Sequences & Series Questions and Answers

The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers. The data are normally distributed and s = 10.326 weeks. Construct and interpret a 99% confidence interval for the population standard deviation of the age (in weeks) at which babies first crawl. 55 32 44 35 38 27 45 38 59 27 38 29 Click the icon to view the table of critical values of the chi-square distribution. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to three decimal places as needed.) A. If repeated samples are taken, 99% of them will have the sample standard deviation between and B. There is 99% confidence that the population standard deviation is between and C. There is a 99% probability that the true population standard deviation is between and

The equation (16 X) = 560 has two solutions. The smaller solution is X = A. The larger solution is x = B. Enter the value of A followed by the value of B for your response.

The function fis given by the set {(-5, 3), (-1, -1), (0, 4), (2, -6), (5, -7)}. Determine f-¹

Which of the following scenarios is possible for a 5th degree polynomial? Select ALL that are possible. A) Two distict x-intercepts B) Only one x-intercept C) No x-intercepts D) Three distinct x-intercepts E) Four distinct x-intercepts

Write a paragraph or a list of steps to explain how you find the solutions to the equation x3-3x2+25x-75=0 Your description should be specific to this equation, and make sure you state the set of all solutions at the end of your explanation.

Which of the following ordered pairs represent a function? How do you know? a. (8, 56). (11, 7). (9, 63), (0, 0) b. (1.7, 2), (1.8, 2). (3.2. 3), (4.3, 4)

We have a triangle with sides a, b, c that are opposite angles A, B, C respectively. Assume that side a = 20, side b = 25, and side c = 7, Determine the measure of angle C to the nearest 0.001 degrees (or 3 decimal places).

Suppose the rate of change of the unit price p of video boards is p'(x)= where x is the number of hundreds of video boards that the supplier will make available to the market daily and p is in dollars. Find the supply equation p(x) for the video boards if the quantity the supplier is willing to make available is 400 video boards when the unit price is 390 dollars.

1. Identify the ratio-in simplest form if required. 1. A math club has 25 members, of which 11 are males and the rest are females. a. What is the ratio of males to all club members? b. What is the ratio of males to females?

Use generating functions to (a) Determine the number of 10-digit ternary sequences in which the digit 2 occurs at least once, and the digit 0 occurs an even number of times. (b) Determine the number of ways to distribute 15 identical balls into three distinct boxes with an odd number of balls in each container.

Omar and Joey would like to save 60,000 information years for a down payment on a house. how much do they need to deposit each month into an account earning 2% interest to reach their goal? a. 553.91 b.832.15 c. 1153.97 d. 1201.71 e. 499.29

Let a and b be elements in a ring R such that ab = ba. Prove the following: 1. a + b is a nilpotent if a and b are nilpotents. 2. ab is a nilpotent if a or b is a nilpotent.

Given the vector u = (-4, -4√3), find the magnitude and direction of u. Select the correct answer below: |u| = 8; θ = 240" |u| = 8; θ = 60° |u| = 8; θ = 150 |u| = 4; θ = 150* |u| = 4; θ = 60° |u| = 4; θ = 240"

The simple interest rate varies jointly as the principal and the time. At a specific interest rate, the simple interest is $1,050 for a loan of $7,000 for 5 years. At the same interest rate, determine the simple interest for a loan of $6,000 for 9 years.

w varies jointly as x and y and inversely as the square of z. If w = 10 when x = 120, y = 8, and z = 12, find w when x = 140, y = 6, and z = 10. Round to the nearest tenth if necessary.

The revenue from selling bicycles varies directly to the number of bicycles sold. When 92 bicycles are sold, the revenue is $15,180. Determine the revenue when 154 bicycles are sold.

Tim and Mark are friends that live across the country from each other. They plan to meet in Canada for a fishing trip. The trip is 1600 miles for Tim and 1500 miles for Mark. If Tim drives 5 miles per hour faster than Tim, and they take the same amount of time to complete the trip, determine the rate for Tim and Mark. Only provide the numerical solution. The unit, miles per hour, is not necessary. Tim: Mark:

Gilbert road is bike 11 miles. After 11 miles, he stopped for one hour before riding his bike for 15 more miles at a speed that was twice his original speed. If the total length of the trip, including the one hour break, took 6 hours, determine Gilbert's original speed and faster speed. Only provide the numerical solution. The unit, miles per hour, is not necessary. Original Speed: Faster Speed:

Nick can plant a row of soybeans in 70 minutes. Matt can plant the same row in 30 minutes. How long will it take them working together to plan this row of soybeans? Only provide the numerical solution. The unit, minutes, is not necessary.

Mike and Peggy are digging holes for time capsules. Together it take them 2.4 hours to dig a hole. If Mike can dig a hole by himself in 3.2 hours, how long would it take Peggy to dig the same hole? Only provide the numerical solution. The unit, hours, is not necessary.

In the troposphere, temperature decreases with elevation by about 6.5 degrees Celsius every 1000 kilometers above ground level. If it is 23 degrees Celsius at ground level in Boston, what is the temperature 7000 kilometers higher? degrees Celsius Generalize your process to a formula for the temperature z kilometers higher for Boston: Temperature =

Two rockets are to be launched at the same time. They will meet at a space station. Rocket A will travel 20,000 miles per hour and Rocket B will travel 18,000 miles per hour. If the Rocket A will reach the space station 0.6 hours before Rocket B, how far is the space station from Earth?

Apply the properties of logarithms to write the expression as a single logarithm. Enter the argument in parentheses. Do not insert any spaces in your answer. In(x) + In 15

Find the formula for an exponential function that passes through the two points given. (-3, 10) and (2, 1)

Consider the plane π: -x + 2y - 5z = 0 and the lines: x = 4m, L₁ : y = -5m, z = 2m x = 4 + 3t, L2: y = 3, z=-t Part(a) [6 points] A line L is perpendicular to the plane π and passes through the intersection point of π and L2. Find the parametric equations of the line L. Part (b) [6 points] Find the point-normal equation of a plane π* that contains the line L₁ and is also perpendicular to π.

The population of a pod of bottlenose dolphins is modeled by the function A (t) = 15(1.2), where t is given in years. To the nearest whole number, what will the pod population be after 5 years?

A vehicular tunnel has a length of 8328 feet. Use the concept of accuracy and significant digits to determine the range of this number The range is from to feet

Solve the system by the method of your choice. 5x=y-3 5x - y = 7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y)|5x=y-3} or {(x,y)|5x - y = 7}. C. The solution set is Ø.

The interest earned on a loan varies jointly as the interest rate and the time. If an investment earns $100 at 2.5% for 4 years, how much interest will be gained at 3.5% for 6 years? Only provide the numerical solution. No units are necessary.

The owners of a new technology store determine that their monthly sales of a product vary directly as their advertising budget and inversely as the price of the product. When $60,000 is spent on advertising and the price of the product is $20, the monthly sales were $840,000. Determine the monthly sales if the advertising budget is increased to $70,000. Only provide the numerical solution. No units are necessary.

What are the three methods we can use to solve an exponential equation?

Solve the system by the substitution method. x + 3y = 5 y = 4x + 6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is. (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Matt is working as a dog walker. His payment varies directly as the number of miles he walks with dogs. For 3.5 miles, Matt is paid $22.40. How much does he get paid if he walks 5.2 miles? Only provide the numerical solution. No $ symbol is necessary.

The logistic model P(t) = 427/1+7.71 e ^-0.018t represents the number of invasive species present in a habitat t years after 1900. (a) Evaluate and interpret P(0). (b) What is the growth rate of invasive species? (c) Use a graphing utility to graph P = P(t). (d) How many invasive species were present in the habitat in 1999? (e) In what year was the number of invasive species 184?

Rewrite the following infinite series using sigma notation. (a) 1+1/2 + 1/3+ 1/4+ 1/5 +....... (b) 1-1/2 + 1/3-1/4+ 1/5 +.......

How much money will there be in an account at the end of 10 years if $12,000 is deposited at 7% interest compounded semi-annually? (Assume no withdrawals are made.) The amount after 10 years will be $ 21,560.32 23,877.47 29,567.32 23.546.67

Find the polar coordinates of a point with Cartesian coordinates (x, y) = (-5,0). Select the correct answer below: (2, π) (5,3π/2) (5, π) (2, 3π/2) (5,2π) (2,2π)

The monthly demand function for a product sold by a monopoly is p = 1,896 - x² dollars, and the average cost is C = 1,000+ 4x + x² dollars. Production is limited to 1,000 units, and x is n hundreds of units. Find the revenue function, R(x). R(x) = Find the cost function, C(x). C(x) = Find the profit function, P(x). P(x) = (a) Find P(x). P(x) =

What is the approximate temperature of the Sun? 6,000 K everywhere. 15 million K everywhere. 15 billion K everywhere. 6,000 K at its core, 15 million K at its surface. 6,000 K at its surface, 15 million K at its core.

convert the vector l-->al -5km with a bearing 135 degrees in cartesian form

How are two nuclei called if they have the same number of protons but a different number of neutrons? lons. Weird. Different elements. Isotopes. Molecules.

A candy distributor needs to mix a 10% fat- content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 15% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

12. Perform the following operations a. 2304five + 121 five b. 3E8 twelve +3TT twelve e. 100101two - 10011two

You need a 55% alcohol solution. On hand, you have a 715 mL of a 80% alcohol mixture. How much pure water will you need to add to obtain the desired solution? You will need mL of pure water to obtain mL of the desired 55% solution.

Find the 7th term in the sequence with the following definition: a₁ = 64 an =an-1 / 2

Trey wants to buy a bond that will mature to 56000 in eight years. How much should he pay for the bond now if it earns interest at a rate of 2.5% per year, compounded continuously? Do not round any intermediate computations, and round your answer to the nearest cent.

Calculate the monthly mortgage payment with the following conditions: $285,000 borrowed, 3.45% interest, 30-year term. What formula did you use to solve this equation? What is your "r" as you put it into your formula?

Given the function of the form f(x) = a ex-h + k a. Identify a, h, and k. b. Identify and plot the reference points. c. Draw the graph. d. State the domain and range in set nota g(x) = 2e* - 5

The population of a city (in millions) at time t (in years) is P(t) = 2.1e0.007t, where t = 0 is the year 2000. When will the population double from its size at t = 0?

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.