Basic Math Questions and Answers

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

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

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

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

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

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

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

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

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

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

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

In the method the distance between groups is defined as the distance between the closest pair of objects where only pairs consisting of one object from each group are considered divisive clustering Ward s linkage clustering O single linkage clustering O average group linkage clustering

Identify the formula used to calculate the root mean square error over a range of forecasted values if the actual value of the time series at time t and the forecast value for time t are denoted by At and Ft respectively O RMSE RMSE RMSE RMSE 71 t 1 71 f 1 IM A F f 1 71 VAT F A F0 72 72 72 At Ft 2

Which of the following probabilities gives the confidence coefficient O P rejecting Hol Ho is false O P not rejecting Ho Ho is false O P not rejecting Ho Ho is true O P rejecting Ho Ho is true

Which of the following is true about the value of the power of the test O low value will help in detecting small differences in sample statistics O low value will enable valid conclusions to be made O small sample sizes incur higher costs than large sample sizes O small sample sizes generate a low value of the power of the test

Which of the following is true about chi square distribution O It is characterized by degrees of freedom O It is computed using the Excel function CHISQ INV TEST O It is a special distribution and is denoted by C It has a left tail area equal to the expected value of the sample

Which of the following denotes the power of the test 0 1 a OB 01 B

For a two sample hypothesis which tests for differences in population parameters 1 and 2 a two tailed test seeks evidence that population parameter O seeks evidence that population parameter 2 is larger than parameter 1 O seeks evidence that population parameters 1 and 2 do not belong to the same data O seeks evidence that population parameter 2 is smaller than parameter 1 O seeks evidence that population parameter 2 is the same as parameter 1

A 100 1 a confidence interval for the population mean u based on a sample of size n with a sample mean and a known population standard deviation o is given by O x x 0 Ox Za 2 0 O 07 Za 2 2 2 n 1 n

For the formula for calculating the confidence level with known standard deviation the value standard normal random variable with a cumulative probability of 1 a 2 O a 2 00 n represents the value of a

The exponential distribution O has the density function f x ex for x 0 O has an expected value X O models the time between randomly occurring events O is described by the familiar bell shaped curve

For a discrete random variable X which of the following computes the expected value O IME IMB 1 1 i 1 DAX

Which of the following is true about probability density functions A graph of the density function must lie at or below the x axis O The total area under the density function below the x axis is 2 0 O It calculates the probability of a random variable lying within a certain interval OP a x P b is the area under the density function between two numbers a and b

3 Supplier Rex 4 Technologies Rex 5 Technologies Rex 6 Technologies Rex 7 Technologies Max s 8 Wavetech Max s 9 Wavetech Max s 10 Wavetech O MAX D4 D7 Item O COUNT D4D7 B Item Cost per Description Cost Quantity Order Graphics Card 89 35 3 115 Monitor Keyboard Speakers HD Cables Processor Hard disk O SUM D4 D7 O COUNTIF D4 D10 Purchase Orders 150 15 D 15 15 120 40 20 5 10 278 27 18 2 250 600 300 50 6 950 2 160 A P Order Order Terms Months No Size 20 AL123 Large 25 15 25 25 30 20 H AL234 Small AL345 Large AL456 Small KO876 Small To find the largest quantity of items ordered from Rex Technologies what Excel formula should be used in A12 KO765 Large KO654 Small

Which of the following is a differentiation between calculating using the functions COUNT and COUNTIF O COUNT calculates the sum of values for a range of cells COUNTIF finds the largest value in a range of cells O COUNT only requires a range of cell and can be obtained without a special criteria COUNTIF requires range and special criteria to be calculated O COUNT requires a range of cells COUNTIF does not require a range of cells only special criteria O COUNT does not require a range of cells COUNTIF requires a range of cells

Middle managers in operations Odevelop advertising plans Odetermine product mix make pricing decisions O develop staffing plans

Net Present Value Method The following data are accumulated by Geddes Company in evaluating the purchase of 150 000 of equipment having a four year useful life Year 1 Year 2 Year 3 Year 4 Year 1 2 3 4 5 6 7 8 9 10 Net Income 42 500 27 500 12 500 2 500 Present Value of 1 at Compound Interest 6 10 12 15 0 943 0 909 0 893 0 870 0 890 0 826 0 797 0 756 0 840 0 751 0 712 0 658 0 792 0 683 0 636 0 572 0 747 0 621 0 567 0 497 0 705 0 564 0 507 0 432 0 665 0 376 0 627 0 467 0 327 0 592 0 424 0 361 0 284 0 558 0 386 0 322 0 247 0 162 Net present value 0 513 Present value of net cash flow Amount to be invested Feedback 0 452 Net Cash Flow 0 404 80 000 65 000 50 000 40 000 a Assuming that the desired rate of return is 15 determine the net present value for the proposal If required round to the nearest dollar Use the table of the present value of 1 presented above 20 0 833 0 694 0 579 0 482 0 402 0 335 0 279 0 233 0 194 24 520 b Would management be likely to look with favor on the proposal Yes because the net present value indicates that the return on the proposal is greater than the minimum desired rate of return of 15 Check My Work a Multiply the present value of 1 factor for each year Refer Exhibit 2 in the text by that year s net cash flow Subtract the amount to be invested from the total present value of the net cash flow Will management be more favorable to a positive net present value or a negative net present value

Natural Foods Inc is planning to invest in new manufacturing equipment to make a new garden tool The new garden tool is expected to generate additional annual sales of 5 000 units at 18 each The new manufacturing equipment will cost 120 000 and is expected to have a 10 year life and a 17 000 residual value Selling expenses related to the new product are expected to be 3 of sales revenue The cost to manufacture the product includes the following on a per unit basis Direct labor Direct materials Fixed factory overhead depreciation Variable factory overhead Total Determine the net cash flows for the first year of the project Years 2 9 and for the last year of the project Use the minus sign to indicate cash outflows Do not round your intermediate calculations but if required round your final answers to the nearest dollar Natural Foods Inc Net Cash Flows Initial investment Operating cash flows Annual revenues Selling expenses Cost to manufacture Net operating cash flows Total for Year 1 Total for Years 2 9 operating cash flow Residual value Total for last year 2 50 3 20 2 40 0 90 9 00 Feedback Year 1 Years 2 9 Last Year Check My Work For Year 1 subtract the amount to be invested from the operating cash flows annual revenues less selling expenses less cost to manufacture For Years 2 10 subtract the selling expenses and the costs to manufacture from the annual

K A chemical manufacturer wants to lease a fleet of 26 railroad tank cars with a combined carrying capacity of 392 000 gallons Tank cars with three different carrying capacities are available 7 000 gallons 14 000 gallons and 28 000 gallons Letting t number of 28 000 railroad tank cars in the fleet 2t 4 7 000 gallon railroad tank cars and 3t 30 14 000 gallon railroad tank cars will be in the fleet for a certain range of t The cost of leasing a 7 000 gallon tank car is 250 per month a 14 000 gallon tank car is 850 per month and a 28 000 gallon tank car is 1150 per month Which of the solutions to the number of each type of tank car in the fleet would minimize the monthly leasing cost 7 000 gallon tank cars 14 000 gallon tank cars and 28 000 gallon tank cars Simplify your answers Type whole numbers

Suppose the revenue is given by 25x R x 4 2 Match the question with the correct answer there are more answer than questions What is the marginal revenue What are the critical points What values will yield a maximum revenue What is the maximum revenue On what intervals is the revenue increasing A MR x 25x B x 5 C 5 U 0 5 D 156 25 E x 5 0 5 F 100 G 5 0 U 5 0 H MR x 25x

Match the graph of the function with correct sign chart for the derivative of the function There are more sign charts than graphs VA 0 A A B C D E F 2 2

Find the derivative 6x y a e 4 3 4 4 G6 12 x 1 2 6e x 3 4 y Ob y y Od 4x4 3 y be fix 6 x 3 4 e x 1 1 x 4 6e e fx x 4 ex x 4 2 4 x 1 3

4x Se de dx a 1 081 4 C 4 b 4 C C Ae d 1 4 4x 4x

Integrate fe dx 7x a 7e x C C Te Ob 1 7x 7 0 0 7e7x Od 1 e C e 7x

Find the derivative y x 7x 6x a y 5x4 21x 6 2 b y x 7x 6x 2 5x 21x 6 y x 7 x 6x 2 O d y x 7x 6x 5x 21x 6

The total revenue for a product is given by R x 20x x where x is the number of units sold What is lim R x x 8 a 91 b 64 c 96 Od 75 Oe 84

Find the derivative of the function y x x 6 a x5 y 5 x2 2 6x C b y 4x 1 C y 4x x d y 4x 1 6