Sequences & Series Questions and Answers

Given a right triangle with one angle measuring 0-40° and the hypotenuse of length 14, find the length x of the side opposite the angle. Round your answer to the nearest hundredth. X=

Keiko is choosing between two exercise routines. In Routine #1, she does only running, burning 10.5 calories per minute. In Routine #2, she burns 18 calories walking. She then runs at a rate that burns 8.25 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Given that y = ax b, take the natural logarithm on both sides. Let Y = In y and X = In x. Consider Y as a function of X. What kind of function is Y?

The 8th term of an arithmetic sequence is 8, and the 20th term is 44. a) Find the first term and the common difference. b) What is the nth term of the sequence?

A random sample of 40 college professors is selected from all professors at a university. The following list gives their ages. 66, 46, 47, 41, 37, 53, 45, 44, 47, 23, 52, 60, 50, 40, 61, 68, 52, 43, 51, 20, 38, 63, 48, 48, 38, 30, 48, 35, 29, 40, 63, 35, 37, 48, 23, 37, 46, 36, 30, 56. Construct a stem-and-leaf plot for the data. Complete parts a. and b. a. Determine the leaves for each corresponding stem. Complete the table below. b. What does the shape of the display reveal about the ages of the professors? A. None of the college professors live to be 70 years old. B. The greatest number of college professors are in their 40s. C. If you are younger than 30, you cannot be a college professor. D. None of the above.

An auditorium has 66 rows of seats. The first row contains 30 seats. As you move to the rear of the auditorium, each row has 2 more seats than the previous row. How many seats are in the 28 th row? How many seats are in the auditorium?

For the following exercise, use the functions f(x) = 3x² + 3 and g(x) = 5x 4 to evaluate or find the composition function as indicated. g(f(-3)) =

For the following exercise, use the pair of functions to find f(g(0)) and g(f(0)). f(x) = 3x - 1, g(x) = 3 + 5x²

Which of the following sets of ordered pairs represents a function? { (6,6), (9,-1), (9,1), (1,7), (1,-7) } {6,3,9,-1,1,7,4,-4,7,8} { (6,3), (9,-1), (1,7), (4,-4), (7,8) } { (6,3), (6,-1), (6,7), (6,-4), (6,8) }

A function N= f(y) gives the number of firefighters, N, in a town in year y. What does f(2014) = 400 represent? The statement f(2014) = 400 tells us that in the year 2018 there were 400 firefighters in the town. The statement f(2014) = 400 tells us that in the year 2014 there were 400 firefighters in the town. The statement f(2014) = 400 tells us that in the year 2014 there were 300 firefighters in the town. The statement f(2014) = 400 tells us that in the year 2018 there were 300 firefighters in the town.

Find the least squares regression line. (Round your coefficients to three decimal places.) (-6, 1), (1, 4), (2, 4), (2, 6)

For the following exercise, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. The graph of f(x) = 1/x2 is vertically compressed by a factor of 1/5 units, then shifted to the left 4 units and down 6 units.

Is the sequence an = 7+ 3n arithmetic? Your answer is (input yes or no) if your answer is yes, its first term is its common difference is 3

Suppose you go to a company that pays 0.05 for the first day, 0.1 for the second day, 0.2 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 30 days?

Write the arithmetic sequence 31, 27, 23, 19, ... in the standard form:

Solve the following system of equations graphically on the set of axes below. y = -1/2x+2 3x - 2y = 12 Plot two lines by clicking the graph.

Please work the problems on a separate piece of paper, take a picture, and upload. 1). Graph: 2x + 3y > 12 2). Graph: 3- y≤-lx-4|

Write the function rule g(x) after the given transformations of the graph of f(x) = 6x. reflection in the x-axis; vertical compression by a factor of 1/3 g(x) =

Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12.50 per person plus tax. Zalia pays for herself and her friend. They have lunch at the museum's cafe. Zala has a sandwich for $5.95, an apple for $1.25 and a drink for $1.69. She is charged tax and also tips her server 15%. If tax is 7.25%, how much did Zalia pay all total for her day at the science museum? a. $41.43 b. $37.68 c. $36.35 d. $24.27 Please select the best answer from the choices provided

Write the equation of the line containing the points (-3, 3) and (9, -3). a. (y - 3) = - 1/2(x + 3) b. (y - 3) = -2(x + 3) c. (y + 3) = -2(x - 3) d. (y + 3) = - 1/2(x - 3)

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation. X y 6 9.6 9 14.4 12 19.2 15 24 a. yes; k= 6; y = 1.6x c. yes; k= 6; y = 6x b. yes; k= 3; y = 3x d. no Select one: A. a B. b C. C D. d

Express in terms of i. √-17 =[] (Simplify your answer. Type your answer in the form a + bi.)

Find the amount that results from the given investment. $100 invested at 10% compounded quarterly after a period of 4 years After 4 years, the investment results in $[]. (Round to the nearest cent as needed.)

An mp3 player is on sale for 30% off the regular price of $39.98. How much is the discount? a. $11.99 b. $13.19 c. $13.33 d. $27.99 Please select the best answer from the choices provided A B C D

Use logarithms to evaluate (647) (0.00916). What is the logarithm of the answer? A. 0.8490 B. 9.8490 - 10 C. 0.7728 D. 9.7728 10

The number on the right represents the completely simplified form of the number on the left. √-289 = ∓17i √-117 = ∓i√117 √-9 = 3i

If a family had three children, Find the probability that at least two of the three children is a girl 3/8 4/8 7/8 None of these

A race between two candidates for mayor looks to be close. Assuming a good random sample, how many voters would need to have their answers included in a poll in order to achieve a margin of error for the support of one candidate of +/- 3.7% at the 90% confidence level?

Evaluate the following expression for x = 2 and y = 4. 8x + 8y/4x The answer is ____

Give three different pairs of numbers whose product is 0. For two numbers to have a product of 0, what must be true about one of the numbers? If the product of factors (x + 3) and (x + 4) is zero, what must be true about one of those factors?

In this math art, the number 216 was chosen. this creates a path of 5. I create a table showing degree locations in five different formats: degree, negative degree, coterminal (0,360), and negative coterminal (-360,0) and radian. You pick whichever degree measures to convert to radian measure.

The table shows pork production in China from 2000 to 2007. Use a calculator to answer the questions. Let 2000 = year 0. a). Find the equation for the line of best fit. b)Use your linear model to predict how many metric tons of pork will be produced in 2025. c). Use your linear model to predict when productions is likely to reach 100,000 metric tons. .

Solve the formula for the specified variable. T = md² for m m=[ ]

Identify the indicated resultant vector using the diagram below. (Hint: Remember that vectors can be moved without changing their magnitude and direction, so the resultant vectors might not be drawn at a location you exact.)

The equation -2x + 2y -8 and the graph below each represent linear functions. Which has the greater slope, and what is its value? a.The graph Slope = 0.5 b. The equation Slope = 1 C. The graph Slope = 1 d. The equation Slope = -1

Solve the radical equation. Check all proposed solutions. x -√(3x-8)=6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { } (Use a comma to separate answers as needed. Simplify your answer.) B. The solution set is Ø.

A ball is thrown upward with an initial velocity of 16 ft/sec from a height of 32 ft above the ground. The height, in feet, of the ball t sec after it is thrown can be represented by s = -16t² + 16t + 32. How long will it take for the ball to reach the ground? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a. 1 sec b. 1.5 sec c. 2 sec d. 2.5 sec

Find the angle between the vectors. (Round your answer to two decimal places.) u = (3, 4), v = (12,-5), (u, v) = u • v θ = ____ radians Find the angle between the vectors. (Round your answer to two decimal places.) u=(-3,0), v = (-5, 4), (u, v) = 3u₁v₁ + 2u₂v₂ θ = ____ radians

The Harringtons go to a restaurant for lunch and their bill is $86.20. After 6.5% tax and tip, they pay a total of $100. If the Harringtons were exceptionally pleased with their service, decide if their tip reflected this. Explain your reasoning.

Q3: Which of the following statements is TRUE of the trigonometric function shown in the graph below? The period of the function is 2 The amplitude of the function is 3. The midline of the function is y=2 Minimum occurs at (3)

Simplify. 36 9.4+8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 36÷9.4+8= B. The expression is undefined.

List the possible rational roots of the equation. 0=22x⁴ - x² + 121 Choose the answer below that lists the potential rational roots. A. ±1, ±11, ±121, ±1/11, ±1/22, ±1/22, ±2/11, ±2/121 B. ±1, ±11, ±2, ±22, ± 1/11, ±1/2, ±1/22, ±2/11, ±2/121 C. ±1, ±11, ±121, ±1/11, ±1/2, ±1/22 D. ±1, ±11, +121, ±1/11, ±1/2, ±1/22, ±11/2, ±121/2

The formula for the future value C of a simple interest investment is C = Q + Qrt, where Q is the original investment, r is the annual interest rate, and t is the time in years. Solve this formula for t.

Nezzie is shopping for items for her daycare because the store is having a sale where everything in the store is 10% off. Nezzie buys a playhouse for $100.29 and a music center for $59.99. She has a coupon for an additional 19% off on the playhouse. Before tax, Nezzie estimates that her total, aher discounts, will be about $122. Determine I Nozzle has estimated correctly. a. Yes. Nezzie has estimated correctly. b. No. Nezzie has taken 25% off from the music center, which is not correct c. No. Nezzie has taken successive discounts on the total, but the coupon is just on the playhouse. d. No. Nezzie has estimated 10% off the original price of the playhouse not the discounted price Please select the best answer from the choices provided A B C D

Evaluate x - y for the given replacement values. x = -2 and y=9 x-y=

Find the θ notation of the following expressions: 3lgn + (1+ 1/2 + (1/2)² + (1/2)³ +......+(1/2)ⁿ)

Evaluate 4x + y for x = 4 and y = - 26.

Evaluate x - y for the given replacement values. x = 1 and y=-22 x-y=

Simplify the expression by combining like terms. 2x-8x+4x-x=

While camping in the forest, Carina decided to go on a hike. From her campsite she first hiked to a waterfall located 3.46 miles west and 2.10 miles north of her campsite. She then hiked to a mountain spring located 2.77 miles west and 4.31 miles south of the waterfall. Find the resultant vector of her two hikes in component form.