Basic Math Questions and Answers

Construct a simple graph that is a tree with vertices P Q R S T such that the degree of R is 4 What is the edge set

1 point Which of the following graphs are trees g e h DA i b f b j a B d O f C g do B D g h

For a data matrix that consists of news article texts build a model that groups together articles that cover similar subjects or themes Use the model to automatically identify similar articles to a new unseen article O Classification O Regression

A machine learning algorithm is trained on past macroeconomic data and company stock indices data to predict the price of a particular commodity within the time horizon of 6 months O Classification O Regression Clustering

A bank s fraud alert model is trained on a large dataset consisting of various features and true authenticity labels of historical transactions both known fraudulent ones as well as verified ones The correct labels are provided at the training stage O Classification O Regression

An online language learning service matches users with tutors All users see the same ranking of tutors which is computed using a pre specified formula that aggregates and weighs past student reviews of each tutor O ML O Not ML

A hedge fund analyst is looking to establish which publicly traded companies react similarly to market shocks To do this she codes a model that aggregates multiple features of each company s past performance into a single vector and then automatically identifies clusters of companies that have had similar performances to each other O ML Not AL

A web scale company wants to determine if a purple button works better to generate clicks among users than a black button They roll out an online experiment for each variant exposing 100 000 users to each treatment They evaluate the results and assess the confidence of the estimated effect that the button color has on clicks O ML Not ML

A linguist is building a part of speech tagger for sentences For every input a sentence the output of the algorithm is a sequence of tags For example in English an input I need help would result in output pronoun verb noun The linguist writes code that directly implements a series of known grammatical rules to complete the task O ML lot M1

x x Given the function if we were to write it in the form f x a x h k determine the value of each parameter a 2 3 h 1 n 3 k 1 a 2 27 h 1 n 3 k 1 Oa 2 h 1 3 n 1 3 k 1 a 2 27 h 1 3 n 3 k 1

1 A baseball is hit from a height of 3 feet at a 60 angle with initial velocity 64 feet per second The following parametric equations model the flight of the baseball x 32t y 16t 32 3t 3 a How much time does it take until the ball hits the ground Round to the nearest tenth and include units in your answer b What horizontal distance did the ball travel before it hit the ground

2 Explain why r 0 and r 0 180 represent the same point in polar coordinates Give an example including a sketch

The order of market research should likely be secondary focus group and detailed primary True False

The major advantage of a SWOT analysis is it includes all major constituencie True False

During the Jacksonian era Americans tended to O feel that society was static and that change was unlikely O see the American political tradition as corrupt and in need of significant Constitutional reform admire rugged individualists such as the heroes of James Fenimore Cooper s novels O be heavily influenced by Enlightenment thought and its emphasis on logic and rational thinking

Romanticism has been defined philosophically as the recognition in man of the capacity of knowing truth intuitively or attaining knowledge transcending the reach of the senses True O False

Miles takes a 350 mile round trip flight to visit his parents To qualify for Gold status at Awesome Airlines one must fly at least 4200 and less than 15400 miles each year How many times would Miles need to visit his parents each year to attain Gold status Express your answer in interval notation

Find three consecutive integers whose sum is 555 Hint if n represents the smallest of the three integers n 1 and n 2 represent the other two numbers

Two brothers Kevin and Charles each inherit 8000 Kevin invests his inheritance in a savings account with an annual return of 3 while Charles invests his inheritance in a CD paying 5 annually How much more money than Kevin does Charles have after 1 year

19 COMPARE Exponential vs Linear Patterns Now that you ve explored exponential growth consider how it compares to linear growth LEARN IT 1 Complete the table with a description of how each function is changing in the pattern and in the graph Visual Pattern raph How are the shapes changing En each step do you see attern ted in the Figure 1 y 10x Linear Figure 2 Figure 3 Figure 1 y 3 Exponential Figure 2 oooooo Figure 3

ch of the following is the indefinite integral of f x 5 52 76 5 5x x dr 5 50 2 2 0 In 5 2 6 5 5x 2 dx 15 51 16 6 dr In 5 5r 2 dr 541 57 5x 75 2 5 5x 2 da 5 5x x dx In 5 5 In 5 T Hotel 5x c 1 BARMAN 52 2 5a In 5 c c 6 c

Calculate the monthly finance charge for the credit card transaction Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long Round your answers to the nearest cent 3000 balance 16 2 500 payment a previous balance method 40 b adjusted balance method X c average daily balance method X

Suppose you see a car with an advertised price of 15 300 at 430 83 per month for 4 years What is the amount of interest paid Round your answer to the nearest cent

Example Consider the simple problem PDE ut x Uxx Sin 3 TTX BCs 1 u 0 t 0 u 1 t 0 u x 0 Sin TX 0 x 1 0 x 1

From the list below select all terms of the binomial expansion of x y 4 6x y 0 3xy 3 x y 4 3

How many bit strings of length 8 contain exactly six 1s Select ALL that applies 20 160 C 8 6 OP 8 6 08 216 28 8 21

Find the cost of each item in 11 years assuming an inflation rate of 11 compounded continuously Round your answers to the nearest cent a phone bill 39 b pair of shoes 66 c new suit 390 d monthly rent 625

What is the coefficient of x 12y 13 in the expansion of x y 25 9 25 13 12 13 13

A permutations of a set of distinct objects is an An ordered arrangements of r elements of a set is called an Ar ordered arrangement r permutation unordered r combination of these objects selection of r elements from the set is called

Seven women and nine men are on the faculty in the mathematics department at a school a How many ways are there to select a committee of five members of the department if at least one woman must be on the committee b How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee

How many permutations of the letters ABCDEFGH contain a the string ED b the strings ABC and DE c the strings ABC and CDE d the strings ABC and BEF

How many ways are there for 5 men and three women to stand in a line so that no two women stand next to each other Hint First position the m and then consider possible positions for the women Give your answer in numerical form

2 3 Determine the Interest earned on each Investment 1 a 1500 at 5 compounded daily for 6 years 2 b 300 at 8 compounded semi annually for 9 5 years c 450 at 3 75 compounded monthly for 20 years Determine the value of or n a 2 6533 1 1 20 b 1 4233 1 0 04 4 marks 6 marks

There are six different candidates for governor of a state In how many different orders can the names of the candidates be printed on a balla

Evaluate a P 10 7 b P 5 3 c C 8 6 d C 4 1

A multiple choice quiz contains 5 questions There are three possible answers to each question a In how many ways can a student answer the questions on the quiz if the student answers every question ways b In how many ways can a student answer the questions on the quiz if the student can leave answers blank ways

4 5 6 A term deposit of 10 months at 4 68 per year paid 64 64 Interest on maturity Calculate the principal Invested 2 marks Tom cashed a 1800 regular interest CSB with an annual rate of 5 4 He received 291 60 in interest during the time he held the bond How long did he hold the bond 2 marks Lai Invested 6200 for 21 months and received 401 82 interest at maturity At what annual rate did Lal invest her money 2 marks

A paragraph written in English contains 258 words At least how many words in this paragraph start with the same late

A bowl contains 10 red balls and 10 blue balls A woman selects balls at random without looking at the a How many balls must she select to be sure of having at least three balls of the same color b How many balls must she select to be sure of having at least three blue balls Write your answer and explanation in space provided

How many days must be selected from the year to guarantee that at least 6 falls in the same month 12x

How many bit strings of length 10 starts or ends with 0

How many strings of four decimal digits a do not contain the same digit twice b end with an even digit c have exactly three digits that are 9s

How many positive integers between 5 and 31 a are divisible by 3 b are divisible by 4 c are divisible by 3 and 4 d are divisible by 3 or 4

An office building contains 27 floors and has 37 offices on each floor How many offices are in the building Answer What principle of counting was applied

Sequences For each of these sequences a write the 1st 2nd 3rd 10th and 100th elements Use a calcu b Say if it looks like it has a limit and what the limit is 2 1 2 3 3 n 5 4 n n 1 1 1 1 n

or the car loan described give the following information A newspaper advertisement offers a 9 000 car for nothing down and 36 easy monthly payments of 302 50 a amount to be paid b amount of interest c interest rate d APR rounded to the nearest tenth of a percent

Assume the car can be purchased for 0 down for 60 months in lieu of rebate A BMW that has a sticker price of 62 420 with factory and dealer rebates of 6 000 Hint See Section 11 2 Example 5 a Find the monthly payment if financed for 60 months at 0 APR Round your answer to the nearest cent b Find the monthly payment if financed at 2 5 add on interest for 60 months Round your answer to the nearest cent c Use the APR approximation formula to find the APR for part b Round your answer to one decimal place d State whether the 0 APR or the 2 5 add on rate should be preferred

Convert the credit card rate to the APR Round your answer to the nearest percent Hint See Section 11 2 Example 6 Nebraska 0 05054 daily rate 9

Calculate the time necessary to achieve an investment goal Give your answer to the nearest day Use a 365 day year First enter the total number of full years then give the remaining days 1 000 at 6 simple interest deposit 550 years days

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 255 000 Round your answer to the nearest cent