient surgeries reach 30%? (Round down to the nearest year.)

Determine the amplitude and period of the function without graphing. y = 5/7sin(-2πx/7)

Use a calculator to help solve the problem. The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 43 years (Round your answer to one decimal place.)

A Diamon Ring sold for $4,025 including Tax. If the tax rate where the diamond was purchased is 6.1%, Find the price of the king before the teix was added. Round to the nearest cent as necessary.

2) On Tuesday, a baker sold 132 cookles. On Wednesday, she sold 108 cookles. Find the percent of change to the nearest tenth of a percent: * A) 81.8% B) 12.7% C) 82.1% D) 24% E) 18.2%

Scoft Set up a Volley Ball net in his Backyard. One of the poles, which forms a right angle with the ground is 6 feet high. to secure the pole, he attached a rope From the top of the pole to a stake 3 Feet from the bottom of the pote. To The nearest tenth of a foot. Find the lenghth of the rope.

Consider the functions f(x) = -7x-5 and g(x) = -1/7(x+5). (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other.

Factor the polynomial 7ab(a − b ) - 5a(a − b ). Select one: a. a(a + b) (7b-5) b. a(a - b)(7b-5) c. (a-b) (7b-5) d. a(a-b) (7b+5)

Find the slant asymptote, if any, of the graph of the rational function. f(x) =(x² + 6x-4)/(x-4) O y= x O y=x+10 O y=x+6 O no slant asymptote

Identify the period of g(x) = cos 8π. Then graph the function and describe the graph of g as a transformation of the graph of f(x) = cos π.

Here is a box and whisker plot for the exam scores students received on their Biology midterm. How many people scored above a 54 if there are 60 students in the class? Select one: a. 50 students b. 15 students c. 40 students d. 30 students e. 45 students

Calculate the amount of interest earned on a $12,500 deposit into an account for 3.5 years with a 2% interest rate.

Graph y = sin(x). Then give the domain in the interval form: range in the interval form: What do you think the function value at:

A pack of pepperoni weighs 16 ounces. 15% of the pepperoni was used on a pizza. What is the weight of the remaining pepperoni in the pack?

High-Tech Products received an invoice dated May 28, 2018, from a manufacturer that sells office equipment. The list price was $21,636. This manufacturer offers its customers a trade discount of 17%. The manufacturer also offers its customers the following cash discount terms: 1/10, n/30. Assuming that High-Tech Products pays the invoice on May 29, 2018, calculate the following. (Round your answers to the nearest cent.) Trade discount dollar amount = Net price = Cash discount dollar amount= Dollar amount paid to the manufacturer=

Alexis works at a health care facility. She has measured the hemoglobin levels of 400 people. The data follows a normal distribution with a mean of 16 g/dL and a standard deviation of 2. What is the chance that if Alexis pulls a file randomly, that that patient would have a hemoglobin level between 12 and 20 g/dL? a. 95% b. 99.7% c. 50% d. 68% e. 20%

In this problem, let us try to maximize the function J = |3x+2y-7z| under the constraint of 2x²+y²+3z² = 5, by applying the Cauchy-Schwarz inequality. The trick is to view J as the absolute value of the inner product of u̲=(√2x, y, √3z) and y = (3/√2,2, -7/√3). Find the maximum value of J.

The following table gives the number of drinks and the resulting blood alcohol percent for a man of a certain weight legally considered driving under the influence (DUI). a. The average rate of change in blood alcohol percent with respect to the number of drinks is a constant. What is it? b. Use the rate of change and one point determined by a number of drinks and the resulting blood alcohol percent to write an equation of a linear model for this data. Number of Drinks 5 6 7 8 9 10 Blood Alcohol Percent 0.21 0.25 0.29 0.33 0.37 0.41 a. What is the rate of change in blood alcohol percent? ________%

If you are given two even functions, then the resulting function through addition will also be even. a) Always True b) Sometimes True c) Never True

Given the functions f(x) = 10x and g(x) = 3x² +10 and h(x) = x −1 what composition of functions would result in the following:

A research study asked 1712 homeowners how many bedrooms were in their homes. The results are shown in the table below. What is the probability that a homeowner chosen at random has 2 or less bedrooms? Number of Bedrooms Number of Homeowners 2 or less 428 3 360 4 616 5 or above 308 (a) about 36% (b) about 21% (c) about 18% (d) about 25%

Monique only has $36 to buy pens and notebooks. Each pen costs $2. Each notebook costs $3. Which of the following graphs represents the possible combinations of pens and notebooks that she may purchase?

Hawks do not like the noise that humans make, so they tend to move out of an area as more and more people move into the area. If p represents the number of thousands of people in an area, and h represents the number of hawks in the same area, the relationship between the hawk population and the human population can be modeled with the equation h(p) = 1000 - p/2. Since hawks eat mice, as the hawk population decreases, the mice population in the area will increase. If m represents the number of mice in the area, this relationship can be modeled with the equation m(h) = 800+ h/5. How many mice would be in the area if 280 000 people live in the area? a) 860 b) 972 c) 572 d) 800

Given g(x) = x/4 +4_and_ƒ(x) = 4x + 1/4 , find g¯'(z), ƒ˜¹(z), (g°ƒ)¯¹(z) and (ƒ-¹ og ¹) (I). What can you conclude?

Suppose you need to choose between two car rental companies. You plan on driving for 8 hours at a constant speed of 60km/h. Company 1 charges $0.20/km and a daily fee of $45. Company 2 charges $0.35/km and a daily fee of $20. Which company will give the lowest price? Use composite functions to determine your answer.

Between any two points, the graph goes up 3 (y) and right 2 (x) slope = Ax

The slope of the tangent line to √(x + y) + √(x y) = 2y at the point (2,2) is: A) 3/5 B) 3 C) -3 D) -(3/5)

A student believes that subtraction problems can be solved by highlighting the distance between two numbers, as shown below: Why will this method not always work? Problem: Evaluate 3 - -4. There are 7 units, so 3 - -4 = 7.

A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least two balls of the same color? Explain your answer.

The height of a radio tower is 700 feet, and the ground on one side of the tower slopes upward at an angle of 10°. (a) How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 150 feet from the base of the tower? (b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 150 feet from the base on the flat side?