Basic Math Questions and Answers

Question 12 Complete the description of the piecewise function graphed below Use interval notation to indicate the intervals P V TTT 2 ifze f x 1 if z 1 ifz e 1

Previous Problem Problem List Entered 0 5 2 3 5 8 21 6 5 8 0 428571 0 714286 0 428571 2 6 0 10 18 20 22 at least one of the answers abore is NOT correct 6 5 8 2u 6 0 10 Next Problem Suppose 3 0 5 and 3 5 3 Then u v 0 5 2 u v 35 3 Answer Preview 0 5 2 3 5 8 6 5 8 6 0 10 3 5 7 7 7 18 20 22 Result correct incorrect correct correct correct correct N Home Netflix Message The first coordinate is incorrect

Question 8 O 9 4 2 32 2 1 6 5 4 3 2 1 1 2 23 4 5 6 2 3 4 5 6 Write the range of the function using interval notation

xercise 7 3 1 For each matrix find its rank 1 3 3 2 4 A 2 9 1 4 2 6 12 4 5 3 7 B 1 2 1 3 2 1 5 6 0 2 6 8 1 3 4 8 7 9 5 7

19 6 5 4 3 MZA 2 1 5 4 2 1 1 2 45 6 2 Lag 4 5

Find the the domain of the function f x O xl x 18 and x 3 O xx 9 and x 2 Oxl x 18 O x x 3 X O xx 18 2 3 2 72 18

For intervals of values enter your answer using interval notation Here are some examples of how interval notation relates to inequalities Interval Notation 3 2 5 3 5 3 2 5 3 5 E 3 3 00 3 x 5 or 7 9 3 5 U 7 9 Inequality With inequalities we use less than or greater than to exclude the endpoint of the interval With interval notation we use use round parentheses With inequalities we use less than or equal to s or greater than or equal to 2 to include the endpoint of the interval With interval notation we use use square brackets To combine two intervals use U an uppercase letter u for union U Use oo two lowercase letter o s for infinity 00 Try it now Enter the interval equivalent to 2 x 5 or z 7

Question 14 For the function f x 62 x 7 evaluate and fully simplify each of the following f x h f x h f x h

Question 15 For the function f x 6x 9 evaluate and simplify the difference quotient

1 1 A car travels 2 miles in 3 minutes at a constant speed 3 a Write an equation to represent the distance the car travels d in miles for m minutes b Write an equation to represent the distance the car travels d in miles for h hours a The equation for the distance the car travels for m minutes is Simplify your answer Use integers or fractions for any numbers in the equation

Letr be a compound proposition involving p and q and suppose the truth table for r is given below pqr 001 010 101 111 Which of the following propositions implies r In other words for each proposition s below is it true that s r Select all that apply A P B p C pVq D PAq

Complete the following truth table p q v q Pq 000 0 1 1 10 0 11 0 20

10 A client s family brought him lunch from Burger King He consumed the following 6 oz Whopper with cheese 1 pint strawberry milkshake 5 oz cup of vanilla ice cream How many milliliters of fluid will you enter on the I O sheet

Problem 2 Find the value for t and the terminal point determined by the t for each point in the figure 0 5 0 5 0 5 Figure 1 t increases in increments of and 0 5 respectively 05

Problem 4 For each t value 1 sketch the angle 2 find the reference angle associated with t and 3 use your answer from part b to find the coordinates of the trigonometric point P t 19m a t b t 2m 3 117 c t m d t 13m

Problem 5 Pittsburgh PA and Miami FL lie approximately on the same meridian Pittsburgh has latitude of 40 5 N and Miami 25 5 N Find the distance between these two cities The radius of the Earth is 3960 miles

Problem 3 Suppose that the terminal point determined by t is the point 3 5 4 5 on the unit circle Find the terminal point determined by each of the following a t b t c T t d 2 t

You look at your budget and decide that you can afford 210 per month for a car Assume that the interest rate on a car loan is 4 and you want to repay the lo in 7 years Identify the following for the car loan where m is the periodic payment in dollars r is the annual interest rate as a decimal n is the number of payments per year and t is the time in years m 210 r 0 04 n t 7 What is the maximum loan you can afford Round your answer to the nearest cent 15363 45

m TTF 0

Which of the following are contradictions Select all that apply OA p OB PV p OC p p OD 0 P OE p 0 Submit answer

40 M 76 a

Complete the following truth table p p q Pq 000 01 A

Complete the following truth table p q r Pqr 000 001 0 1 0 0 11 100 101 1 10

Which of the following statements are true Select all that apply DA 9 2 if and only if 7 14 21 OB 7 14 21 and 9 2 OC 9 2 or 7 14 21 OD 7 14 21 if and only if 9 2 OE 7 14 21 if and only if 9 2

Complete the following truth table bd 00 01 10 d v b A

Assume that the probability of a 25 year old male living to age 26 based on mortality tables is 0 992 If a 15 000 dollar one year term life insurance policy on a 25 year old male costs 100 dollars what is its expected value What is the expected value The expected value is dollars CLIES

A player can bet on a line by placing a chip at location A in the figure to the right By placing the chip at A the player is betting on 1 2 3 0 and 00 This bet pays 3 5 to 1 which means that if a player wins the player wins 3 5 dollars as well as keeping his or her bet When the player loses he or she loses 1 Recall that there are 38 numbers on a roulette wheel Determine the expected value of betting on the roulette wheel The expected value of betting on the roulette wheel is EX C 0 1 4 10

Assume that it costs 2 to play a state s daily number The player chooses a three digit number between 000 and 999 inclusive and if the number is selected that day then the player wins 500 this means the player s profit is 500 2 498 If the player buys 20 chances on 20 different numbers what is the expected value for the player There is an expected Type an integer or a c of gain loss

A lottery costs 1 dollar to play Bella must pick four digits in order from 0 to 9 and duplicates are allowed If she wins the prize is 7 000 dollars First calculate the expected value of the lott Determine whether the lottery is a fair game If the game is not fair determine a price for playing the game that would make it fair What problem solving technique should be used OA The analogies principle OB The three way principle C Relate a new problem to an older one OD Be systematic COD Select the correct choice below and if necessary fill in the answer box to complete your choice The expected value of the lottery is dollars Round to the nearest cent as needed

A buyer is planning to purchase a franchise to sell decorations for the home The table to the right shows average weekly profits rounded to the nearest hundred for a number of the current franchises If the buyer were to purchase a franchise what would the expected weekly profit be The expected weekly profit is dollars Round to the nearest cent as needed Weekly Profit 100 dollars 200 dollars 300 dollars 400 dollars 500 dollars 600 dollars Number Who Earned This 4 11 13 14 8 4

Use a calculator to evaluate the amortization formula P 1 1 1 n m for the values of the variables P r and t respectively Assume n 12 Round your answer to the nearest cent 14 000 5 5 yr Enter a number

Use a calculator to evaluate the present value of an annuity formula nt 1 P m 1 r for the values of the variables m r and t respectively Assume n 12 Round your answer to the nearest ce 50 5 9 yr

Self employed persons can make contributions for their retirement into a special tax deferred account called a Keogh account Suppose you are able to contribute 15 000 into this account at the end of each year How much will you have at the end of 20 years if the account pays 3 annual interest Round your answer to the nearest cent

A game has two four sided dice having the numbers 3 6 9 and 2 on their faces Outcomes in the sample space are pairs such a 3 6 and 2 2 a How many elements are in the sample space b Express the event the total showing is even as a set c What is the probability that the total showing is even d What is the probability that the total showing is greater than 6 Identify the problem solving method that should be used Choose the correct answer below OA The Analogies Principle OB The Draw Pictures Principle C The Be Systematic Principle D The Choose Good Names for Unknown Strategies Principle a How many elements are in the sample space 16 b Express the event the total showing is even as a set 3 3 3 9 6 6 6 2 9 3 9 9 2 6 2 2 Type an ordered pair Use a comma to separate answers as needed c What is the probability that the total showing is even Type an integer or a simplified fraction

Find the amount of periodic payment necessary for the deposit to a sinking fund Round your answer to the nearest cent Amount Needed A 9 000 Frequency n annually Rate r 0 5 Time t 8 yr

Use a calculator to evaluate an ordinary annuity formula nt A A m 1 r n for m r and t respectively Assume monthly payments Round your answer to the nearest ce 50 5 3 yr

Assume that a person is working for a company that has a mandatory drug testing policy It is estimated that 1 of the employees use a certain drug and the company is giving a test that is 97 accurate in identifying users of this drug Calculate the positive predictive value for the drug test The positive predictive value is Type an integer or decimal rounded to three decimal places as needed

K The residents of a small town and the surrounding area are divided over the proposed construction of a sprint car racetrack in the town as shown in the table on the right If a newspaper reporter randomly selects a person to interview from these people a what is the probability that the person supports the racetrack b what are the odds in favor of the person supporting the racetrack 8 9 a The probability is Type an integer or a simplified fraction b What are the odds in favor of the person supporting the racetrack OA 8 to 1 OB 1 to 8 OC 8 to 9 OD 1 to 9 Live in Town Live in Surrounding Area Support Opp Racetrack Racet 38 3 049 4 975 61

A person wants to purchase a DVD drive for his laptop computer Assume that 81 of the drives are made outside the United States Of the U S made drives 2 are defective and of the foreign made drives 7 are defective Determine the probability that the drive purchased is U S made and is not defective The probability is Type an integer or decimal rounded to four decimal places as needed

Imagine a subject is taking part in a study to test a new cold medicine The probability that the subject is taking drug A is 10 that it is drug B is 40 and that it is drug C is 50 From past clinical trials the probabilities that these drugs will improve the subject s condition are A 40 B 30 and C 60 What is the probability that the subject will improve given that he is taking dru B The probability is Type an integer or a decimal

Assume that a softball player has 0 20 probability of getting a hit in each at bat Assume that the player bats four times What is the probability that she gets a hit only in her first at bat The probability is Round to four decimal places as needed SCCCB

A container contains 40 green tokens 10 blue tokens and 2 red tokens Two tokens are randomly selected without replacement Compute P FIE E you select a blue token first F the second token is blue P FIE Simplify your answer Type an integer or a fraction

The given urn contains green G blue B and red R balls Assume that two balls are being drawn without replacement from the urn to the right What is the probability that neither ball is red B B B B The probability is Tyne an integer or decimal rounded to three decimal places as needed B B B

You are to randomly pick one disk from a bag that contains the disks shown below Find P face blue the probability of picking a disk with a face given that the disk is blue Blue Yellow Blue Pink Pink Yellow Yellow Blue Pink Yellow Find P face blue P facelblue Simplify your answer

K When an object is dropped on a certain earth like planet the distance it falls in t seconds assuming that air resistance is negligible is given by s t 19t where s t is in feet Suppose that a medic s reflex hammer is dropped from a hovering helicopter Find a how far the hammer falls in 2 sec b how fast the hammer is traveling 2 sec after being dropped and c the hammer s acceleration after it has been falling for 2 sec a The hammer falls 76 feet in 2 seconds Simplify your answer b The hammer is traveling ft sec 2 seconds after being dropped Simplify your answer c The hammer s acceleration is ft sec sec after it has been falling for 2 sec Simplify your answer

K Raggs Ltd a clothing firm determines that in order to sell x suits the price per suit must be p 180 0 75x It also determines that the total cost of producing x suits is given by C x a Find the total revenue R x b Find the total profit P x c How many suits must the company produce and sell in order to maximize profit d What is the maximum profit e What price per suit must be charged in order to maximize profit a R x b P x c d The maximum profit is e The price per unit must be suits

20 The client tells you she drank the following 1 2 glass of ginger ale each glass 8 oz 1 cup coffee each cup 5 oz 1 TBS milk How many milliliters did she drink

18 Dilantin phenytoin suspension 125 mg per 5 mL is available Dilantin suspension 250 mg po q8 h has been ordered How many teaspoons will you give

7 Ativan 2 mg po HS has been ordered Ativan lorazepam 0 5 mg tablets are available How many tablets will you give

You have Calan verapamil 80 mg in the med drawer Calan 120 mg po daily was ordered How many tablets will you give