Basic Math Questions and Answers

Choose the correct histogram below A Frequency Click here to view the heights of the players Frequency 62840 O C 62840 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in Q Data table Team A Team B Team C Toam D OB Frequency PANO O D Frequency 6284 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 64 5 66 5 68 5 70 5 72 5 74 5 76 5 78 5 80 5 Height in 65 65 79 78 75 75 65 72 79 66 69 65 71 72 70 74 66 74 70 80 72 68 79 66 74 79 79 74 80 80 69 67 77 72 66 69 75 68 66 79 80 68 72 75 69 68 67 67 66 70 80 70 78 75 66 73 65 80 67 70 80 67 69 75 D X Q fam

The manager at a coffee shop counted the customers once each hour over a few busy weekends The results she obtained are summarized in the bar graph to the right use it to answer parts a through d a What was the largest number of customers in the coffee shop and how often did it occur The largest number of customers was s It occurred time s b What was the most frequently occurring nonzero customer count The most frequently occurring nonzero customer count was c For how many hours were the customers counted hours d For what fractional part of the total number of hours were there more than seven customers in the coffee shop Type an integer or a simplified fraction Frequency 15 12 1 9 0 1 2 3 4 5 6 7 8 Number of Customers 10 11

Izzy had an 81 and an 85 on his first two tests and believed that he did well enough on his final exam to keep his B average However when he got his grade he received a D He checked with his instructor and learned that the instructor had made a mistake by transposing the digits when he recorded the final exam grade If Izzy s incorrect average mean for the class was 68 what was his correct final exam score Izzy s correct final exam score is Type a whole number COLL

K Use the frequency table that contains the EPA mileage for 44 domestic cars to construct the corresponding histogram Click the icon to view the frequency table Choose the correct graph below O A Frequency PNADOO C Frequency TILIA A TR D K D T 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 MPG 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 MPG Data table MPG Frequency 19 2 Q 20 4 21 5 22 2 23 3 24 9 25 2 26 1 27 3 B 28 4 OB talye 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 MPG O D Frequency 29 7 MAMMMN 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 MPG 30 2 X 5

The points scored by Division A and Division B in the championship game in a recent 20 year period are given to the right Use classes of width 10 points starting at 0 to construct a back to back graph of the data Choose the correct graph below O A O C Aanba Frequency 10 B 0 9 10 19 20 29 30 39 40 49 50 59 Points Scored A 0 9 10 19 20 29 30 39 40 49 50 59 Points Scored B O D Frequency 0 9 10 19 20 29 30 39 40 49 50 59 Points Scored A B A G 0 9 10 19 20 29 30 39 40 49 50 59 Points Scored B 35 20 35 24 13 13 34 20 28 13 6 24 18 27 31 21 48 34 24 13 13 21 18 27 20 28 35 25 31 19 31 34 20 13 26 19

a What do the data in each graph represent i Graph A Distance of School Bus from School ii Distance from school km Number of students 16 12 8 4 0 Graph B Number of Students on a School Bus 32 24 16 d 8 0 8 00 8 30 9 00 Time h n 8 00 8 30 9 00 Time h b Identify the independent and dependent variables c Why are the points connected on one graph but not on the other

1 of 13 Consider the triangle shown in the figure Let A 11 and B 5 in feet and the angle t radians 4 A t B Find the area of the triangle The angle involved is a special angle Give an exact answer Use symbolic notation and fractions where needed

Use the definitions of the trigonometric functions to establish the given basic identity 1 cot 1 Refer to the triangle in the figure tan 1 Complete the passage to prove the given identity 1 cot t tan t

Fill in the blanks to show that the identity 1 sin a Suggestion Multiply the left side by 1 sin a 1 sin a 1 sin a 1 1 sin a 1 sin a 1 sin a 1 1 sin a 1 sin a 1 sin a 1 sin a 1 sin a 1 1 sin a 1 sin a 1 sin a 1 1 sin a a cos a 1 sin a is true cos a 1 sin a

in the blanks to express sec t in terms of sin t if cos t is negative t 1 cos t sin t cos t 1 sin t cos t sin t

9 and the trigonometric point P a is in the third quadrant Use a trigonometric identity to find cos a 10 Express numbers in exact form Use symbolic notation and fractions where needed Suppose sin a cos a

Macmillan Learning Use the definitions of the trigonometric functions to establish the basic identity 1 cos t sec 1 Refer to the triangle in the figure C Fill in the blanks to prove the given identity 1 cos t sec t

For the given function f z find the derivative a at the given point a first finding b a f x 92 8x 29r a 30 f a

Percent of sales method At the end of the current year Accounts Receivable has a balance of 450 000 Allowance for Doubtful Accounts has a credit balance of 4 000 and sales for the year total 2 030 000 Bad debt expense is estimated at 1 4 of 1 of sales a Determine the amount of the adjusting entry for uncollectible accounts 5 075 V b Determine the adjusted balances of Accounts Receivable Allowance for Doubtful Accounts and Bad Debt Expense Accounts Receivable 450 000 V Allowance for Doubtful Accounts Bad Debt Expense c Determine the net realizable value of accounts receivable Feedback X 5 075 Check My Work a Remember that since accounts receivable are created by credit sales uncollectible accounts can be estimated as a percent of credit sales If the portion of credit sales to sales is relatively constant the percent may be applied to total sales b Under the percent of sales method the amount of the adjustment is the amount estimated for Bad Debt Expense c Remember that net realizable value is the amount that is expected to be collected or realized

Percent of sales method At the end of the current year Accounts Receivable has a balance of 450 000 Allowance for Doubtful Accounts has a credit balance c 4 000 and sales for the year total 2 030 000 Bad debt expense is estimated at 1 4 of 1 of sales a Determine the amount of the adjusting entry for uncollectible accounts b Determine the adjusted balances of Accounts Receivable Allowance for Doubtful Accounts and Bad Debt Expense Accounts Receivable Allowance for Doubtful Accounts Bad Debt Expense c Determine the net realizable value of accounts receivable

Journalize each of the following petty cash transactions a Issued a check to establish a petty cash fund of 650 If an amount box does not require an entry leave it blank Petty Cash Cash Feedback Store Supplies 650 Check My Work a Recall that the only time Petty Cash is used is when the fund is initially established or increased Feedback b The amount of cash in the petty cash fund is 210 Issued a check to replenish the fund based on the following summary of petty cash receipts store supplies 258 and miscellaneous selling exper Record any missing funds in the cash short and over account If an amount box does not require an entry leave it blank 650 Miscellaneous Selling Expense Cash Short and Over Cash 258 163 0000

ach of the following petty cash transactions a Issued a check to establish a petty cash fund of 650 If an amount box does not require an entry leave it blank 88 Petty Cash Cash Feedback Check My Work b The amount of cash in the petty cash fund is 210 Issued a check to replenish the fund based on the following summary of petty cash receipts store supplie and miscellaneous selling expense 163 Record any missing funds in the cash short and over account If an amount box does not require an entry leave it blan Store Supplies Miscellaneous Selling Expense Cash Short and Over

Bank reconciliation The following data were gathered to use in reconciling the bank account of Reddan Company Balance per bank 19 000 Balance per company records 9 680 Bank service charges 20 Deposit in transit 2 700 Note collected by bank with 120 interest 5 100 Outstanding checks 6 940 a What is the adjusted balance on the bank reconciliation Feedback Check My Work b Journalize any necessary entries for Azalea Company based on the bank reconciliation If an amount box does not require an entry leave it E Miscellaneous Expense Cash 88

4 6 pts If 6 000 is invested at an interest rate of 4 1 per year compounded quarterly find the amount due at the end of the given number of years Round your answers to the nearest cent a 4 years b 6 years c 8 years

Gaspar also rides a scooter He travels 2 ft farther for every 1 second than Paloma does What is Gaspar s ratio of feet traveled to seconds traveled Show your work

An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic Step 2 of 2 Suppose a sample of 675 new car buyers is drawn Of those sampled 270 preferred foreign over domestic cars Using the data construct the 90 confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars Round your answers to three decimal places Answer How to enter your answer opens in new window Tables Keyboard Previous st

Refer to the accompanying data display that results from a sample of airport data speeds in Mbps The results in the screen display are based on a 95 confidence level Write a statement that correctly interprets the confidence interval Choose the correct answer below TInterval 13 046 22 15 x 17 598 Sx 16 01712719 n 50 O A We have 95 confidence that the limits of 13 05 Mbps and 22 15 Mbps contain the true value of t mean of the population of all data speeds at the airports OB The limits of 13 05 Mbps and 22 15 Mbps contain 95 of all of the data speeds at the airports OC The limits of 13 05 Mbps and 22 15 Mbps contain the true value of the mean of the population of all data speeds at the airports D We have 95 confidence that the limits of 13 05 Mbps and 22 15 Mbps contain the sample mean of the dots

The figure below shows the distribution of elevation in miles across the earth s surface Positive elevation denotes land above level negative elevation shows land below sea level that is the ocean floor fraction of earth s surface per mile of elevation 2 Adapted from D Freedman R Pisani R Purves and A Adikhari Statistics 2nd Edition New York Norton 1991 Your answer is incorrect elevation miles a Select each correct description of the elevation of most of the earth s surface Much of the earth s surface is either around 3 miles below sea level or exactly at sea level O It appears that essentially all of the surface is between 4 miles below sea level and 2 miles above sea level Most of the earth s surface is above sea level O Very little of the surface is around 1 mile below sea level O It appears that essentially all of the surface is between 4 miles below sea level and sea level O Most of the earth s surface is below sea level O Much of the earth s surface is either around 4 miles below sea level or 1 mile below sea level eTextbook and Media Your answer is incorrect

Determine whether the statement makes sense or does not make sense and explain your reasoning The death rate from this new strain of flu is catastrophic because 25 of the people hospitalized with the disease have died Choose the correct answer below GELEE OA This makes sense because the percentage of the hospitalized people is less than 50 OB This does not make sense because it is not clear whether the facts are derived from a sample of patients which is representative of the entire population of the patients suffering from th disease OC This makes sense because the sample of patients is representative of the entire population of patients suffering from the disease OD This does not make sense because the percentage of the hospitalized people is less than 50

Use the display of data to find the mean median mode and midrange Round to the nearest tenth as needed R The mean of the data is The median of the data is Round to the nearest tenth as needed Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode of the data is Use a comma to separate answers as needed OB There is no mode for the given data The midrange of the data is MEER Round to the nearest tenth as needed 8 9 10 11 12 13 14 15 Score

Monday 1 Find the number that makes an equivalent fraction 6 12 10 20 3 Find the number that makes an equivalent fraction 5 50 76 7 D 5 Shade in the equivalent fraction and answer 6 with shaded fraction 1x3 2 represent an equivalent in 000 2 Fill in the missing equivalent fraction 12 3 4 5 6 59 10 7 14 21 28 35 42 04 29 1 25 6 729 2 Answers 20 4128

Tuesday 1 Find the number that makes an equivalent fraction 16 3 18 3 Find the number that makes an equivalent fraction 36 5 30 5 Shade in the equivalent fraction and answer with shaded fraction 2x216x2 2 7 Determine which letter best represents an equivalens fraction 1 18 20 2 Fill in the missing equivalent fraction 48 16 20 24 9 18 36 45 54 4 2 786 6 9311 FF 2x100 200 2x 2 3 5 6 7 Answe

5 Shade in the equivalent fraction and answer with shaded fraction 1x3 2x3 2 D 6 6729

5 1 For the purpose of evaluating the impact damage of soybeans striking a steel wall it can be assumed that the collision is elastic The modulus of elasticity units of Pa of the soybean can be estimated from the equation In E 20 12 0 55 In M 0 87 where M is the moisture content in percent wet basis Equation for E taken from Misra and Young 1981 a Estimate the maximum force which would be experienced by a soybean of average weight and density having a moisture of 13 w b when it impacts a solid wall at velocities of 1 3 and 5 m s Assume the Poisson s ratio of the soybean is 0 35 Solution hints Calculate the E value using the above equation Remember to use 13 instead of 0 13 for the M value in the equation The young s modulus of steel is much larger than that of the soybean as a result k2 0 The major diameter intermediate diameter and minor diameter of soybean are 7 29 6 43 and 5 38 mm The average of the minor and intermediate diameter 5 905 mm can be used for the value D

2a How much money would need to be deposited today in order to grow to 50 000 in an account earning 3 5 compounded quarterly after 20 years Round to the nearest cent 2b How long would it take for a deposit of 10 000 to triple if placed into an account paying 2 75 interest compounded continuously Round your answer to one decimal place

Use Newton s method with the specified initial approximation x to find x3 the third approximation to the root of the given equation Round your answer to four decimal pl 2x3 3x 2 0 x 1 x3

1 point Consider the relation R whose digraph is given below Co 8 t without

13 This graph shows the number of cars n in the school parking lot as a function of time t Number of Cars in the School Parking Lot Number of cars 60 40 20 0 n 08 00 Time 16 00 a Identify the independent and dependent variables Justify your choices b Why are the points on the graph not connected c Estimate the domain and range of the graph Are there any restrictions on the domain and range Explain

1 point Consider the relation Rwhose digraph is given below 4 00 8 3 List the equivalence classes of R Separate your answers using commas In sets containing more than one element write them from smallest to largest without sp

livia was recently promoted to manager at the coffee shop where she has been working She will now be earning 1 000 each month and has decided to eate a budget to control her spending and save for her first apartment Use the Budget Template to fill in Olivia s budget information Although the amount she spends on gas groceries and utilities changes each month assume her budgeted and actual amounts are the same When you have completed her budget answer the two questions at the bottom of the template Budget Template Expenses Gas Car payment Car insurance Phone bill Nails Health insurance Clothing Groceries Utilities Streaming service 40 average per month 250 per month 100 per month 60 average per month 30 per month 50 per month 50 per month 50 average per month 45 average per month 50 per month

1 point Consider the relation R on the set whose digraph is given below 1 3 5 Is R an equivalence relation OA Yes B No 4 C R is not symmetric D R is not transitive E None of the above 2 because select all that apply A R is reflexive symmetric and transitive B R is not reflexive

point Let denote the set of all integers Determine whether each of the relations on Z given below are reflexive symmetric transitive or none of the above Select all that apply a xy 1 OA Reflexive B Symmetric C Transitive D None of the above b x y 0 OA Reflexive B Symmetric C Transitive D None of the above c x 2y A Reflexive B Symmetric C Transitive D None of the above d x y is an integer A Reflexive B Symmetric C Transitive D None of the above

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition He wants to first determine the percentage of adults who have heard of the brand How many adults must he survey in order to be 90 confident that his estimate is within six percentage points of the true population percentage Complete parts a through c below a Assume that nothing is known about the percentage of adults who have heard of the brand n Round up to the nearest integer

Refer to the accompanying data display that results from a sample 13 046 22 15 of airport data speeds in Mbps Complete parts a through c below x 17 598 Sx 16 01712719 n 50 distribution table Click the icon to view a t df a What is the number of degrees of freedom that should be used for finding the critical value to 2 IT TInterval number

Time from start of journey h b How much gas was ir the tank at the stai the journey Was the tank full at this time Explain 0 An oven is turned on at a room temperature of 20 C and it takes 10 min to reach a temperature of 190 C A tray of cookies is placed in the oven to bake for 10 min The oven is then turned off and returns to room temperature after 15 min Sketch a graph of temperature as a function of time Label each section of the graph and explain what it represents

5 To raise a flag Sepideh pulls the rope steadily with both hands for a short time then moves both hands up the rope and pulls again She does this until the flag has been raised Which graph best represents the height of the flag Give reasons for your choice Graph A Graph B Height m Height m Time s Graph C Time s Height m Height m Time s Graph D Time s

13 A student drew a graph to represent this situation Jonah is watching television After 3 min his mom enters the room to ask him a question He turns the volume down a bit answers his mom then turns the volume back up Two minutes later Jonah s dad turns on the dishwasher so Jonah gradually turns up the volume After a further 3 min a commercial comes on so Jonah presses the mute button Describe any errors in the student s graph Volume of a Television Volume scale 80 60 40 20 0 to Time min 8 10

13 Which of the following is equivalent to An B 0 0 O An B O AUB O An B

Homework 15 Distribution Date 10 30 2023 Due Date 11 02 2023 1 An exploratory drill hole was made in a stiff saturated clay The sand underlying the clay was observed to be under artesian pressure Water in the drill hole rose to a height of 18 ft above the top of the sand layer If an open excavation is to be made in the clay how deep can the excavation proceed before the bottom heaves 25 ft 4 18 ft 16 ft Saturated clay Exploratory drill hole Sand G 2 7 Moisture content w 40 NOTE Show all the calculation steps

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Two friends take a 2000 mile cross country trip together but they drive their own cars Car A has a 14 gallon gas tank and averages 40 miles per gallon while car B has a 22 gallon gas tank an averages 20 miles per gallon Assume both drivers pay an average of 2 35 per gallon of gas a What is the cost of one full tank of gas for car A For car B b How many tanks of gas do cars A and B each use for the trip c About how much do the drivers of cars A and B each pay for gas for the trip a The cost for car A is 32 90 per tank and the cost for car B is 51 70 per tank Round to the nearest cent as needed b Car A uses 3 57 tanks and car B uses 4 55 tanks for the trip Round to two decimal places as needed c The driver of car A pays 117 45 for the trip and the driver of car B pays 235 24 Round to the nearest cent as needed

The impact of the recession of 2009 has seen an ensuing slow recovery which has lasted well into 2013 Since the slowing of the recession Americans have seen a small increase in disposable income averaging less than one percent a month in 2013 Despite the small gains in income Americans are looking to place more discretionary money into savings plans and investments than into vacations and luxury items Source Bureau of Economic Analysis U S Department of Commerce 2013 Retrieved from http www bea gov newsreleases national pi pinewsrelease htm CODE If an individual saves 5 700 and elects to place the total dollar amount into a savings account earning 2 75 APR compounded monthly how much will the original deposit grow to in 12 years The initial deposit plus interest equals Round to the nearest dollar as needed

Part 1 of 2 15 10 5 0 Normal curve with u 2 0 4 u 2 o 2 2 a 4 Part 2 of 2 b 15 10 and standard deviation 0 5 10 15 05 X 10 15 C

In Arizona where there are 320 sunny days per year it requires 321 acres of land to generate 300 MW of average annual power If there are only 159 sunny days per year in Pennsylvania how many acres of land would it require to generate the same average annual power Please round to the nearest acre Note assume that a cloudy day delivers 0 watts acre of solar power This is not true but it simplifies the problem for us

For the following situation find the average monthly expense that you would use in budgeting for the given expense Note Annual means once a year and semiannual means twice a Lan pays a semiannual premium of 450 for automobile insurance a monthly premium of 165 for health insurance and an annual premium of 400 for life insurance The average monthly expense is Round to the nearest cent as needed