Sequences & Series Questions and Answers

Find the indicated sum. 8+22+36 +50+...+(14n-6)

If a sequence has a first term of an =12 and a common difference d=-7. Write the formula that describes this sequence. Use the formula of the arithmetic sequence. Hint: (Use the brackets for subscripts eg for an you can use a(n)

What can you say of the Moon if you see it in the middle morning sky? It is third quarter, with the bulge to the East. It is third quarter, with the bulge to the West. It is New Moon. It is first quarter, with the bulge to the East. It is first quarter, with the bulge to the West.

In a 1 to 10 billion scale, where the Sun has the size of a grapefruit, how far from the Sun would Earth be? About 1 light year. About 15 meters. About 150 kilometers. About 1 meter. About 1 kilometer.

What is the Geosynchronous motion of the Moon? Unlike the Earth, the Moon does not rotate around its axis. The alternation of full moon and new moon cycles. The Moon rotates around its axis in the same time it takes the Earth to make a full revolution around the Sun. The Moon rotates around its axis in the same time it takes the Moon to make a full revolution around the Earth. The Moon takes 365 days to make a full revolution around its axis.

Calculate the following expression 10³ ÷ 10⁴

Calculate the following expression: 10⁴-10²

Use the quadratic formula to solve the equation. 8p+5p² = - 3

Find the slope of the line that goes through the points, (2,6) and (-4,-7).

Solve right angle triangle ABC , with C = 90° A = 32.5° b = 33.7 cm. find B = a ≈ CD =

A town's population has been growing linearly. In 2003 the population was 58,000. The population has been growing by 2700 people each year. Write an equation for the population, P, 2 years after 2003. P = Use the formula to find the population in 2009:

Solve each inequality analytically, writing the solution set in interval notation Support your answer graphically (Hint: Once part (a) is done, part (b) follows from the answer to part (a)) (a) 6-(x+2) <0 (b) 6-(x+2) 20

what is the largest three digit number that you can make if you use twenty stripes?

Given the geometric sequence:0.2,0.06,0.018,... Which term in the sequence would have a value of 0.000486? 9 4 6 12

An individual began a fitness program by running 4 km on the first day, and then increased the distance by one third of a km on each run. Combining all the runs, how far had the individual gone after the 12th run? 70 km 20 km 78 km 96 km

Use the given information to find the unknown value. y varies inversely with the square of x. When x = 9, then y = 6. Find y when x = 3. y = 2

Wayne has $14,500 in a high interest savings account with 3.66% annual interest compounded monthly. Assuming he makes no deposits or withdrawals, how long will it take for his investment to grow to $20,000? Round answers to the nearest tenth of a year.

Post one initial response of at least 150 words but not more than 350 words responding to the following. Do you think there should be interest rate caps on payday loans or not? Defend your answer. •Determine the interest that would be charged on a two-week $300 payday loan if the interest rate is 520%, and the interest is compounded at the end of the two weeks. Explain how you came to your answer. • Suppose a friend or family asked you how it could be possible that an annual interest rate is higher than 100%. Write out an explanation of what you might say to them.

1. Graph each function WITHOUT a calculator and upload a picture of your graph. a.y=-9(3)* b. y = 2x+5 c. y = 3(2)x-¹+4

How long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously? Round your answer to one decimal place. It will take about STER years.

What is the solution of 5 + In 3x = 8? 5+ ln 3x = 8 In 3x = 3 Inx = 1 x = e¹ x = e = 2.72

A student says that the graph of f(x)= (1/4)^(x+2) + 1 is a shift of the parent function 2 units up and 1 unit to the left. Describe and correct the student's error.

3. Use the Change of Base Formula to evaluate. Show your work. log, 30

4. Use the properties of logarithms to evaluate the expression. Show your work.

3. Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account, answer the following questions. Show your work. a. How much money will be in the account after 3 years? b. How many years will it take for the account to contain $3000?

> Unit 2-Radical Functions & Equations ✓ Unit 3- Exponential & 4. A population of 1,860,000 decreases 1.5% each year. a. Write an exponential function to model the situation. b. Find the population after 12 years.

Barbara can seek financing by issuing either debt or equity. If Barbara devotes minimal effort to her job, her salary will remain at $80,000. If Barbara works hard, she stands a 50 percent chance of getting a promotion and a raise to $120,000, so that her expected income will be $100,000. Barbara's disutility of working hard is $16,000, and her cost of funds is $25,000. Assume that information is asymmetric and that everyone is risk neutral. Also, Barbara keeps the full surplus from her hard work. In equilibrium, Barbara issues A. equity; works hard B. equity; shirks C. debt; works hard D. debt; shirks

Type only your answer in the space provided below. Do not round until the final answer. Then round to the nearest tenth. A helicopter flies from the airport on a course with a bearing of 17°. After flying for 98 miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 227°. How far did the helicopter fly on the final lege of its journey? The distance the helicopter flew was approximately_________ miles. Hint: Law of Sines

describes the radius r, in inches, of circle x seconds after it was formed. The function A(x) = x² describes the area A of a circle with radius x. Find (Aor)(2) to the nearest whole number.

You can use the function f(x) = 331.4 +0.6x to approximate the speed of sound in dry air, where x is the temperature in degrees Celsius. Evaluate f-¹(350). Brieve PORCE ☎ SE ro everest EROTICA PR

a. If $80,000 is invested at 8%, compounded annually, find the future value in 2 years. $93312 (Simplify your answer. Round to the nearest cent as needed.) b. If $80,000 is invested at 8% interest, compounded continuously, the future value is $93,880.87. How does this compare to the result from part (a)? The amount found with continuous compounding yields $ more. (Round to the nearest cent as needed.)

You can use the expression d = 1.2√h to approximate the visibility range D, in miles, from a height of h feet above the ground. How far above ground is an observer whose visibility range is 84 miles? The observer is feet above the ground.

What is a simpler form of the radical expression? √√81x208 Select one: O a. 3x5|y²| O b. 9x25 O c. 9x25 A O d. 3|x5|y²

How many grams are in 25 milligrams? 25 mg = [?] g

Which of the following is the value of Σ(4k+1)? (1) 53 (2) 45 (3) 37 (4) 80

How many hectometers is 97 millimeters?

Round to 4 significant figures. 42,561

One factor of x³ + 2x² - 11x - 12 is x + 4. Identify all remaining factors. x+1 x + 3 x-3 x-1

Which is a third degree polynomial with -1 and 1 as its only zeros? Ox³ - x²-x+1 Ox³ - x² + x - 1 3 x³ - 3x² + 3x − 1 Ox³ + 3x² + 3x + 1

A real root of ³ - 3x²+x+7= 0 lies between two consecutive integers. Find these two integers. between -1 and 0 between -2 and -1 between Qland 1 at -1

Round to 2 significant figures. 0.000789

How many times does the graph y = (x + 3)² touch the x-axis?

Given P(x) = -5x¹ − 3x³ + 11x² + 16x - 9, which of the following is true? (Select all that apply.) As x → ∞, P(x) → As x-00, --8. P(x) → -∞0. As x → -∞, P(x) → ∞. As x → ∞, P(x) → ∞.

Find the local minimum for f(x) ƒ(x) = x³ − 5x² + 3x + 2. (-3,7) (0.3, -2.5) (0.3, 2.5) (3,-7)

What are the domain and range of f(x) = x³ - 5x² + 2x - 8? Domain: x2 -0.45; Range: All Real Numbers Domain: All Real Numbers; Range: ys -8 Domain: All Real Numbers; Range: y 2 -8 Domain: All Real Numbers; Range: All Real Numbers

On each bounce, a ball dropped from 100 feet rises to 1/2 the height from which it has fallen. How high does the ball rise, in feet, on the 10th bounce? select one: 25/128 25/64 25/512 25/256

The number of kilograms, y, of a radioactive element that remains after t hours can be modeled by the equation y = 0.23(0.91)t What is the rate of decrease of this radioactive element? 23% per hour 91% per hour 77% per hour 9% per hour

To help pay for Wally's estimated $25,000 in college expenses, Brandon and Trevor make a deposit into a college fund at the beginning of each half-year over the course of 17 years. If this fund earns 6% interest, compounded semiannually, how large must these deposits be in order to pay for the estimated expenses? Round your answer to the nearest cent.

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?

Determine the amount of money that will be accumulated in an account that pays compound interest, given the initial principal of $29,600 invested at 2.84% annual interest for 6 years compounded (a) daily (n=365); (b) continuously. (a) Swill be accumulated in an account that pays interest that is compounded daily (Round to the nearest cent as needed)