Binomial theorem Questions and Answers

At 10 17 a m you pass a police car at 55mph that is stopped on the freeway You pass a second police car at 55mph at 10 53 a m which is located 39 miles from the first police car If the speed limit is 60mph can the police cite you for speeding Find your average velocity from the 10 17 a m to 10 53 p m mph Round value above to 2 decimal places By the MVT since the average velocity over the interval was Select an answer limit of 60mph the police Select an answer site you for speeding than the posted speed

The specifications for a plastic liner for a concrete highway project calls for thickness of 5 0 mm 0 08 mm The standard deviation of the process is estimated to be 0 02 mm The upper specification limit for this product 5 080 mm round your response to three decimal places The lower specification limit for this product 4 920 mm round your response to three decimal places The process is known to operate at a mean thickness of 5 0 mm The process capability index Cpk response to three decimal places round your

Which of the following is are mentioned in the WSJ article as a way to maximize the benefits of compounding Select all that apply A Minimize investing fees and expenses B Minimize taxes owed C Take some risk in order to increase expected return D Reduce excessive risk by diversifying E Invest in alternative assets like commodities and cryptocurrencies

Require NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Identify the degree sequence of each of the following graphs Multiple Choice O 2 2 2 2 3 2 2 2 2 3 3 2 3 3 3 3

Identify the steps used in Algorithm 1 to find the maximum element in the following finite sequence 1 8 12 9 11 2 14 5 10 4 Algorithm 1 procedure maxtas a2 an Integers max a for 1 2 to n If max a then max a return maximax is the largest element

rst determine the quadrant for 0 then find x y and r and finally give all six trigonometric ratios for given the following information and tan 0 0 lives in quadrant C y T 1 sin 0 2 cos 0 3 tan 0 4 5 csc 0 6 cot 0 S csc 0

1 point Two cars leave Tulsa at exactly the same time from the same spot One car travels at 40 mph straight east while the other car travels at 30 mph straight north The path taken by the two cars forms a right triangle at their starting point in Tulsa How far apart are the two cars after two hours Hint Draw a diagram and use the Pythagorean Theorem E 100 200 50 1 000 hypotenuse b C They will be miles apart after two hours

At the end of each quarter a 48 year old individual puts 1400 in a retirement account that pays 9 7 interest compounded quarterly a When the individual reaches age 60 what is the value of the account b If no further deposits or withdrawals are made to the account what is the value of the account when the individual reaches age 65 CITO a Up to age 60 the individual s deposits form an ordinary annuity because the deposits are made at the end 1 1 of each period Therefore the formula does not continue to behave as an annuity and a different formula should be used When the individual reaches age 60 the value of the account will be Do not round until the final answer Then round to the nearest cent as needed FV PMT should be used After age 60 the account

Solve the system by the method of substitution Check your solutions graphically Sy x 3x 7 ly 2x 7 x y x y x y 4 2 1 smallest x value largest x value 2 3 XX

Let P be an n x n orthogonal projection matrix, i.e., P2 = P and PT = P. Which of the following is necessarily true? P has an eigenvalue equal to 0. The rank of P is equal to 2. The rank of P is equal to 1. P has an eigenvalue equal to -1. Each eigenvalue of P is equal to either 0 or 1.

Write the fifteenth term of the binomial expansion of (a² + b) ²² The fifteenth term is

You and friends go to the gym to play badminton. There are 4 courts, and only your group is waiting. Suppose each group on court plays an exponen- tial random time with mean 20 minutes. What is the probability that your group is the last to hit the shower?

The average number of cigarettes smoked per person in a year in the top ten countries for smoking are shown next. Greece 4363 Malta 2705 Hungary 3285 Bulgaria 2521 Kuwait 3065 Belarus 2315 Japan 2923 Belgium 2213 Spain 2865 Turkey 2081 For the above data set, find the mean, median, midrange, and mode. Round to one decimal place, if necessary. (a) Find the mean. The mean is 2833.6 cigarettes smoked per person in a year. (b) Find the median. The median is _________cigarattes smoked per person in a year.

When rolling a die 20 times, what is the probability of rolling exactly 4 three times? 24.3% 19.3% 23.7% 50%

According to a report from a particular university, 47% of female undergraduates take on debt. Find the probability that none of the female undergraduates have taken on debt if 7 female undergraduates were selected at random. What probability should be found? A. P(2 female undergraduates take on debt) B. P(0 female undergraduates take on debt) C. P(7 female undergraduates take on debt) D. P(1 female undergraduate takes on debt) The probability that none of the female undergraduates take on debt is ______.

A pass code is to consist of three capital letters followed by two digits. Determine the number of different pass codes possible if repetition is not permitted. 2,304,600 1,757,600 1,356,800 1,404,000

(a) The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a stratified sample of attendees? The organizers assign each attendee a different number. Using a random number table, the organizers draw 56 of those numbers at random. Then, the organizers select the attendees assigned to the drawn numbers. Every set of 56 attendees is equally likely to be drawn using the random number table. The organizers form 7 groups of attendees based on the attendees' employment statuses. Then, the organizers select 8 attendees at random from each group. (b) A botanist at a nursery wants to inspect the health of the plants at the nursery. Which of the following best describes a systematic sample of plants? All of the plants that are in one particular room at the nursery are easily accessible. So, the botanist selects the 72 plants in this particular room. The botanist forms 6 groups of plants based on the ages of the plants (in months). Then, he selects 12 plants at random from each group. The botanist takes a list of the plants and selects every 3rd plant until 72 plants are selected. The organizers form groups of 8 attendees based on the day the attendees registered. Then, the organizers randomly choose 7 groups and select all of the attendees in these groups. (c) Counselors at a college want to poll students about how much time the students spend studying. Which of the following best describes a random sample of students? The counselors use a computer program to draw 78 students at random and select these students. Every set of 78 students is equally likely to be drawn by the computer program. The counselors form groups of 13 students based on the students' majors. Then, the counselors select all of the students in 6 randomly chosen groups. The counselors take a list of the students and select every 3rd student until 78 students are selected.

Students at a major university are complaining of a serious housing crunch. Many of the university' sstudents, they complain, have to commute too far to school because there is not enough housing near campus. The university officials respond with the following information: the mean distance commuted to school by students is 15.7 miles. Assuming that the university officials' information is correct, complete the following statements about the distribution of commute distances for students at this university. (a) According to Chebyshev's theorem, at least? of the commute distances lie within 2.5 standard deviations of the mean, 15.7 miles. (b) Suppose that the distribution is bell-shaped. If approximately 99.7% of the commute distances lie between 5.2 miles and 26.2 miles, then the approximate value of the standard deviation for the distribution, according to the empirical rule, is .

A pet store has 5 cats. Here are their weights (in pounds). 11, 13, 7, 7, 6 Send data to calculator Find the mean weight of these cats. If necessary, round your answer to the nearest tenth.

A pet store has 6 cats. Here are their weights (in pounds). 16, 5, 7, 8, 15, 7 Send data to calculator Find the mean weight of these cats. If necessary, round your answer to the nearest tenth.

The organizer of a conference is selecting workshops to include. She will select from 3 workshops about anthropology and 10 workshops about psychology. In how many ways can she select 7 workshops if fewer than 2 must be about anthropology?

A certain train has 10 cars that are being lined up on a track. One of the cars the engine, and another is the caboose. The engine will be the first car in line. The caboose will be the last car in line. In how many ways can the cars be lined up?

(20 pts) Write the multiplication table of a finite field of 16 elements using the irreducible polynomial f(x) = x4 + x + 1. Find the multiplication inverse of the element x² + x³.

Use generating functions to find the number of ways to select 8 balls from a collection of red, blue and white balls if there are many balls of each colour and you must choose at least 4 white balls.

Solve the following equation by completing the squares. Organize the steps in the correct order. 2²-8x-2=0 Begin Find and add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Simplify the radical. Factor the trinomial. x=4±3√2 Add 2 to both side. Take the square root on both side of the equation. Isolate x by adding 4 to both side of the equation.