Binomial theorem Questions and Answers

A researcher must estimate the mean temperature in degrees Fahrenheit with the following sample temperatures 66 2 22 8 83 8 71 1 36 2 28 31 4 33 3 Assuming the population of temperatures are normally distributed find the 90 confidence interval Round the answers to two decimal places Enter your answer as an interval of the form LB UP The researcher is 90 confident that the population average temperature is within the temperature interval

Question 2 1 point A state wide poll of 1600 adults estimated monthly amount spent for in home intern legislator wants to be 99 confident Ho confidence interval based on the sample s

In the long run some firms will respond by

of police patrols 15 20 18 12 25 21 17 23 14 C Gallons of gas used by police department 471 539 511 344 717 637 482 647 321 a Find the correlation coefficient round to 3 decimal places and use correct notation b Find the coefficient of determination round to 3 decimal places and use correct notation How much of the variation in y can be explained by the line of best fit round the percentage to 1 decimal place d Use the Table A 6 from your notes to determine if your value of r is a linear correlation Show your work e If the linear correlation coefficient exists then it is appropriate to use the linear regression equation to make predictions Find the linear regression equation round to 2 decimal places and use correct notation f Use the linear regression equation to predict the output for 22 police patrols round to 2 decimal places

2 12 a Is the function X 2 e ezt a solution to the system X x 2 X Justify your answer

View Policies Show Attempt History Current Attempt in Progress The following information is available for Sandhill s Activewear Inventory Net sales Cost of goods sold a 2025 554 000 1 950 000 1 677 000 2024 2023 1 373 300 564 000 1 772 000 1 310 00 322 00 935 00

Supplies Prepaid Insurance Salaries and Wages Payable January 31 2025 Unearned Service Revenue Supplies Expense Insurance Expense Salaries and Wages Expense Service Revenue Jan 31 Debit Jan 31 800 1 560 800 520 1 610 Credit Prepare the closing entries at January 31 2025 List all debit entries before credit entries If no entry is required select No account titles and enter O for the amounts Credit account titles are automatically indented when the amount is entered Do no manually Date Account Titles and Explanation To close revenue account 1 050 To close expense accounts 890 4 170 Debit Credit

the following square roots of 36 cos 60 i sin 60 a Find the roots of the given complex number in trigonometric form Let 0 0 360 smaller 8 value larger 8 value 0 b Write each of the roots in standard form 1 70 O Z1 Z c Represent each of the roots graphically Imaginary Imaginary Imaginary Imaginary axis axis axis axis 10 10 10 10 5 5 5 5 Real Real Real 10 axis 10 5 Real 10 axis 10 axis 10 5 5 10 5 5 10 5 5 10 axis 10 10 10 10 O i

3 Use the graph of y p x below to find the values to the right 6 5 4 3 2 1 8 7 6 5 A 3 2 1 0 1 2 1 2 3 4

A card is drawn from a well shuffled deck of 52 cards Find the probability of drawing a red jack The probability is Simplify your answer Type an integer or a fraction

In order to receive full credit on all hypothesis tests the following work must be shown Clearly indicate Ho and H Write down the formula for the test statistic and all the values that go into the formula Draw a diagram that has the correct distribution number of tails and labeling Show how the Critical Value Method was used to reach the initial conclusion Write the formal conclusion Answer any follow up questions When Bridges Blue Cheese Dressing is packaged in 473 milliliter bottles the variance of the volume should not exceed 2 56 ml A sample of 21 fills from a large production run found a sample variance of s2 3 89 ml2 Use a 0 01 significance level to test the claim that the variance is greater than 2 56 ml you may assume that the volumes are normally distributed Based on this result should the company be concerned about its production runs Please note you are given s and o2 in this problem exactly what is requested in your formula

by Jayme I think the purpose of progressivism education is to allow our students to become and they should know how to use that role positively It is important to use class materia engaged members of society They should know that they have a purpose in the world assignment or read a certain book It is important to be transparent and excited about and make them meaningful Never leave students wondering why they have to do an the material we are teaching Our students reciprocate our attitudes so we need to be positive in the room I think the role of the teacher in this aspect is almost like a mentor We are preparing the students for more than college We need to prepare them for anything they can experience outside the classroom The students have an interesting role because they can decide what they learn and what they don t It really is up to them to make the most of their schooling experience 5 Which quotation best conveys the author s message A It is important to use class materials and make them meaningful B Never leave students wondering why they have to do an assignment or read a certain book I think the role of the teacher in this aspect is almost like a mentor We need to prepare them for anything they can experience outside the classroom In the paragraph the word reciprocate means to Ajoin a teacher in their understanding of the material Banswer in a way that is expected by the people around you experience the same feelings for someone respond to an action by making

7 6pts Let R be the remainder associated with the nth partial sum approximation to the alternating series 00 1 k 1 k3 k 1 Find an upper bound for R in terms of n How many terms of the series must be summed to approximate the series with an error less than 10 4

se Taylor s theorem to obtain an upper bound for the error of the approximation Then calculate the value of the error Round your answers to six decimal places 0 5 0 5 4 cos 0 5 0 5 2 4 4 S 1

For questions 6 10 a university claims that 82 of it The student senate polled 150 randomly selected gra taken them four years to graduate Use a 10 significa 6 List the null and alternative hypotheses Label the 7 State the level of significance

Determine the 1st and 2nd degree Taylor Polynomial approximations L x y Q x y fo f x y ln x y 1 near the point 0 0

Express the Taylor series for f x sin x centred at x Enter the first five coefficients Co C1 C2 C3 C4 7 6 as c x 7 Cn 6 n 0

Write an explicit formula for the arithmetic sequence 101 377 138 727 28 28 7

Let N x be the statement x has visited North Dakota where the domain consists of the students in your school Match each quantification of N x given in logical form with and expression in English 3xN x VxN x V 3xN x 3x N x A There is a student in your school who has not visited North Dacot B There are no students in your school who have visited North Dace C Every student in your school has visited North Dacota D Someone from your school has visited North Dacota

Match operations on sets with their definitions AnB AUB VA B VA A x x EA VxEB B x x EA A xEB C U A D x x EA A XE B

8 What is the equation that best models the data from the table after the data has been linearized 1 point y 4 4 X 2 7 13 19 22 426 30 18 2 120 0 715 4 1 768 3 5 775 9 10 508 5 Olog y 0 12502x 0 427231 Oy 1 350 76x 1 350 76 y 29 4755 1 21728 Oy 5 927 281og x 3 880 59

10 1 A simple beam AB supports five equally spaced loads P see figure a Determine the deflection 8 at the midpoint of the beam b If the same total load 5P is distributed as a uniform load on the beam what is the deflection 82 at the midpoint c Calculate the ratio of 8 to 82 P P P P L L L L L L 6 6 6 B

10 5 A simple beam ABCD has moment of inertia I near the supports and moment of inertia 21 in the middle region as shown in the figure A uniform load of intensity q acts over the entire length of the beam Determine the equations of the deflection curve for the left hand half of the beam Also find the angle of rotation 0 at the left hand support and the deflection Smax at the midpoint B 9 21 C 1 L

4 Fire Station A gets a report of a forest fire that is 40 miles east and 30 miles north of the station house Fire Station B sights the fire to be 24 miles west and 45 miles north of Station B What is the distance from each fire station to the fire Assume the firefighters do not follow roads but travel in a straight line to the fire Select all that apply F Station A is 50 miles away H Station B is 69 miles away J Station B is 51 miles away G OF and H OF and J Land G Both stations are 50 miles away I Station A is 70 miles away

portant aspect of computer graphics is the ability to transfo bordinates of points within an image For formation purposes a point x y is represented as the colu X xX y To rotate a point multiply a point s column ma appropriate rotation matrix R to form the matrix product F oplo to rotate a point by 45 in the

Parent functions are the most basic form of any function For this assignment decide which are the proper characteristics of the function listed below Exponential Function Equation Oy x Oy x Dy y x x 3 y x x 3 y x Oy y x Dy x y 20

Espa ol Jessica has scored 93 73 and 82 on her previous three tests What score does she need on her next test so that her average mean is 78 0

A group of students from neighboring cities raises money to build a shared skate park The students need to justify the location of the skate park to get approval from their city councils to build it 1 There are two main streets one that goes through each city as shown Explain how they could find a location between the streets that is the same distance from each main street Main Street A 6 Main Street B 2 If students from a third city participate in funding the skate park its main street crosses the other two at two separole points to form a triangle Can you still use information from the previous answer to find a location that is the same distance from the main street of each city Explain 3 Each of the three cities has a high school If the students want to have the skate park equidistant from all three high schools explain which point of concurrency they should use and how they would locate that point

dow Nuttel said a in the meantime rrect something moment without e Privately he mal visits on a much towards posed to be hen he was will bury l and your ll just give ow there nice Which of the following passages from The Open Window helps to advance the theme that humans are doubtful of most things A in the meantime you must try and put up with me B A most extraordinary man a Mr Nuttel could only talk about his illnesses C It was an unfortunate coincidence that he should have paid his visit on this tragic anniversary

Match each function name with its equation vy z Y y z z y y 2 y r Y Y 1 a Quadratic b Linear c Cube root d Reciprocal e Absolute Value f Reciprocal Squared g Cubic h Square Root

Solve the inequality a 5a 66 Give your answer in interval notation Enter DNE if there is no solution 11 6 invalid interval notation

You have 3 pairs of pants 4 shirts and 5 pairs of shoes You can use them to wear different outfits You are a participant in a peace conference with 10 participants Everybody shakes everybody else s hand There are handshakes altogether A family of five is taking an extended vacation Every day at lunch they stand in line at a cafeteria in a different order than ever before On the last day however they can t help repeating a previous order Their vacation lasted days

If x a is a factor of a polynomial function p x which statement is true A The binomial x a is also a factor of p x 1 The value of p a must be 0 The value of p a must be 0 There is an x intercept of the function at a 0 B C D a What keywords are important b If a binomial is a factor that means the remainder must be c Can you identify which unit topic this question comes from Think of if x 5 was a factor what would x really be e What answer choice is best

Put the equation that is in general form y x 6x 8 into standard form y x h k Answer y

PARI 4 SALES TAX DISCOUNTS USE YOUR CUSTOMER ORDERS TO CALCULATE THE SALES TAXA X 1 What is the total cost of order number one if you include 4 5 sales tax and a 20 tip Answer

3 Suppose that X and Y are two independent random variables P X a Y b P X a P Y b for any a b and X Binom n p and Y Binom m p Compute the probability P X Y k and show that X Y has a binomial distribution with parameters n m and p Hint Use n m m m 8 F 1 0

5 Poisson Approximation Mass produced needles are packed in boxes of 1000 On overage 1 needle in 2000 is defective a Find the probability that a box contains 2 or more defectives using the binomial distribution you may want to use R to compute the actual probability

1 Use the binomial theorem to expand 3x y 5

The distance in the x direction between two control points on a vertical aerial photograph is 5 3 in If the distance between these same two points is 4 0 in on a second photograph having a scale of 1 24 000 determine the scale of the first vertical aerial photograph scale 1 Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculation Carry out all intermediate results to at least four digit accuracy to minimize roundoff error If the focal length of the camera is 6 in and the average elevation at these points is 130 ft determine the flying height in ft from which each photograph was taken X first photograph elevation Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculation Carry out all intermediate results to at least four digit accuracy to minimize roundoff error ft 12100 ft second photograph elevation

f x g x f x g x f x g x Many like to remember that the derivative of a product is the derivative of the first function times f x g x f x g x f x derivative of first second first derivative of second g x dx For the given equation y 2x 5x2 1 if we let f x 2x and g x 5x21 then y 2x 5x g x 5x 1 as the second function Note that since y is the product of two differentiable functions we can use the product rule to find As a precursor to using the product rule complete the following statements If f x 2x then f x 2 If g x 5x 1 then g x 10x A 2 10 r 3 Step 2 With f x 2x f x 2 g x 5x2 1 and g x 10x we are now ready to substitute these continue to simplify

vased on these questions Note You may repeat th How many 10 digit nh

Each license plate in a certain state has six characters with repeats allowed Here are the possibilities for each character Possibilities The 26 letters of the alphabet The 26 letters of the alphabet The 26 letters of the alphabet The 10 digits 0 through 9 The 10 digits 0 through 9 The 10 digits 0 through 9 How many license plates are possible in this state 0 Character First Second Third Fourth Fifth Sixth X

1 What is the purpose of the zero position adjuster 2 What resistance value would be displayed by your ohmmeter if it is connected to a shor

Test the given claim Assume that a simple random sample is selected from a normally distributed population Use either the P value method or the traditional method of testing hypotheses Company A uses a new production method to manufacture aircraft altimeters A simple random sample of new altimeters resulted in errors listed below Use a 0 05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32 2 ft which was the standard deviation for the old production method If it appears that the standard deviation is greater does the new preduction method appear to be better or worse than the old method Should the company take any action 41 79 25 72 40 10 19 55 7 53 108 108 What are the null and alternative hypotheses A Ho o 32 2 ft H o 32 2 ft OC Ho o 32 2 ft H o 32 2 ft VE H G 32 2 ft H o 32 2 ft Find the test statistic Bound OB Ho 32 2 ft H G 32 2 ft D Hoo 32 2 ft H o 32 2 ft FH o 32 2 ft H o 32 2 ft

ntervals Questi Pa In a survey of 3307 adults 147 Construct a 99 confidence int

Express 3 2i 6 8i in a bi form Enter a number in each box

uestion 15 hen assessing sources to use i ormation that is credible and nsidered credible sources for a

Let 7 3 be a point on the terminal side of 0 Find the exact values of cos0 csc 0 and tan 0 cose csc0 0 C 2 X

In how many ways can four aces be drawn from a deck of cards Order is not important way s

Question eyewitness to a crime said th Id not remember the order T y many license plates must th