Basic Math Questions and Answers

For each of the following strings of symbols indicate whether the string is or is not an expression of sentential logic Question 12 E g F A B Yes it is an expression No it is not an expression Question 13 J v K L A Yes it is an expression Select one answer 3 points Select one answer 2 points

What is the age distribution of patients who make office visits to a doctor or nurse The following table is based on information taken from a medical journal Age group years Percent of office visitors Under 15 15 24 25 44 45 64 65 and older 15 10 25 15 35 Suppose you are a district manager of a health management organization HMO that is monitoring the office of a local doctor or nurse in general family practice This morning the office you are monitoring has eight office visits on the schedule What is the probability of the following USE SALT a At least half the patients are under 15 years old Round your answer to three decimal places Explain how this can be modeled as a binomial distribution with 8 trials where success is visitor age is under 15 years old and the probability of success is 15 Let n 8 p 0 25 and compute the probabilities using the binomial distribution Let n 8 p 0 85 and compute the probabilities using the binomial distribution Let n 8 p 0 15 and compute the probabilities using the binomial distribution Let n 15 p 0 15 and compute the probabilities using the binomial distribution b From 2 to 5 patients are 65 years old or older include 2 and 5 Round your answer to three decimal places c From 2 to 5 patients are 45 years old or older include 2 and 5 Hint Success if 45 or older Use the table to compute the probability of success on a single trial Round your answer to three decimal places d All the patients are under 25 years of age Round your answer to three decimal places 0 000 e All the patients are 15 years old or older Round your answer to three decimal places

Trevor is interested in purchasing the local hardware sporting goods store in the small town of Dove Creek Montana After examining accounting records for the past several years he found that the store has been grossing over 850 per day about 65 of the business days it is open Estimate the probability that the store will gross over 850 for the following Round your answers to three decimal places USE SALT a at least 3 out of 5 business days b at least 6 out of 10 business days X c fewer than 5 out of 10 business days X d fewer than 6 out of the next 20 business days x You may have computed the probability of two tails of the distribution Consider which area of the distribution is appropriate If the outcome described in part d actually occurred might it shake your confidence in the statement p 0 65 Might it make you suspect that p is less than 0 65 Explain Yes This is unlikely to happen if the true value of p is 0 65 Yes This is likely to happen if the true value of p is 0 65 No This is unlikely to happen if the true value of p is 0 65 No This is likely to happen if the true value of p is 0 65 e more than 17 out of the next 20 business days If the outcome described in part e actually occurred might you suspect that p is greater than 0 65 Explain Yes This is unlikely to happen if the true value of p is 0 65 Yes This is likely to happen if the true value of p is 0 65 No This is unlikely to happen if the true value of p is 0 65 No This is likely to happen if the true value of p is 0 65

Given the Fourier transform t sinc f the inverse Fourier transform of X f 400sinc 5f 20 is 01 x t 2000n e j4nt O 2 None of the answers 03 x t 200m 0 2t ej40nt 4 x t 80n 0 2t ej8nt 5 x t 200m 0 2t e j20nf

About 20 of people in America use a certain social media website In a group with 15 people assume that it is a random sample of people in America what are the following probabilities Round your answers to three decimal places USE SALT a At least one of them uses the website b More than two of them use the website c None of them use the website 0 035 d At least 13 of them do not use the website

8 6 B Period Determine whether the information implies that YZ VW If parallel state the reason why XY 1 XV XZ XW 3 AXYZ AXVW B D XY 2 YV 8 Determine whether the information implies DEBC Explain 5 6 A 4 ZVYZZWZY E Date XZ ZW 3 C B A W 6 A 4 E 6 C

A multiple choice exam has six possible answers for each question For each correct answer you are awarded 6 points For each incorrect answer 1 point is subtracted from your score For answers left blank points are added or subtracted a If you do not know the correct answer to a particular question is it to your advantage to guess Explain b If you do not know the correct answer but can eliminate one possible choice is it to your advantage to guess Explain a Select the correct choice below and if necessary fill in the answer box within your choice No it is a disadvantage to guess because the expectation is Simplify your answer OA www Yes it is to your advantage to guess because the expectation is Simplify your answer OC No it is neither an advantage nor disadvantage to guess because the expectation is 0 B

O Points 0 of 1 If the odds against an event are 5 6 then the probability that the event will fail to occur is The probability is Type an integer or a simplified fraction

If the probability that an event will occur is odds in favor of the event occurring are The odds are Simplify your answer 1 9 then the probability that the event will not occur is 8 9 and th

What does the content of the robots txt file tell a web crawler Select one O A Which pages of the website it is not allowed to access B Which pages of the website have changed since the last crawl C The order in which it should feed pages to the front queue D The order in which it should feed pages to the back queue O O

3 There are 12 blocks in a bag They have the following letters on them A A ADD GGGOOO O We choose 4 blocks from the bag and as we know there are 495 ways of doing that ie 495 four element subsets In how many of those 495 sets are there enough blocks to form the word DAD enough blocks to form the word DOG In this problem please write the actual numbers eg 24 rather than 2 3

3 Jimmy wants to sign up for a gym membership His two options are Goodlife and LA Fitness Goodlife fitness has a 100 sign up fee and then charges 40 a month while LA Fitness Charges 50 a month with no sign up fee a Write an equation to represent the cost Cafter m months of going to the gym for each of the two options 4T

d Compute the standard deviation for ages of super shoppers The standard deviation of a discrete probability distribution is found by x p x Use 45 66 and the following table to help you compute the standard deviation o for ages of shoppers Round your answers to four decimal places X P x 0 23 0 05 34 45 0 42 0 18 56 0 12 67 0 23 0 xP x 23 0 05 1 1500 34 0 42 14 2800 8 1000 6 7200 x 23 45 66 22 6600 34 45 66 11 6600 0 6600 10 3400 x 22 6600 2 513 4756 11 6600 135 9556 0 4356 106 9156 Add together the x 2p x Round your answer to four decimal places x P x 25 6738 57 1014 0 0784 12 8299 Finally take the square root of x p x Round your answer to two decimal places x P x x p x 513 4756 0 05 25 6738 135 9556 0 42 57 1014 0 0784 12 8299

Annual surveys of bird nests in a certain park consider the random variable x representing the number of eggs in each nest The expected value of the distribution was found to be 1 2 eggs The probability of a nest having at least one egg was 72 The probability of more than 4 eggs was 2 The standard deviation of the distribution was 1 2 eggs Match the numerical values from the problem to the corresponding symbols If a symbol does not have a corresponding value and cannot be easily computed from the given information then enter NA For the purposes of this problem consider a value hard to compute if a calculator is required to make the computation convenient such as taking a square root or exponentiating a value Symbol Numerical Value fl 0 P x 4 P x 5 P x 0 P x 0 1 2 1 2 0 72 0 28 X x

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings The club is selling Chinese fortune cookies at a price of 1 per cookie Each cookie contains a piece of paper with a different number written on it A random drawing will determine which number is the winner of the dinner for two at a local Chinese restaurant The dinner is valued at 35 Since the fortune cookies were donated to the club we can ignore the cost of the cookies The club sold 563 cookies before the drawing a Lisa bought 17 cookies What is the probability she will win the dinner for two Round your answer to three decimal places 0 030 What is the probability she will not win Round your answer to three decimal places 0 970 b Lisa s expected earnings can be found by multiplying the value of the dinner by the probability that she will win What are Lisa s expected earnings in dollars Round your answer to two decimal places 1 05 How much did she effectively contribute to the hiking club in dollars Round your answer to two decimal places x

What are the chances of you catching a virus A health agency estimated that on average 9 of the U S population gets sick with the flu virus every year Suppose that the chance someone with the flu transmits it to another individual is 91 If you were to mee a person at random find the following probabilities a P person has the flu 0 09 b P person transmits the flu given person has the flu 0 91 c P person has the flu and transmits the flu

The estimate using rounded numbers is Type an integer or a decimal Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performe by hand or in your head Then use a calculator to perform the computation How reasonable is the estimate when compared to the actual answer 0 87 x 505 The exact value is Type an integer or a decimal How reasonable is the estimate when compared to the actual answer OA The values are exactly equal B The values are very different OC The values are approximately equal This question 1 point s possible Submit test

Identify the pattern in the list of numbers Then use this pattern to find the next number 3 6 9 15 24 39 Fill in the next number in the list possible 3 6 9 15 24 39

OA 16 blocks B 22 blocks possible Use the four step method in problem solving to solve the problem Andrea decided to rollerblade to her mother s house Three blocks from her home one of the wheels on her skate broke and she had to walk the remaining eight blocks to her mother s She could not repair her skate and had to walk all the way back home How many more blocks did Andrea walk than she skated OC 19 blocks O D 11 blocks Submit test

The next number is This question 1 point s possible www later Identify a pattern in the given list of numbers Then use this pattern to find the next number More than one pattern might exist so it is possible that there is more than one correct answer 58 49 40 31 22 Submit test

6 As in sudoku fill in the missing numbers in the 3 by 3 square so that it contains each of the digits from 1 through 9 exactly once Furthermore for this square the rows the columns and the two diagonals must have different sums O A 6 9 5 7 2 1 8 3 4 O B Use reasoning to help you choose the square that satisfies the condition that the rows the columns and the two diagonals have different sums 6 8 2 9 1 3 5 4 SOLLE 7 7 O C 6 8 1 7 2 4 3 2 1 9 5 4 O D 6 5 2 3 1 7 9 8 4

Obtain an estimate for the following computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head Then use a calculator to perform the computation How reasonable is your estimate when compared to the actual answer 7 66 1 27 15 24 Round each number to the nearest integer An estimate of the sum is The actual sum is Type an integer or a decimal How reasonable is your estimate when compared to the actual answer OA Not reasonable The estimate seems a little higher compared to the actual answer OB Not reasonable The estimate seems a little lower compared to the actual answer OC Reasonable The estimate seems a little lower compared to the actual answer D Reasonable The estimate seems a little higher compared to the actual answer

possible The following problem describes procedures that are to be applied to numbers Repeat the procedure for four numbers of your choice Write a conjecture that relates the result of the process to the original number selected Select a number Multiply the number by 40 Add 40 to the product Divide this sum by 20 Subtract 2 from the quotient OA The result is one more than double the original number B The result is double the original number C The result is one more than the original number OD The result is the original number

point s possible Submit test Solve the problem with estimation but do not use a calculator Use rounding to make the resulting calculations simple A 1 700 B 1 800 OC 1 600 O D 1 900 Estimate the cost to buy a refrigerator for 799 a stove for 759 and a dishwasher for 249

Assume that postings lists are gap encoded using Gamma codes Using this encoding suppose that the postings list for the term Palestine is the bit sequence 1111 1111 1011 1100 1101 0011 1110 0000 0 and the postings list for the term Occupation is the bit sequence 1111 1111 1100 0000 0011 1011 1101 111 What Doc IDs match the following query Palestine AND NOT Occupation Select one O O 1 1031 1032 1063 2 1031 1 31 3 998 1000 1032 4 998 1000

If you spend 99 78 in how many ways can you receive change from a one hundred dollar bill Change can be received in possible ways

OA 4 OB 0 OC 2 O D 6 point s possible Identify a pattern in the list of numbers Then use this pattern to find the next number 26 22 18 14 10 Submit test

Repeat the following procedure for the four given numbers Add 5 Double the result Subtract 4 Divide by 2 Subtract the original selected number The 1st number is 1 The 2nd number is 6 The 3rd number is 9 The 4th number is 12 The result is Double the result The result is a Write a conjecture that relates the result of the process to the original number selected Subtract 4 The result is Divide by 2 The result is Simplify your answer b Represent the original number as n and use deductive reasoning to prove the conjecture in part a Add 5 The result is Subtract the original number Simplify your answer Simplify your answer Simplify your answer Simplify your answer

possible Use the four step method in problem solving to solve the problem A car rents for 220 per week plus 0 25 per mile Find the rental cost for a three week trip of 700 miles OA 835 00 OB 1 185 00 OC 175 00 OD 395 00

2x2 18 x 3x 6x 9 Evaluate lim If an answer does not exist enter DNE

Date 1 24 2024 Simplify each expression 1 567 3 192m n 2 56x 4 240j4

Use the compound interest formula to compute the total amount accumulated and the interest earned 7500 for 5 years at 6 5 compounded monthly The total amount accumulated after 5 years is Round to the nearest cent as needed

By cutting away an x by x square from each corner of a rectangular piece of cardboard and folding up the resulting flaps a box with no top can be constructed Volume as a function of x T81 184 Domain of the function for volume TEL If the piece of cardboard is 44 inches long by 24 inches wide find a function in the variable x giving the volume of the resulting box TEL Determine the domain of the function for volume Enter your answer using interval notation

Determine whether each statement is true or false You have one submission for each statement a According to the law of demand if price goes down demand goes up OTrue False b According to the law of supply p s x is an increasing function OTrue False c According to the law of demand p True False d x is an increasing function d The intersection of the demand and supply curves corresponds to the market equilibrium quantity OTrue False e The intersection of the demand and supply curves corresponds to the market equilibrium price OTrue False

A rectangular field is to be enclosed by 200 feet of fence One side of the field is a building so fencing is not required on that side Area as a function of x 5000 x Fenced Area Domain of area function 1 5000 Building If x denotes the length of one side of the rectangle perpendicular to the building determine the function in the variable x giving the area in square feet of the fenced in region X Determine the domain of the area function Enter your answer using interval notation I

A billboard designer has decided that a rectangular sign should have 5 t margins at the top and bottom and 2 ft margins on the left and right sides Furthermore the billboard should have a to area of 950 m nuding the margins If x denotes the width in feet of the billboard including the margins find a function in the variable x giving the area of the printed region of the billboard Area as a function of a Determine the domain of the function for area Enter your answer using interval notation Printed Region Domain of the function for area MY NE

Simplify the expression by first factoring each numerator and denominator x 1 x 2x 3 3x 2x 1 4x 12 toring techniques

Simplify the expression by first pulling out any common factors in the numerator and then expanding and or combining like terms from the remaining factor 3x 2 2 x 4 3x 2 1 2 3x 2

Solve the equation by factoring the left hand side and then setting each factor equal to zero Enter your answers as a comma separated list 2x x3 0 X 3 2 1 X

2 Determine the slope and y intercept of y x 1 Graph the line 3T Slope y intercept 1 0 1 6

1 Explain whether each of the following are linear relations 4A a X 1 0 1 2 Y 2 1 4 7 b y 3x

15 The following table represents the Log frequencies weight for a set of terms in three documents Term Jerusalem Freedom Palestine Select one Doci a 1 91 b 33 c 91 d 12 33 3 04 2 17 1 70 Doc2 Doc3 0 2 70 2 00 1 90 0 Peace 0 Based on this table what is the cosine similarity between doc1 and doc2 after length normalization is 2 30 2 08 2 70

O Points 0 of 1 The members of the Student Activity Council on your campus are meeting to select two speakers for a month long event celebrating artists and entertainers The first names of the choices are Ben Will Stewart Hilary Kate and Jay How many different ways can the two speakers be selected The two speakers can be selected Save different ways

Watch the video and then solve the problem given below Click here to watch the video A friend wants to go to a new restaurant The menu has 5 appetizers 10 entrees and 6 dessert options How many different meals appetizer entr e and dessert are possible Type your answer

The Adeeva s gross monthly income is 4200 They have 18 remaining payments of 210 on a new car They are applying for a 30 year 78 000 mortgage at 7 5 The taxes insurance on the house are 480 per month The bank will only approve a loan that has a total monthly mortgage payment of principal interest property taxes and homeowne insurance that is less than or equal to 28 of their adjusted monthly income Click here for table of Monthly Payments a Determine 28 of the Adeeva s adjusted monthly income Round to the nearest cent Monthly Principal and Interest Payment per 1000 of Mortgage Rate 9 40 45 3 0 10 10 12451 10 36354 10 60655 1085263 55 60 65 70 15 11 30005 11 35480 ILGIORS 1187018 8 0 12 13276 85 90 95 100 12 39857 12 66758 12 99976 13 21507 10 74605 105 13 49350 110099 11 0 13 77500 1136897 o 1168090 15 20 605980 7 39688 632649 764993 7 90794 6 39956 8 17083 687887 7 16431 743573 775299 05593 136440 867823 899726 9 32131 965022 9 98380 1032188 1066430 843857 171107 8 98828 927012 9 55652 25 5 27837 5 55832 984740 10 14267 10 44225 584990 6 14087 644301 675207 706779 7 38991 7 71816 K05227 8 39196 8 75697 9 08701 9 44182 9 80113 10 16469 30 4 77415 506685 5 36822 5 67789 599551 6 32064 665302 699215 7 33765 168913 104623 840454 877572 9 14739 952323 990291

A library buys 8 more books for children than for adults Let x represent the number of children s books and let y represent the books for adults Complete the table using the equation x y 8 X 9 37 227 y 1 60 L

A researcher says that there is a 80 chance a polygraph test lie detector test will catch a person who is in fact lying Furthermore there is approximately a 7 chance that the polygraph will falsely accuse someone of lying a If the polygraph indicated that 36 of the questions were answered with lies what would you estimate for the actual percentage of lies in the answers Hint Let B event detector indicates a lie We are given P B 0 36 Let A event person is lying so AC event person is not lying Then P B P A and B P AC and B P B P A P BA P A P BA Replacing P A by 1 P A gives P B P A P B A 1 P A P B AC Substitute known values for P B P B A and P B A into the last equation and solve for P A Round your answer to two decimal places P A 0 397 b If the polygraph indicated that 64 of the questions were answered with lies what would you estimate for the actual percentage of lies Round your answer to one decimal place

A researcher says that there is a 80 chance a polygraph test lie detector test will catch a person who is in fact lying Furthermore there is approximately a 7 chance that the polygraph will falsely accuse someone of lying a If the polygraph indicated that 36 of the questions were answered with lies what would you estimate for the actual percentage of lies in the answers Hint Let B event detector indicates a lie We are given P B 0 36 Let A event person is lying so AC event person is not lying Then P B P A and B P AC and B P B P A P B A P A P BA Replacing P A by 1 P A gives P B P A P B A 1 P A P B A Substitute known values for P B P BIA and P B A into the last equation and solve for P A Round your answer to two decimal places P A x b If the polygraph indicated that 64 of the questions were answered with lies what would you estimate for the actual percentage of lies Round your answer to one decimal place

An adjustable brace is placed against a tree to support a beam perpendicular to the tree The brace and beam are 12 feet long The brace can slide up the tree and can transverse left and right along the beam tree B A beam brace Question 2 1 Part A 25 points Write a function that expresses the distance the brace is from the tree A as a function of the distance from where the

3h 1 2h 7 Evaluate L 4 for L h Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Write your answer as a simplified fraction Give exact simplified answers