Math - Others Questions

EACH PROBLEM WILL BE GRADED 0 12 1 Check if the following formula is a tautology p r q p p q r p 1000 goticfy the following

r q p p g r p formula is a tautology 2 How many elements ne 101 102 1000 satisfy the following state ment n is divisible by 5 or by 6 and n is not divisible by 9 3 Prove that the relation R defined on the set X Z by mRn3m 7n2 is divisible by 10 is an equivalence relation Determine its equivalence classes 5 R 2024 R How many different equivalence classes does this relation have 4 Let f n 3n 5 and g n n be two fungtin the functions

4 Let f n 3n 5 and g n n be two functions defined on Z Which of the functions f g fog gof are injective Please explain precisely why 5 Show that the operation r y x y xy is commutative associative and distributive with respect to x y x y 1 Which element is the inverse of 4 with respect to

What are all possible shapes of trees of height 2 with k leaf 01 02

13 Dimensions of a Mirror A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12 while the angle of elevation to the top of the mirror is 11 Find the vertical dimension of the mirror See Figure 16 150 cm

The following figure shows the four possible configurations of a double red B 4 The following figure shows the rearrangement that fixes the Double Red violation sider this tree that was obtained by inserting J into a red black tree using the algorithm fo ary search tree and coloring the new node red We now have a double red violation C F G K J 12 H OG What is the right child of F after the rearrangement OK H OG What is the left child of J after the rearrangement OK OJ What is the left child of H after the rearrangement OK OJ OH

Solve the equation 5 q 2q 3 1 The solution set is 3 10

At a restaurant If a party has eight or more people the gratuity is automatically added to the bill If x is the cost of the meal then the total bill C x with a 17 gratuity and an 8 sales tax is given by C x x 0 08x 0 1x Evaluate C 280 and interpret the meaning in the context of this problem Round to the nearest cent If the cost of the food is S then the total bill including tax and tip Is S X 3

Question 28 of 28 1 point 1 Question Attempt 1 of Unlimited Determine the average rate of change of the function on the given Interval Express your answer in exact simplest form f x x 1 Part 1 of 3 a on 2 0 The average rate of change of the function is Part 2 of 3 b on 2 5 The average rate of change of the function is 00

Evaluate the function f x x 6x for the given value of x Simplify your answer f x h

17 18 and 3 19 The slope of the line is 20 00 21 22 Determine the slope of the line passing through the given points Write your answer in exact simplified form 5 2 4 3 23 24

13 Find and simplify f x h Simplify your answer f x 7x 5x 6 f x h

A student decides to finance a used car over a 6 yr 72 month period After making a down payment of 1000 the remaining cost of the car including tax and Interest is 15 192 The amount owed y A t in S is given by A t 15 192 211 t where t is the number of months after purchase and Ost 72 Determine the t intercept and y intercept and interpret their meanings in context Amount Owed on Vehicle after r Months Amount Owed Part 0 4 Part 1 of 4 12000 4000 2000 O A 15 192 211 Number of Months t

Evaluate the function f x x 6x for the given value of x Simplify your answer f x h

Solve the equation 3a a l 4 2a 8a a 3 4a 3 The solution set is 010

Solve by completing the square and applying the square root property Express the solution set in exact simplest form 4m 2 28m 3 0 The solution set is 0 16 3

olve the Inequality and write the solution set in Interval notation if possible Write numbers as simplified fractions or Integers 8 4x 19 5 The solution set is DO 0 0 Innl

Solve by completing the square and applying the square root property Express the solution set in exact simplest form 2y y 2 6 3y

comes to playing basketball and tall people are more efficient because they can ch the basket easily allowing for more points per game as well as more rebounds and blocked shots If you watch National Basketball Association NBA games regularly you certainly notice that many players are quite tall We will explore the distribution of NBA player heights using a sample of players active in the 2019 2020 season by making a histogram of HEIGHT INCHES with bins stating at 68 inches and bin width of 2 inches We will then determine the z scores for players who are 71 inches 5 11 and b 84 inches 7 0 The dataset consists of the NBA player s name team and height measured in inches for players active in the 2019 2020 season Aaron Gordon Player Aaron Holiday Adam Mokoka Abdel Nader Admiral Schofield WAS Z Variable symmetric Numerical Variable Team Height Inches ORL Data value a x x S IND LUSE SALT OKC Import the dataset into SALT for analyzing Data value b x x CHI After you have clicked the tab for your selected topic and read the problem answer the questions below a Use SALT to summarize the data and fill in the following table rounding values to four decimal places as needed Data value a is N 80 529 73 77 77 77 b Create a histogram with Starting Point and Bin Class Width values asked for The distribution for this variable is mound shaped and is Mean 78 393 Our sample s minimum value is not Standard Deviation 3 4505 c Determine the relative standing for the two data values of interest using the z score formula appropriate for samples Round your answers to two decimal places standard deviations below Median 78 Find the data value with a z score of 3 rounded to two decimal places x 2 5 X Minimum Value standard deviations above to determine the number of standard deviations each data value is away from the mean Find the data value with a z score of 3 rounded to two decimal places X Z S X 69 the mean whereas data value b is the mean Remember to take the absolute value of the z scort maximum is histogram in SALT it can be observed that almost all A Maximum Value 89 d Most data points are within three standard deviations of the mean In other words most observations will have a score that is larger than 3 and less than 3 at least roughly further than 3 standard deviations below the mean Our sample s further than 3 standard deviations above the mean Upon further inspection of the observations would have a z score between 3 and

Make an appropriate substitution and solve the equation 2 7 2 7 72 0 The solution set is 3

2 pints Manny a calendar year taxpayer uses the cash method of accounting for his sole proprietorship In late December he performed 42 000 of legal services for a client Manny typically requires his clients to pay his bills immediately upon receipt Assume Manny s marginal tax rate is 37 percent this year and next year and that he can earn an after tax rate of return of 7 percent on his investments Required a What is the after tax income if Manny sends his client the bill in December b What is the after tax income if Manny sends his client the bill in January Use Exhibit 3 1 Note Round your answer to the nearest whole dollar amount c Based on requirements a and b should Manny send his client the bill in December or January Complete this question by entering your answers in the tabs below Required A Required B Answer is complete but not entirely correct Required C What is the after tax income if Manny sends his client the bill in December

Reaction time is the amount of time it takes to respond to a stimulus and for automobile drivers it is an important factor in staying safe while on the road by avoiding rear end collisions Reaction times vary from driver to driver and tend to be longer than one might think A recent study determined that the time for an in traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1 24 seconds and standard deviation of 0 45 seconds If we let X denote reaction time for automobile drivers use the appropriate Normal Distribution to determine each of the following 1 What is the probability that a driver has a reaction time less than 0 6 seconds 2 Approximately what proportion of drivers have a reaction time more than 2 5 seconds 3 Within what limits centered about the mean would you expect driver reaction times to lie with 95 probability What are the z scores for these limits 4 What is the reaction time for which only 1 of drivers have a shorter reaction time What is its z score 5 What is the reaction time for which only about 5 of drivers have a longer reaction time What is its z score 4 X 6 Approximately what proportion of drivers have a reaction time within three standard deviations of the mean After you have clicked the tab for your selected topic and read the problem answer the questions below a To model the random variable X defined by the selected scenario use the Normal Distribution with mean 1 24 and standard deviation 0 45 USE SALT b Determine each of the following values rounded to four decimal places 1 2 3 The smaller value is The larger value is 5 X Z score with a corresponding z score of with a corresponding z score of

Make an appropriate substitution and solve the equation 9x 3 3 9x 3 108 0 The solution set is 0 0

Suppose that a linear system has fewer equations than variables What can you determine about the solution set of the system

Tawana owns and operates a sole proprietorship and has a 37 percent marginal tax rate She provides her son Jonathon 17 000 a year for college expenses Jonathon works as a pizza delivery person every fall and has a marginal tax rate of 15 percent Required a What could Tawana do to reduce her family tax burden b How much pretax income does it currently take Tawana to generate the 17 000 after taxes given to Jonathon c If Jonathon worked for his mother s sole proprietorship what salary would she have to pay him to generate 17 000 after taxes ignoring any Social Security Medicare or self employment tax issues d How much money would the strategy in part c save Complete this question by entering your answers in the tabs below Required A Required B Answer is not complete Required C Required D How much money would the strategy in part c save

Write the expression in terms of i and simplify 7 35 11

in pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion

Write the expression in terms of i and simplify 9 81 i 10

Write the expression in terms of i and simplify 28 i

in pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion

Write the expression in terms of i and simplify 225 0 i

where R is the Sem how that Ifrsino drido 24 R 3 Y 29 Cose above The Intial line 020 circle

A z score is a measure of relative standing for an observation because it tells us the number of standard deviations and direction an observation is from the mean In other words when we use the standard deviation as our measurement unit the absolute value of the z score tells us how far an observation is from the mean in number of standard deviations It is positive when the observation is found above to the right or greater than the mean and negative when the observation is found below to the left or less than the mean The following is the formula to compute the z score for an observation x from a population with mean and standard deviation d Alternatively when working with a sample instead of a population this formula is used with sample mean x and sample standard deviation s Recall the following summary statistics for our sample of white wine pH measurements Z Variable Name pH Wines with low pH taste tart and crisp whereas wines with higher pH are more susceptible to bacterial growth A pH of about 3 0 to 3 4 is most desirable for white wines z X X S 3 0 1 25 x 0 Z X X S X X 5 z score for pH of 3 4 3 4 1 25 Determine the relative standing for a pH of 3 0 and a pH of 3 4 by computing a z score for each observation using the rounded values above and rounding each z score to two decimals z score for pH of 3 0 3 1883 0 1510 3 1883 0 1510 N Mean X Standard Deviation 4 898 3 1883 0 1510 Median 3 18 Minimum Value 2 72 Taking the absolute value of each z score gives the following interpretations for each pH Maximum Value 3 82

In the Probability section on the left panel you can enter data values into the probability statement to determine the probability or proportion for an age in defined regions Probability P x Data value here Probability proportion for the indicated region here According to our normal model what approximate age is the boundary for the youngest 15 of Congress members Enter 0 15 into the probability field so SALT will compute the boundary age and display the age in the data value field Rounded to one decimal place approximately 15 of members of Congress are expected to be younger than X years according to our model

By default the standard normal distribution is displayed with mean 0 and standard deviation 1 Change the mean and standard deviation values to display the normal distribution with mean 26 8 and standard deviation 4 3 Settings Distribution Selection Normal Distribution Mean St Dev 91 Notice there are two horizontal axes on the graph the x axis displays values of the random variable with the specified mean and standard deviation while the z axis displays corresponding z scores in the standard normal distribution The y axis displays the relative likelihood for the values of this random variable x to take on a given value We will use this distribution calculator to specify the probability that values of the random variable will fall within a range of values Look along the horizontal axes and locate x 26 8 The corresponding z score when x 26 8 is z 0 locate z 1 0 The corresponding x value when z 1 0 is x 26 8 Look again and

A 3 1 Point J C H G uppose we want to remove F In a binary search tree we nev emove a node with two children Instead we replace it with nother node Which node will take the place of F K Q3 2 1 Point G Save Answer Q3 3 H After removing the node containing the original G is the result a red black tree Yes No int K Last saved on Jan 27 at 9 01 AM Now we want to remove C from the preceding tree That s a black leaf so we can t just remove it Instead we bubble up Afterwards what is the color of B red black Save Answer Last saved on Jan 27 at 9 04 AM

1 Assume that we want to verify if the following formula is a tautology by drawing a truth table with 8 rows p g p Vr p V g r How many ones true sentences are there in the column representing p V q r p q p Vr the entire considered formula

Andrea Apple opened Apple Photography on January 1 of the current year During January the following transactions occurred and were recorded in the company s books 1 Andrea invested 13 500 cash in the business 2 Andrea contributed 20 000 of photography equipment to the business 3 The company paid 2 100 cash for office furniture 4 The company received 5 700 cash for services provided during January 5 The company purchased 6 200 of office equipment on credit 6 The company provided 2 750 of services to customers on account 7 The company paid cash of 1 500 for monthly rent 8 The company paid 3 100 on the office equipment purchased in transaction 5 above 9 Paid 275 cash for January utilities Based on this information the amount reported as Owner Capital on the balance sheet at month end would be Multiple Choice 31 400 39 200

Sanborn Company has 10 employees who earn a total of 2 100 in salaries each working day They are paid on Monday for the five day workweek ending on the previous Friday Assume that year ended December 31 is a Wednesday and all employees will be paid salaries for five full days on the following Monday The adjusting entry needed on December 31 is Multiple Choice Debit Salaries Expense 6 300 credit Salaries Payable 6 300 Debit Salaries Expense 4 200 credit Salaries Payable 4 200 Debit Salaries Expense 10 500 credit Salaries Payable 10 500 Debit Salaries Payable 6 300 credit Salaries Expense 6 300 Debit Salaries Expense 6 300 credit Cash 6 300 T

After preparing and posting the closing entries for revenues and expenses the income summary account has a debit balance of 33 000 The entry to close the income summary account will be Multiple Choice Debit Owner Withdrawals 33 000 credit Income Summary 33 000 Debit Income Summary 33 000 credit Owner Withdrawals 33 000 Debit Income Summary 33 000 credit Owner Capital 33 000 Debit Owner Capital 33 000 credit Income Summary 33 000 Debit Owner Withdrawals 33 000 Credit Owner Capital 33 000

The following information is available for Brendon Company before closing the accounts What will be the amount in the Income Summary account that should be closed to Brendon Capital J Brendon Capital J Brendon Withdrawals Services revenue Depreciation Expense Equipment Wages expense Interest expense Insurance expense Rent expense Multiple Choice 80 000 64 400 43 000 112 000 32 000 187 000 12 000 71 400 3 300 11 700 24 200

Perpetual Inventory Using FIFO Beginning inventory purchases and sales for Item Zeta9 are as follows Oct 1 Inventory 7 15 24 Sale Purchase Sale 58 units 16 43 units 64 units 18 21 units Assuming a perpetual inventory system and using the first in first out FIFO method determine a the cost of the goods sold on October 24 and b the inventory value on October 31 a Cost of the goods sold on October 24 b Inventory value on October 31

12 An encryption program creates the appropriate verification and confirmation code in the following scheme regarding the multipliers of a password entered into the system Password Examples given in accordance with the Schema A 2600 180 350 Verification B 900 Code 32 22 5 2 52 7 According to the password program given above which of the following passwords entered into the system has the largest confirmation code Confirmation code C 480 18 34 D 294

3 The set G 0 2 4 6 is a group with the operation xo y defined as the remainder of dividing the number xy 3x 3y 6 by 8 i In G the element 0 o 0 o 0 is equal to ii The neutral element of o in G is iii The inverse element 0 in G is

2 Let the functions g 1 4 0 5 and h 0 2 0 4 be given by the formula g x h x 4x x2 Which of them the four possible answers are both of them only g only h neither of them is an injection a surjection a bit

Entries for Sale of Fixed Asset Equipment acquired on January 8 at a cost of 152 470 has an estimated useful lif of 18 years has an estimated residual value of 8 650 and is depreciated by the straight line method a What was the book value of the equipment at December 31 the end of the fourth year 120 510 Feedback Check My Work b Assume that the equipment was sold on April 1 of the fifth year for 111 947 1 Journalize the entry to record depreciation for the three months until the sale date If an amount box does not require an entry leave it blank Round your answers to the nearest whole dollar if required 88 Feedback Check My Work The depreciation account of the fixed asset being sold or discarded needs to be updated to reflect the months of use in the year it is being discarded or sold The straight line method of depreciation calculates the amount of depreciation to be recognized each year 2 Journalize the entry to record the sale of the equipment If an amount box doe not require an entry leave it blank Do not round intermediate calculations

91 3 Determine with support an equation for a rational function of the form y h x that satisfies the given conditions a Vertical asymptotes of x 1 and 3 b Vertical asymptotes of x 2 and c A hole at 3 2 and a vertical asymptote of a 1 d g 2 0 and h 2 0 a vertical asymptote of a 2 and a hole at and a y intercept of Specifically d

215 A 7 246 X 2 a 213 B 8 There are exponent expressions in each of the triangles in the figure below Accordingly what is the value of a in the triangle in the middle of the bottom row The exponent expression in the triangle on the top row is obtained by multiplying the exponent expressions in the two closest triangles on the bottom row C 9 D 10

rove that the relation R defined on the set X Z by mRn 3m 2 n is divisible by 5 is an equivalence relation Determine its equivalence classes 0 R 7 R 1 many different equivalence classes does this relation h

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by VA t 2t 2 and VB t 5 t respectively Complete parts a through c below 10 0 01 2 3 4 0 1 2 3 4 L hour s 4 hour s while Anna rides 8 miles in hour s while Benny rides 8 miles in V 0 0 1 2 3 4 5 What does this mean geometrically A The area under the line representing Benny s velocity from 0 to 1 is more than the area under the line representing Anna s velocity from 0 to 1 OB The line representing Benny s velocity is decreasing while the line representing Anna s velocity is increasing OC The lines intersect at a t value before the given time indicating that Benny has passed Anna OD The area under each line from 0 to 1 is the same for both riders 4 b If the bikers ride for 1 hour who rides farther Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals A Since Benny rides 4 5 mile s and Anna rides 3 mile s Benny rides farther OB Anna and Benny both ride mile s OC Since Benny rides mile s and Anna rides mile s Anna rides farther hour s hour s 07 13 012 34 c If the bikers ride for 8 miles who wins the race Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals OA They tie in the race because they both ride 8 miles in O B Benny wins the race because she rides 8 miles in OC Anna wins the race because she rides 8 miles in Save