Binomial theorem Questions and Answers

Assignment 9 Problem 19 1 point Are the following statements true or false 1 For any scalar c and any vector 7 we have cu c 2 ix ki j k 3 If and are any two vectors then w w 4 The value of x is always zero 2

Factor and simplify 2 cot x sec x sec x cot x Choose the correct simplification below OA sec X OB cos x O C tan x O D 1

A group of 50 people are going to run a race The top 6 finishers advance to the finals our neu

Prove the given identity tan x cot x sec x csc X Choose the correct proof below OA tan x cot x sin x COS X sin x cos x 2 sin x cos x sin x cos X 1 sec x csc X OC tan x cot x sin X COS X 2 sin 2 X COS X sin x cos x 1 sin x cos X sec X CSC X O Search OB tan x sin 3 COS sin sin sec S OD tan x sin x cOS X 2 sin sin 1 sin x cc sec x cs

is The line passes through 4 1 Name the coordinates of two other possible points on the line 8 The slope of a line is

write an expression describing all the angles that are coterminal with 259 Please use the variable k in your answer Give your answer in degrees but do not include a degree symbol in your answer degrees

Question 3 Convert the angle 150 to radians Give the exact value and use pi for

a Use the definition given below with right endpoints to express the area under the curve y x from 0 to 1 as a limit The area A of the region S that is bounded above by the graph of a continuous function y f x below by the x a and on the sides by the lines x a and x b is the limit of the sum of the areas of approximating rectangles f x Ax lim nia A lim R lim f x Ax f x x 11e 71 1 f x Ax lim n n1x2 b Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part a 1 2 3 n n 2

Expand the binomial by using Pascal s Triangle to determine the coefficients 2v 3 5

pts If log 4x 4 4 then x You may enter the exact value or round to 4 decimal places

9 17 Weighted average cost of capital ABBC Inc operates a very successful chain of needs to raise funds for its planned expansion into the Northwest The firm s balance yogurt and coffee shops spread across the southwestern part of the United States and sheet at the close of 2015 appeared as follows Cash Accounts receivable Inventories Net property plant and equipment Total assets 2 010 000 4 580 000 1 540 000 32 575 000 40 705 000 Long term debt Common equity Total debt and equity 8 141 000 32 564 000 40 705 000 times its book At present the firm s common stock is selling for a price equal to value and the firm s investors require a 15 percent return The firm s bonds command a yield to maturity of 8 percent and the firm faces a marginal tax rate of 21 percent At the end of the previous year ABBC s bonds were trading their par value a Describe ABBC s capital structure b What is ABBC s weighted average cost of capital c If ABBC s stock price were to rise such that it sold at 3 5 times its book value and the cost of equity fell to 13 percent what would the firm s weighted aver age cost of capital be assuming the cost of debt and tax rate do not change d Thought exercise Historically ABBC has owned each of its yogurt shop stores The firm s new CFO has asked you to consider the potential effect on the firm s cost of capital if it were to sell the stores to a real estate investor with an agreement to lease them back i e rent them No computations required

A steady flow compressor is used to compress helium from 15 psia and 70 F at the inlet to 200 psia and 600 F at the outlet The outlet area and velocity are 0 01 ft and 100 ft s respectively and the inlet velocity is 55 000 ft s Determine the mass flow rate and the inlet area The gas constant of helium is R 2 6809 psia ft lbm R Ibm s Round the final answer to five decimal places ft2 Round the final answer to three decimal places The mass flow rate is The inlet area is

3 to K Q All the graphs above have equations with form y abx Which graph has the greatest value for b Select an answer Which graph has the least value for b Select an answer Which graph has the greatest value for a

0 10 pts 399 Details The graph below shows a 5 4 3 2 5 A 3 2 1 2 3 4 5 1 transformation of y 2 2 3 4 5 Write an equation of the form y A 2 k for the graph above

5 Select the correct answer Jacob is solving the equation below using successive approximations 2 4 3 2 He started from a graph where he found the solution to be between 1 and 2 Using the lower and upper bounds from the graph Jacob did the following work for the first iteration Step 1 Step 2 Step 3 Step 4 Step 5 Rewrite the equation so that it equals zero on one side 2 4 3 2 2 4 3 2 0 Evaluate the rewritten equation at the lower and upper bounds To find the solution that lies between 1 and 2 set these values as the lower and upper bounds while finding the solution 20 4 3 2 0 333 22 4 3 2 2 1 889 Take the average of the lower and upper bounds 1 2 2 1 2 4 3 2 0 636 Evaluate the rewritten equation at z Since this value is positive replace the previous lower bound so that and z 2 the bounds are now z

A jury pool consists of 25 people 13 men and 12 women Compute the probability that a randomly selected jury of 12 people is all male

Calculate 3 4i Give your answer in a bi form and please show your answers to 2 decimal places if necessary

Find a formula for the inverse of the function described below An organization determines that the cost per person of chartering a bus is given by the formula 250 6x C x x where x is the number of people in the group and C x is in dollars OC 1 x 250 x 6 OC x 226 250 E x 6 6 C 1 x x 250 C x 2 50 6

1 Given the graph of f x complete the following table by indicating whether each value is zero positive or negative Point A B C LL F f x f x f x y f x VA E B

21 29 Is job satisfaction going down In the last 10 years several authors have stated that people are miserable in their jobs and have become increasingly unhappy over time Job satisfaction scores from participants in the General Social Survey GSS in 1975 and 2006 were studied Higher scores indicate greater satisfaction with 2 5 being a neutral score Here are summaries of scores for 1975 and 2006 16 Sample Size 1165 2177 Year 1975 2006 Mean 3 37 3 32 Standard Deviation 0 81 0 80 a Is there a significant decrease in mean scores from 1975 2006 What do these data show about job satisfaction in 1975 compared to 2006 b The paper from which the data came includes several years from 1972 2006 1975 was the year with the highest mean score What if any effect does this information have on your assessment of

4 3 2 3 st q The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 1 12 10 9 7 6 2 6 7 J

Suppose you work in a call center You call people up and offer to sell them an upgrade to their 13 mobile phone plan You have a success rate of 15 or 0 15 or That means that you sell 100 the product to 15 of the people you call Use the binomial distribution spreadsheet or do calculations by hand if you d rather to answer the following questions Question 1 Find the probability that no sales are made after you make 10 calls 2 Find the probability that you make 3 or more sales after you make 20 calls 3 Suppose your manager wants you to average 5 sales per day What is the minimum number of calls that you should make to ensure that you meet that goal 4 How many calls should you plan to make each day if you want to have a 95 chance of making at least Type answers below T

9 The total fee for withdrawing money at an ATM in a foreign country is a 3 50 foreign cash withdrawal fee plus a 2 currency conversion fee Write an equation to represent the total fee F dollars for withdrawing d dollars

2 5 What is the least value of n such that every collection of n points in the plane all with integer coordinates must contain at least two points for which the line segment connecting the two points con tains a point other than an endpoint with integer coordinates

mat is the annual worth in the following situation First cost 50 000 annual cost 20 000 Salvage value 10 000 Life 3 years interest rate 10 15 000 O 27 900 O 33 907 O 37 084

What is the annual worth of the following car wash Initial cost 150 000 Salvage value in 8 years 65 000 Annual income 45 000 Interest rate O25 009 28 999 32 980 44 786

What is the annual worth of the following project First cost 45 000 Annual cost 31 000 Life 8 years salvage value 10 000 Interest 10 32657 35999 38569 O 45666

6 points Determine whether each of the following statements is true or false 1 K3 4 is not planar 2 K2 3 is not planar 3 K2 4 is planar 4 K2 5 is not planar 5 K3 2 is planar 6 K is not planar

How much would you have in 6 years if you purchased a 1 000 6 year savings certificate that paid 4 compounded quarterly Round your answer to the nearest cent 1269 7 X

Find the cost of a home in 30 years assuming an inflation rate of 1 compounded continuously if the present value of the house is 215 000 Round your answer to the nearest cent

Alfalfa pellets are placed on a horizontal plywood surface and the plywood is gradually tilted until the pellets begin to slide across the surface Sketches of the forces acting on a single pellet are shown below 0 00 R F n F a If Fg is the gravitational force acting on the pellet develop expressions for the magnitudes of F and F as a function of Fg and the angle 0 at which the plywood is inclined If the weight of a pellet is 0 35 g 0 00343 Newtons evaluate the magnitudes of F and F when 0 10 b Estimate the angle 0 at which the pellets will begin to slide

A nickel weighs about 0 1763668 ounce Find the weight of a nickel to the nearest hundredth of an ounce OZ

13 S Book Hint Print erences Handy Home sells windows 80 of sales and doors 20 of sales The selling price of each window is 270 and of each door is 640 The variable cost of each window is 160 and of each door is 420 Fixed costs are 699 600 1 Compute the weighted average contribution margin Weighted average contribution margin 2 Compute the break even point in units using the weighted average contribution margin Numerator 1 1 Denominator 3 Compute the number of units of each product that will be sold at the break even point Windows units Break Even Units Break Even Units Check

When Brett Kavanaugh was nominated to be a Supreme Court justice a survey of 1124 Americans showed that 51 1 of them disapproved of Kavanaugh A newspaper published an article with this headline Majority of Americans Disapprove of Kavanaugh Use a 0 10 significance level to test the claim made in that headline Use the P value method Use the normal distribution as an approximation to the binomial distribution Let p denote the population proportion of all Americans who disapproved of Kavanaugh Identify the null and alternative hypotheses Ho P H P Type integers or decimals Do not round

Find the chromatic number of each of the graphs given below I 3

1 point For what value s of t does the equality hold true t If there are more than one value separate them by commas t 6t 0 5t 5 0 8

What Social Media platforms do you use What information do they collect about you What do they do with it

graph below AD1 shows where the economy was operating before fiscal policy was implemented and AD2 shows the effects of a successful fiscal policy with no crowding out On the graph drag AD2 to its correct position if the fiscal policy led to complete crowding out To refer to the graphing tutorial for this question type please click here Price Level SRAS LRAS AD1 Q AD2

The government of a country has decided to lower income taxes in an attempt to expand the economy to the full employment output level Assume the policy is successful Shift the appropriate curve to the correct position To refer to the graphing tutorial for this question type please click here LRAS SRAS1 AD1

2 of 13 In the night sky of October 2015 Jupiter and Venus appeared to be very close neighbors The figure shows the distances in astronomical units from Earth to Venus and Jupiter then How far in miles was Venus from Jupiter at that time By definition 1 astronomical unit is the mean distance from Earth to the sun about 92 96 million miles Jupiter 6 15 Distance Venus 9 86 0 61 Earth Use decimal notation Give your answer to at least one decimal place million miles

Using the 2019 marginal tax rates provided in the table below find the marginal and average tax rates for the incomes shown Give all answers to two decimals Taxable Income 0 9 700 9 701 39 475 39 476 84 200 84 201 160 725 160 726 204 100 204 101 510 300 Over 510 300 1st attempt Part 1 2 points Tax rate 10 Part 2 2 points 22233 12 24 35 37 What would be your federal income tax if your taxable income was 111 000 00 S What is the average tax rate for 111 000 00 in taxable income How much tax would you owe if your income increased by 25 000 to 136 000 00 See Hint See Hint

Replace the with either E or to express a true statement Isaac Newton y y is a living Swedish playwright Isaac Newton Vy y is a living Swedish playwright E

The sprocket assembly for a 70 cm bike is shown below How fast does the rider have to pedal RPM in order to go 21 km hr on level ground 5 00 cm B 63 66 RPM 75 82 RPM Fig 8 44 35 0 cm Copyright 2015 Pearson Canada Inc 12 5 cm I

The food at the Horn Toad Restaurant is awful I had a sandwich there once and the bread was stale This argument commits the fallacy of O affirming the consequent hasty generalization O post hoc ergo propter hoc biased sample

A cam is in the shape of a circular sector as shown in figure below What is the perimeter of the cam A 9 17 cm B 8 54 cm 7 95 cm Fig 8 39 165 58 1 875 cm Copyright 2015 Pearson Canada Inc

9 Whether our argument concerns public affairs or some other subjects we must know som all of the facts about the subject on which we are to speak and argue Otherwise we can ha materials out of which to construct arguments Aristotle Rhetoric Argument Not an argument No answer text provided

The owners of a recreation area are filling a small pond with water Let W be the total amount of water in the pond in liters Let T be the total number of minutes that water has been added Suppose that W 15T 600 gives W as a function of T during the next 70 minutes Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values amount of water in the pond in liters Onumber of minutes water has been added Oamount of water in the pond in liters Onumber of minutes water has been added Set of Values Choose one Choose one

The Sugar Sweet Company delivers sugar to its customers Let C be the total cost to transport the sugar in dollars Let S be the amount of sugar transported in tons The company can transport up to 20 tons of sugar Suppose that C 110S 3500 gives C as a function of S Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values O amount of sugar transported in tons O cost to transport sugar in dollars O amount of sugar transported in tons O cost to transport sugar in dollars Set of Values Choose one Choose one

4 5pts How many full sib progeny are needed to achieve an accuracy of 0 9 if the h for a trait is 0 34 What does this mean in terms of management

B Chpt 8 What is common stock preferred Stock Similonities Differences