Binomial theorem Questions and Answers

1 When BN obtain the solution of Bessel s equation for the index B and compare and interpret which has been generated solution considering larg z 1 n n B 1 B 2n for index B JB z n 0

The scores for 20 students on a 50 point math test are 31 41 38 43 37 46 49 45 36 32 48 40 50 35 44 42 39 33 34 and 47 Part 0 3 Part 1 of 3 a Find the percentile rank for a score of 32 A test score of 32 is equivalent to the th st nd rd percentile

1 2 3 P LLL Find the radius of convergence of the following power series a b c k k 1 R lim LK We apply the ratio test thus ak 2 d k ak 1 e k k f lim IMBIMBIM8 k h We apply the root test thus 3k k 4k 5k ko 1 2kkk 1 2 1 k 1 k 1 k 1 k 1 lim 1 kx 1 1 k 1 2kkk k 1 2k 2k k k 4kkk kk ko k 1 k k 1 k 1 Jimm 1 1 6 1 2 5 1 1 1 2 1 1 k 2kkk k 1 kk g h i 24 log k 2k k 3 k 1 kk 1 2kkkzk lim 1 2 1 k 1 1 2kkk k 1 2k 1 k 1 1 2kkk

black C black green blue Choose the correct answer below OA This statement is false The element black is not an element of the second set OB This statement is false The set black is not an element of the second set OC This statement is false No set is a proper subset of itself O D This statement is true O E This statement is false The second set is a proper subset of the first set not the other way around

Prove the following one side first derivative formula using Taylor s expansion 3f xo 4f xo h f xo 2h O h f xo 2h

Rewrite these expressions using fractions 3 2 7 X 2 8 6 Z 8 1 1 1 1 1

cate the answer choice that best completes the statement or answers the question SAFETY In August 2001 the American Automobile Association reported that 73 of Americans use seat belts In a random selection 10 Americans in 2001 what is the probability that exactly half of them use seat belts Oa 0 50 or 50 Ob 0 73 or 73 Oc 0 23 or 23 HEM

Which transformation of the graph of f x 2 will result in the graph of g x 2 5 The graph will shift down 5 units The graph will shift right 5 units The graph will shift left 5 units The graph will shift up 5 units DOO

8 in K A triangular prism with its measurements is shown Find the surface area of the prism 10 in 12 in 15 in 10 in

x y 7 Use binomial theorem to expand Simplify

4x 4 3 use binomial theorem to expand Simplify

Find the first 4 terms and the 8th term of the sequence 5n 3 2n

7 Find the specified term of the arithmetic sequence a a7 9 2 as 10 1

C Because we want to compare with Rent a Center who measures payments in weeks how many weeks would it take you to pay off the credit card bill assuming 4 weeks in a month

se the simple interest formula to determine the missing value p r 4 t 9 months i 66 p Round to the nearest cent as needed

10 1 point What is the axis of symmetry for the graph a x 4 b x 4 10 8 6 C y 6 SW d y 6

x 7x 2x 3 x 3 The rational expression What are p x r x and q x can be rewritten in the equivalent form of p x A p x 3x 2x 6x 16 r x 45 and q x x 3 B p x 3x 2x 6x 16 r x 117 and q x x 3 p x x 4x 12x 38 r x 117 and q x x 3 p x x 4x 14x 45 r x 0 and q x x 3 C D

mage below Shows a letterboxed image with an aspect ratio of 16 9 displayed on a screen with an aspect ratio of 4 3 The screen is 36 inches Answer the following questions and round answers to nearest a Width of TV b Height of TV c Height of Image d Percent of the screen s area occupied by the image QUESTION 21 A screen has a diagonal of 50 inches and a height of 14 inches What is the aspect ratio

Tell whether each statement is sometimes always or never true 39 The graph of a quadratic function is a straight line 40 The range of a quadratic function is the set of all real numbers 41 The highest power in a quadratic function is 2 42 The graph of a quadratic function contains the point 0 0 43 The vertex of a parabola occurs at the minimum value of the function 44 The graph of a quadratic function that has a minimum opens upward 9 1 Identifying Quadratic Functio

A random sample of 25 observations was taken from a normally distributed population with a population variance of 16 A sample mean of 84 is computed 95 confidence interval for population mean is 84 1 96 0 8 84 1 96 0 8 84 1 645 0 8 84 1 645 0 8 84 2 06 0 8 84 2 06 0 8 84 1 96 1 2 84 1 96 1 2 Not enough information is given to compute the confidence interval 84 2 06 1 2 84 2 06 1 2

140 E Solve for x 48 H G 3x 13

1 Consider the recurrence relation with base conditions an 7an 1 10an 2 ao 2 a 7 a Find the roots of the characteristic equation for this recurrence relation

Extend 3 x 3 x to a basis for P2 Enter your answers as a comma separated list

Find the arc length of a circle with the given radius r and central angle 0 Give the answer in the given unit of measure r 52 cm 0 12 rad Answorl

5 3 Name Uriel Podris Period log 3 2x 1 log 3 3 log 3 x is the value of x

What are the solutions to the quadratic equation below x 2 6x 6 0

Find the rectangular equation of the curve given by the parametric equations below Then graph the curve and show its orientation Assume that I can be any real number x y Rectangular equation to 09 3 OX X

Let an denote the nth term of a geometric sequence Let ao 256 and an 1 0 5 Part A Write an explicit formula for this sequence an Part B To the nearest whole number what is the sum of the first 25 terms

x 3 x 1 x 3 x 1 For the rational function f x a Find the vertical asymptote s b Find the x intercept s c Find the horizontal asymptote d Find the y intercept s e Sketch the graph of y f x

Solve the system using substitution 5x 2y 3 5x y 1 No solution Infinite number of solutions

Write the expression in rectangular form x yi and in exponential form re 6 i 6 ICCER and the exponential form of the given expression is The rectangular form of the given expression is Simplify your answers Use integers or decimals for any numbers in the expressions Do not round until the final answer Then round to three decimal places as needed

1 a A fair die is flipped 18 000 times Use the Central Limit Theorem to estimate the probability that the number of 6 s is between 2950 and 3050 ndard deviation is 10 If 70 of the class

4 Consider the following grid Suppose that starting at the point labeled A you can go one step east north or up at each move This procedure is continued until the point labeled B is reached Up North A East How many different paths from A to B are possible

3 The probability are 0 4 0 2 0 3 and 0 1 respectively that a delegate to a certain convention arrived by air bus automobile or train What is the probability that among 9 delegates randomly selected at this convention 3 arrived by air 3 arrived by bus 1 arrived by automobile and 2 arrived by train

You rent an apartment that costs 1100 per month during the first year but the ren is set to go up 9 5 per year Write a recursive formula to show what the rent is during the nth year of living in the apartment

Question 4 25 points In the following Earliest Start Time ESP graph assume each unit of time is an hour START A 0 B 0 2 O 2 hours 3 hours O4 hours 3 3 C 3 D 3 5 E 8 F 7 6 G 15 In the EST graph how long does it take to do just task C

write as simple Triy function CSC X secx tan x

Find f x and simplify f x 5x In x Which of the following shows the correct application of the product rul OA 20x X B 5x 20x Inx X c 5x Inx 20x O X D 5x Inx 20x

Find the graphical solution to the linear inequalities Jy 2x 4 lz 0 y 0

On average patients visit their dental hygienist once every 224 567 days Round this figure to the nearest whole day The figure 224 567 days rounded to the nearest whole day is days

In lecture we discussed the graphical intuition behinds Newton s method for finding the root of some function f x Given an iterate Pn the next iterate comes from finding the root of the function L x where L is the tangent to f x at the point x Pn What is L x From your answer to a find the root L x and show that it reproduces the formula for Newton s method

2 A parabola has a vertex of 1 1 and passes through the point 2 2 Which one of the followin equations represents this parabola 3 a y x 2 2 x x 1 1 y c y 3 x 1 1 d y x 1 1

The histogram shows the student loan default rates for the 44 regions in a particular country a Describe the shape of the histogram b How many regions had a student loan default rate between 11 and 11 99 c How many regions had a student loan default rate of 13 or higher a Choose the correct answer below OA Normal OB Right Skewed OC Left Skewed P Uniform Frequency ON WAGON 09 8 10 12 14 16 Default Rate Percent 18

24 Show that the Laurent expansion of f 2 1 e 1 about P 0 has the form 1 2 1 B2k zk 2k 1 1 k 1 24

Suppose you are testing the null hypothesis 65 against the alternative u 65 The calculated test statistic value Zcalculated is 1 99 Which of the following a reasonable conclusion Cannot reject the null hypothesis at 5 level of significance Cannot reject the null hypothesis at 10 level of significance Reject the null hypothesis at 1 level of significance Reject the null hypothesis at 5 level of significance

We want to test Ho 10 vs H u 10 at x 0 05 A 95 confidence interval for calculated from a given random sample is 9 8 19 9 Based on this we O cannot make any decision at all because the distribution of the population is unknown cannot make any decision at all because 9 8 19 9 is a 95 confidence interval what we needed is a 5 confidence interval cannot make any decision at all because the value of the test statistic is not available reject Ho fail to reject Ho

Plot the point that has the given polar coordinates x 2 2 0 0 2 2 0 0

Determine the common ratio r the fifth term and the nth term of the geometric sequence 7 15 25 125 28 56 as 11

Click the icon to view the scatterplots Match the values of r to the scatterplots Scatterplot 1 r Scatterplot 2 r Scatterplot 3 r Scatterplot 4 r Scatterplot 5 r Tig plots 0 354 0 768 1 1 and 0 768 Scatterplots 15 14 13 12 11 104 8 6 4 2 0 0 Or Scatterplot 1 2 0 0 2 0 4 0 6 0 8 1 X Scatterplot 4 0 2 0 4 0 6 0 8 1 Q Q 8 6 4 24 04 0 0 2 0 4 0 6 0 8 1 X 8 6 4 2 Scatterplot 2 04 0 Scatterplot 5 0 2 0 4 0 6 0 8 o Q 1 2 5 Q Q 3 Scatt 0 0 2 0 4 X

Claim Fewer than 11 4 of homes have only a landline telephone and no wireless phone Sample data A survey by the National Center for Health Statistics showed that among 14 012 homes 5 77 ha landline phones without wireless phones Complete parts a and b a Express the original claim in symbolic form Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone Type an integer or a decimal Do not round b Identify the null and alternative hypotheses Ho IKKEID H