Binomial theorem Questions and Answers

Use the approach in Gauss s problem to find the sums of the arithmetic sequences below do not use formulas a 1 2 3 4 29 b 1 3 5 7 2409 c 6 12 18 600 d 1000 990 980 10 a The sum of the sequence is b The sum of the sequence is c The sum of the sequence is www

One winter night the temperature fell 13 degrees between midnight and 5 A M By 9 A M the temperature had doub from what it was at 5 A M By noon it had risen another 11 degrees to 43 degrees What was the temperature at midnight The temperature at midnight was degrees

The pattern 1 8 27 64 125 is a cubic pattern named because 1 1 1 1 or 1 8 2 2 2 or 2 and so on Use this pattern to complete parts a through d below a What is the least 4 digit number greater than 1000 in this pattern b What is the greatest 3 digit number in this pattern c What is the greatest number in this pattern that is less than 104 7 d If this pattern was produced in a normal spreadsheet what is the number in cell A14

Factor by grouping 15a 20a b 12ab 16b O A 5a 4b 3a 4b OB 5a 4b 3a 4b OC 5a 4b 3a 4b OD 5a 4b 3a 4b

Choose the correct answer Dormant for so many centuries the gigantic beast Mount Etna awoke in 2001 causing panic Which of the following helped you infer that the reference above is about a volcano O Antonyms O General context O Figurative language O Denotation

18 Which of the following substances will make an acid base reaction with NaOH OA KOH OB Metal hydride OC HCI OD NH3

L atm 17 A 0 223 mole sample of a gas is held at 33 0 C and 2 00 atm what s the volume of the gas R 0 0821 mol K A 5 60 L B 2 80 L C 0 302 L D 0 604 L

13 In a certain chemical reaction 2 hydrogen chloride molecules in aqueous solution react with solid zinc The reaction produces zinc chloride in aqueous solution and hydrogen gas Which of the following reaction equations correctly describes this reaction O A 2HCI aq Zn s ZnCl aq H g O B HCI aq Zn s Zn Cl aq 2H 1 O C HCI aq 2Zn s 2ZnCl aq H g O D 2HCl g 2Zn s 2ZnCl s H g

Simplify 11 2 1 8 2 5 1 5 Select the correct choice below and if necessary fill in the answer box to complete your choic 11 2 1 8 2 5 1 5 OB The expression is undefined OA

Directions Give the coordinates and classify the extrema for the graph of each function Use your graphing calculator to approximate if needed 11 f x 2x 4x 5 fix 12 f x x 6x 9x 5 5x

Consider the function f x 2x 1 Calculate the quotients below f x f a x a f x h f x

Complete the chart Grams Grams Kilograms Milligrams Centigrams 800 Kilograms Milligrams 800 Centigrams

What is the range of the middle 50 of the data H 0 1 2 3 4 5 6 7 O 12 6 9 10 11 12 13 14 15 16 17 18 19

What is the terminal point of the vector a 1 4 based at P 2 1

v i 3j 7k w 2i6j 5k Compute the dot product v w

9 Let T R3 R be a linear transformation such that T 1 1 1 2 0 1 T 0 1 2 3 2 1 and T 1 0 1 1 1 0 find T 2 1 0

Question 6 Points 2 Provided the options below match the correct choice with its corresponding option 1872 a Republican leaders agreed to the demands i b President Grant was re elected 1873 iii 1877 iv 1879 c As the economy improved the controversy died down d A series of bank failures triggered a five year depression O b ii d iii a iv c Oi b ii a iii c iv d O a ii b iii c iv d O i c ii d iii a iv b Complete Later Complete Questi 5 1 9 13 17 21 25 29 33

Given the following functions find g 1 f x 5x 4 g x x 4

Show that the given planes 221 4x2 4x3 4 22 2x3 2 and 221 322 0 have east one common point

The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of 112 and a standard deviation of 9 Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than 116 48 33 42 O 71

Evaluate f s 5 3x x dx a 39 b 5 c 16 25 d 65

16 What percent of the total population is found between the mean and the standardized z score 1 25 Use the standard normal distribution table and enter your answer to two decimal places

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places Z 0 90

3 Given U 3 2 5 find a a unit vector in the direction of U

Use the operational properties to find the following Laplace Transforms Indicate P1 P2 P3 or P L t5 cos 5t a b t sinh 3t

Growth Company s current share price is 19 95 and it is expected to pay a 1 30 dividend per share next year After that the firm s dividends are expected to grow at a rate of 4 3 per year a What is an estimate of Growth Company s cost of equity The required return cost of capital of levered equity is Round to two decimal places b Growth Company also has preferred stock outstanding that pays a 2 30 per share fixed dividend If this stock is currently priced at 28 05 what is Growth Company s cost of preferred stock The cost of capital for preferred stock is Round to two decimal places c Growth Company has existing debt issued three years ago with a coupon rate of 5 9 The firm just issued new debt at par with a coupon rate of 6 8 What is Growth Company s cost of debt The pre tax cost of debt is d Growth Company has 5 2 million common shares outstanding and 1 1 million preferred shares outstanding and its equity has a total book value of 50 2 million Its liabilities have a market value of 20 5 million If Growth Company s common and preferred shares are priced as in parts a and b what is the market value of Growth Company s assets The market value of assets is million Round to two decimal places e Growth Company faces a 38 tax rate Given the information in parts a through d and your answers to those problems what is Growth Company s WACC The weighted average cost of capital is Round to two decimal places

0 Your company has two divisions One division sells software and the other division sells computers through a direct sales channel primarily taking orders over the internet You have decided that Dell Computer is very similar to your computer division in terms of both risk and financing You go online and find the following information Dell s beta is 1 17 the risk free rate is 4 3 its market value of equity is 67 7 billion and it has 705 million worth of debt with a yield to maturity of 6 4 Your tax rate is 40 and you use a market risk premium of 5 5 in your WACC estimates a What is an estimate of the WACC for your computer sales division The weighted average cost of capital for your computer sales division is to two decimal places Round b If your overall company WACC is 12 1 and the computer sales division represents 37 of the value of your firm what is an estimate of the WACC for your software division The WACC for your software division is Round to two decimal places

Which of the following is not a common cause of what we call a model performance failure mode O Having too small of a data sample for model training O Having mostly irrelevant features O Having no hyperparameter exploration in the model building phase Having too large of a data sample for model training

Which of the following statements regarding model estimation bias and variance is false Estimation bias typically is caused by small sample sizes ML algorithms with more model complexity tend to have higher estimation variance High estimation bias is when an ML algorithm can t fit the true pattern leading to underfitting O Model estimation variance can be reduced by adding more data or averaging different models

3 01 9 12 15 18 Make a scatter plot of the points in the table and then select the type of function from those below that would best represent the data X 0 2 7 10 11 13 15 y 6 2 1 238 2 3 8 1 The data is best represented by a quadratic function 2 The data is best represented by a linear function 3 The data is best represented by an exponential function

The store does not have a bathroom and the park does not have an ice skating Which statement is equivalent to the given sentence OA The store has a bathroom and the park does not have an ice skating rin OB The store has a bathroom and the park has an ice skating rink OC It is false that the store has a bathroom or the park has an ice skating ris OD It is false that the store has a bathroom and the park has an ice skating

J Problem 3 25 Draw the influence line for the force in member KJ CJ and CD To get full credit you should present the calculation procedure L K A 00 88 C J 08880 880 B 6 ft 6 ft 6 ft D I E 6 ft 6 ft Figure 06 P38 39 Copyright 2012 Pearson Coucation publishing en Ha H 300 200 F 6 ft G 8 ft

What is the direction of the vector defined by 5 12 Give your answer in degrees rounded to the nearest tenth

Find the derivative y x 4 x5 ay 6x 7 5x 6 b y 4x 5 5y 6 C y 7x 8 9x 10 Ody 2x 3 4x 5 ey 3x 4 6x 7

x ay 5 2x 6y b In the system of equations above a and b are constants If the system has one solution which of the following could be the values of a and b A a 3 b 10 B a 3 b 12 C a 3 b 4 D a 10 b 3

What rate of interest compounded annually is required to double an investment in 8 years The rate of interest required is Round to two decimal places as needed

What will a 160 000 house cost 4 years from now if the price appreciation for homes over that period averages 6 compounded annually The future cost of the house will be Do not round until the final answer Then round to the nearest cent as needed

To get a B in math Alexandria Pappas must average 80 on five tests Scores on the first four tests were 84 75 82 and 79 What is the lowest score that she can get on the last a B The lowest possible score for getting a B is CIED

A project provides cash inflows of 2 000 each year for seven years What is the payback period if the cost is 16 475

What is the expectation for playing Keno by picking two numbers and paying 5 to play The payoff for picking two numbers is 60 Round your answer to two decimal places

2 Given the function f x y 2 sin x 8 and a line r t 4 4t i 4tj Find the lateral area above r t from 4 0 to 4 8 and below f x y

5 5 lb of potatoes cost 2 18 How much would it cost to buy 3 lb of potatoes I

The length of a rectangle is six times its width If the perimeter of the rectangle is 98 in find its length and width length i in width i in X 5

Approximately 1 percent of women ages 40 50 have breast cancer A woman has a 83 percent chance of a positive test from a mammogram given she has breast cancer a true positive result A woman has a 6 percent chance of a positive test from a mammogram given she does not have breast cancer a false positive result Complete the table below then answer the questions below the table Give all answers as decimals to 4 decimal places Negative test result Has breast cancer Does not have breast cancer Positive test result Total Total What is the probability a woman has breast cancer given that she just had a positive test Give answer as decimals to 4 decimal places

ward game uses the deck of 20 cards wn to the right Two cards are selected at tom from this deck Calculate the ability of selecting a monkey on the first v and a lion on the second draw both and without replacement 1 2d 3d a simplified fraction t 2 3 2 4 5 10 20 30 40 50 cards are to be selected with replacement Determine the probability the first card selected shows a monkey and the second show Type an integer or a simplified fraction cards are to be selected without replacement Determine the probability the first card selected shows a monkey and the second s

Watch help video This season the probability that the Yankees will win a game is 0 56 and the probability that the Yankees will score 5 or more runs in a game is 0 59 The probability that the Yankees win and score 5 or more runs is 0 46 What is the probability that the Yankees would score 5 or more runs when they lose the game Round your answer to the nearest thousandth

f is continuous lim f x does not exist X4 2 f 2 does not exist lim f x f 2 x 2 d x 4 X f is continuous lim f x does not exist X 4 f 4 does not exist lim f x f 4 X 14 F

Perform the experiment tally your results and calculate the probability Toss a coin 100 times Make sure that each time the coin is flipped it rotates several times in the air and lands on a table or on the floor Keep a record of the results of this experiment Suppose the results of this experiment were as follows Let H tossing a head and T tossing a tail HHTHTTHTTTHHHHHTTTTH HHTTHTHTHTH HTTHTHTTH TTHHHTHTTHTHTHTTH HHT HTTHTH HTTTHHHTTHTHTH HT TTHHHHTH HH TT HTTTH T Based on the given results what is P heads Enter the probability as a fraction

The game of Dungeons and Dragons uses nonstandard dice Consider a die with eight sides marked one two three four five six seven and eight Write a sample space for rolling a pa dice Die One Die One 1 2 3 4 5 6 7 8 1 2 3 4 5 6 1 1 1 0 0 2 2 3 1 3 2 0 0 0 0 4 3 5 1 0 0 5 3 0 0 7 2 8 Die Two 3 4 0 0 1 4 2 3 0 0 0 0 0 0 0 6 2 0 0 6 4 7 1 0 0 0 0 7 4 0 0 8 2 8 3 0 Die Two 5 6 7 1 5 0 0 0 8 1 8 0 0 2 6 2 7 0 0 3 5 0 0 3 7 0 0 0 0 4 6 0 0 4 8 5 5 5 6 0 0 0 0 6 8 0 0 0 0 6 7 0 0 7 6 0 0 7 8 0 0 8 7 0 0

Suppose you and an opponent each pick one of the spinners shown here A win means spinning a higher number Construct a sample space to answer the question and tell which of the two spinners given you would choose in each case F plays C A D O spinner F O spinner C O either spinner Need Help 5 Read It Additional Materials acce B E 6 2 6