Math - Others Questions

Thursday 1 thousands 2 5 282 Express the value shown hundreds tens 4 6 3 Use or to compare the two numbers 84 48 The 2 in the ones place is 6 823 895 The 8 in the hundreds place is place 7 2 293 ones 35 The 2 in the hundreds place is 2 8 Convert 388 884 to expanded form 4 Express the value shown hundreds tens 45 3 thousands 3 Rewrite in standard form 3 000 800 50 7 the value of the 2 in the hundreds place ones 19 the value of the 8 in the hundred thousands the value of the 2 in the thousands place 1 2 3 4 5 3 857x10 7 8 9 10

Wednesday 1 Express the value shown hundreds 3 3 Use or to compare the two numbers 1 874 1 874 5 6 346 tens ones 51 3 The 6 in the ones place is 6 133 481 The 3 in the thousands place is place 7 686 The 6 in the hundreds place is ten thousands 4 8 Convert 96 824 to expanded form Express the value shown thousands 23 7 hundreds 7 the value of the 6 in the thousands place 4 Rewrite in standard form 800 000 40 000 4 000 700 30 ones the value of the 3 in the ten thousands the value of the 6 in the ones place 57 2 3 elahe 8 41737X105 4 7 8 9 10

fairness O There are multiple definitions and ways to measure fairness and these often contradict each other O For many companies investing in algorithmic fairness may come at the expense of execution speed or model performance Most customers users individuals do not observe issues of algorithmic fairness so solving them does not impact the bottom line O Solving issues of algorithmic fairness often requires access to sensitive data which is

Which of the following is not a common way to get interpretable insights from a model Use feature importance plots to understand which features are contributing value to the model Use a precision recall curve to show classifier performance at different thresholds Use an instance based explanation method such as LIME or SHAP Use Partial Dependency Plots to show how an individual feature influences model decisions holding all else constant

Which of the following best describes an allocative harm within the topic of algorithmic fairness A discriminatory system that withholds certain opportunities freedoms or resources from specific groups A system that reinforces negative stereotypes along the lines of identity or protected class A system that has higher false positive rate for a historically marginalized community O A system that allocates opportunities to people through automated classification

3 Use or to compare the two numbers 96 151 15 691

9 617 274 The 7 in the thousands place is the value of the 7 in the tens place

6 5 384 351 The 5 in the tens place is the value of the 5 in the millions place

9 914 The 9 in the hundreds place is the value of the 9 in the thousands place

8 Convert 3 142 to expanded form

Problem 5 Solve the linear programming problem You may find it useful to use desmos com to graph the constraints Maximize P 3x 2y subject to x y 3 2x y 8 T 0 y 0 The maximum is P at x and y

A special food for athletes is to be developed from two foods Food X and Food Y The new food is to contain at least 16 milligrams of Vitamin A at least 20 milligrams of Vitamin B and at least 12 milli grams of Vitamin C Each pound of Food X costs 1 50 and contains 1 milligram of Vitamin A 5 milligrams of Vitamin B and I milligram of Vitamin C On the other hand each pound of Food Y costs 2 50 and contains 2 milligrams of A 1 milligram of B and I milligram of C How many pounds of each food should be used in the mixture in order to meet the preceding requirements at a minimum cost What is this minimum cost

Problem 6 Solve the linear programming problem You may find it useful to use desmos com to graph the constraints Maximize P 3x 2y subject to 2x y 20 2x 3y 24 The maximum is P at x and y y 6 x 0 y 0

1 5 points Draw a representation using base 10 blocks of the number 1 325 2 10 points Illustrate 0 638 0 562 using base 10 blocks 3 10 points Illustrate 2 123 1 439 using base 10 blocks

Consider the poset H represented by the following Hasse diagram h g b Give each of the following If any do not exist explain why 14 1 All minimal elements of H 14 2 All maximal elements of H 14 3 All upper bounds of b c 14 4 All lower bounds of g h 14 5 The LUB of b c 14 6 The greatest element in H 14 7 The least element if H f a

I can calculate the total cost of a stock investment I got it I m still learning it Determine a the cost of the stock and b the total paid 5 David Daly owns 215 shares of Atwood Tire His cost per share is 18 90 The online commission is 14 95 1 point

I can determine the annual percentage yield How I Did Circle one I got it I m still learning it 4 Mabel Causino has 35 000 to invest in a certificate of deposit for 4 years The CD earns 4 75 interest compounded daily What is the annual percentage yield 1 point

Suppose that the temperature at a point x y on a metal plate is T x y 4x 4xy y An ant walking on the plate traverses a circle of radius 3 centered at the origin What are the highest and lowest temperatures encountered by the ant NOTE Enter exact answers Highest Temp Lowest Temp

A patient took 200 milligrams of an antibiotic in a single dose At the end of each subsequent hour the amount of antibiotic in the patient s body was 11 percent less than it was at the beginning of the hour Approximately how many milligrams of the antibiotic were in the patient s body 7 hours after the dose was taken 0 0 0 0 0 123 0 115 5 88 5 77 0 3 9

Given the following functions find g 1 f x 5x 4 g x x 4

Starting from the transformation under diffeomorphisms for the connection coefficients Tuen Tex Te a Prove that the covariant derivative of a vector behaves in turn as a vector

Show that the given planes 221 4x2 4x3 4 22 2x3 2 and 221 322 0 have east one common point

In a chemical process the amount of a certain type of impurity in the output is difficult to control is thus a random variable Speculation is that the population mean amount of the impurity is 0 20 grams per gram of output It is known that the standard deviation is 0 1 grams per gram of output An experiment is conducted to gain more insight regarding the speculation that the population mean is 0 20 a The process was run on a lab scale 50 times and the sample average x turned out to be 0 23 grams per gram Perform analysis and comment on the speculation on the population mean b What if the process was run 30 times and the sample average x turns out to be 0 19 grams per gram

In the diagram below we have C T 76 and CTB 42 C A S Find B 1 CDU 76 2 EDU 3 UCD O 42 X E V

0 Let A X a a2 9 b and B b with real entries such that A XB where 1 1 17 31 k x be two 2 x 1 matrices and k R If a a 3 b b and k 1 b2 2b b2 then the value of k is JEE Main 2021

2 During a 66 day monsoon season daily rainfall can be modeled using a cosine function of the form R d Acos B d h k where R is in centimeters and d is in days assume A 0 and B 0 If the rainfall fluctuates between a low of 3 cm on day 12 and a high of 15 cm on day 45 create a model to determine when the rainfall is at least 13 cm R 13 on 37 2 54 9 OR 13 on 35 3 54 2 none of these

115 X to Find the value of x in the diagram Lines that appear parallel are parallel

2x 7 x 75 Find the value of x in the diagram Lines that appear parallel are parallel

Consider the following function and assume an initial bracket of 1 2 please find the iterative value of the root at the end of two iterations using the bisection method f x x 3 01 02 O 1 35 1 75

2 A regular hexagon on the pseudosphere H is inscribed in a c cosh r 3 Find the exact value of cosh s where s is the length of ea Please do not use a calculator Please fully justify your answer

What is the sum of the measures of angles 3 5 and 7 line g line h 12 4 3 5 6 7 85 image not drawn to scale g h

Find the measures of the indicated angles below g j E H C D G J

Find the unknown angle measures X 48 y 99 Drawing is not to scale 26 120 118

Find the value of x G X E 66 F

In a large city the road system is set up like a Cartesian plane where streets are indicated by the number of blocks they are from Street A and Street B For example a baseball field is located 4 blocks west of Street B and 33 blocks north of Street A Treat the intersection of Street A and Street B as the origin of a coordinate system with East being the positive x axis Answer parts a d a Write the location of the baseball field using rectangular coordinates Type an ordered pair b Write the location of the field using polar coordinates Use the east direction for the polar axis Express 0 in degrees Type an ordered pair Round to two decimal places as needed c A different ballpark is located 10 blocks west of Street B and 28 blocks south of Street A Write the location of this ballpark using rectangular coordinates Type an ordered pair d Write the location of this ballpark using polar coordinates Use the east direction for the polar axis Express 0 in degrees 0 Type an ordered pair Round to two decimal places as needed

Find the unknown angle measures X 24 47 58 Drawing is not to scale 20 C to

2 Breakeven quantity analysis The Acme Candy Company is preparing to offer a new product called the Minty Dark Chocolate Bite Bar The material costs per unit of the new candy bar are 0 10 for chocolate 0 02 for sugar and 0 03 for mint flavoring Labor costs are estimated to be 0 10 per unit candy bar Building a production line facility devoted to the new candy bar will have two fixed costs cost 150 000 paid in full at the start of candy bar production and operating costs for the facility are estimated to be 200 000 per year Show all work starting with listing and labeling given information In all calculations first show theoretical equations used and include any assumptions made time value of money is not to be considered in this problem INTEINEN GUTE d Hand draw and label a complete breakeven analysis graph for the new candy bar product showing all essential conceptual features of the breakeven analysis graph does not have to be to a precise scale but you must label all variables axes and essential features of your

10 8 6 4 Slope q 10 8 6 4 2 y intercept K 4 6 8 10 2 4 6 8 10 What is the slope of the graph Leave your answer as a reduced fraction a Identify the y intercept Write as a coordinate Write an equation in slope intercept form for

x 2x 15 x 2x 8 2x 15x 8 2 x 2x 8 x 13x 40 2 x 25 2 X X 6

Williams Optical Inc is considering a new lean product cell The present manufacturing approach produces a product in four separate steps The production batch sizes are 45 units The process time for each step is as follows Process Step 1 Process Step 2 Process Step 3 Process Step 4 5 minutes 8 minutes 4 minutes 3 minutes The time required to move each batch between steps is 5 minutes In addition the time to move raw materials to Process Step 1 is also 5 minutes and the time to move completed units from Process Step 4 to finished goods inventory is 5 minutes The new lean layout will allow the company to reduce the batch sizes from 45 units to 3 units The time required to move each batch between steps and the inventory locations will be reduced to 2 minutes The processing time in each step will stay the same Determine the value added non value added and total lead times and the value added ratio under the present and proposed production approaches If required round percentages to one decimal place Present Approach Proposed Approach 20 min Value added time Non value added time Total lead time 20 min min min min min

The table provided below gives the sales details of the number of android smart phones at an electronic retail store for the p 6 weeks The time series appears to be relatively stable without trend seasonal or cyclical effects Hint Use a value of 0 8 2 3 4 5 6 A Week 1 2 3 4 5 6 What is the value of the mean absolute percentage error for the given data O 16 60 O 21 72 O 29 97 B Units Sold 88 44 54 65 72 85

c Sketch the function f x 3 x 1 2 x 1 and its inverse in the same graph REMEMBER NO GRAPHING SOFTWARE ALL GRAPHS HOITADUMAA nar MUST BE DONE BY HAND Drawing tools are acceptable but be precise USE DIFFERENT COLOURS FOR EACH CURVE

Divisive clustering method is different from agglomerative clustering methods in that divisive clustering methods O separate objects into a particular cluster in one step O can only have a single subject in each cluster separate n objects successively into finer groupings O can only have a pair of subjects in each cluster

Sujito Electronix makes headphones for 22 and sells them for 32 Sujito has sold at least 50 headphones on average per week in the past though the actual demand is unknown Sujito has also often run short of supply in the past After three months of release the headphones are sold at 40 percent discount The spreadsheet below shows Sujito s sales and demand for the headphones We take demand at 51 and quantity produced at 55 2 3 4 Selling Price 5 Cost 6 Discount Price 7 8 9 10 Demand 11 Produced Quantity 12 13 Quantity Sold 14 Surplus Quantity O 51 B Newsvendor Model for Sujito s Headphones O 55 04 Data 050 Model Which of the following is the value for quantity sold 32 22 19 20 51 55

The spreadsheet below shows the net income model for a company that sells shoes 2 3 4 5 Sales 6 Cost of Goods Sold 7 A Net Income Model Administrative Expenses 8 Selling Expenses 9 Depreciation Expenses 10 Interest Expenses 11 Taxes 12 13 14 15 Gross Profit 16 Operating Expenses 17 Net Operating Income 18 Earnings Before Taxes 19 20 Net Income O B15 B16 B17 B18 O B5 B17 Data O B18 B11 Model Which of the following formulas would be used to calculate the net income value using only the information in the Model not in the Data section 10 000 000 6 400 000 500 000 900 000 750 000 70 000 620 000 3 600 000 2 150 000 1 450 000 1 380 000

Which of the following is the first stage of joining clusters in agglomerative hierarchical clustering O by joining two clusters that are closest to each other O by joining two clusters farthest away from each other O by separating clusters into finer groups O by joining two clusters that are not at a Euclidean distance

Dresden Pharmaceuticals has decided to go ahead and start clinical trials on a potential new drug The total R D costs are estimated to reach around 875 000 000 with clinical trials mounting to 145 000 000 The current market size is estimated to be around 3 000 000 and is expected to grow at 4 percent every year The market share Dresden hopes to capture in the first year is 7 percent and is projected to grow by 25 percent each year for the next 4 years A monthly prescription is anticipated to generate revenue of 420 while incurring variable costs of 150 A discount rate of 8 percent is assumed 2 A Dresden Pharmaceuticals 4 Market Size 5 Unit monthly Rx revenue 6 Unit monthly Rx cost S 7 Discount Rate per cent 8 9 10 R D 11 Clinical Trials Data O 1 149 876 000 O 1 494 838 800 O 2 373 996 000 Project Costs B 3 000 000 420 150 8 875 000 000 145 000 000 Calculate the projected profit for the third year

In the linear trend equation Ft k at btk identify the term that signifies the trend O bt Ok 0 Ft k at

If the actual value of a time series at time t and the forecast value for time t is denoted by At and Ft respectively then the formula for the mean absolute deviation over a range of forecasted values is O MAD MAD MAD MAD A Ft 2 t 1 72 72 A1 F f 1 72 72 A4 F t 1 72 AL F f 1

2 Given the function f x 3 x 1 2 a Determine the equation of the inverse of the f x 0 3 x 1 2 x 2 y 1 2 2 f x x 1 2 13 1 X 2 y 1 APP x 32 y 1 x 2 1 y b Is the inverse of f x a function If not restrict the domain of f x such that its inverse is a function Include ALL possibilities A