Math - Others Questions

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

In a lower one tailed hypothesis test chosen level of significance 0 10 sample size 55 and t test statistic 1 76 Which of the following is the conclusion O The null hypothesis is rejected There are many sampling errors O The null hypothesis cannot be rejected O This is a high probability and the conclusion is difficult

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

The Ransin Sports Company has noted that the size of individual customer orders is normally distributed with a mean of 112 and a standard deviation of 9 Which of the following is the answer for the probability that the next individual who buys a product will make a purchase of more than 116 48 33 42 O 71

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

Using Chebyshev s theorem for standard deviation calculate the percentage of data that lie within five standard deviations of the mean 96 50 89 75

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

2 Sketch a possible graph of the function f x on the grid below such that all the conditions below are met T 1 4 D x ERI 3 x 3 R lyERI Osy 4 f 2 3 f 1 2 The x intercepts are 3 and 3 The y intercept is at 4 Make sure to clearly draw the points on the graph

Your patient is ordered 1 2 g m2 day to infuse for 120 minutes The patient is 145 cm tall and weighs 68 kg The 5 g medication is in a 0 5 L bag of 0 9 NS Calculate the rate in which you will set the pump 8 25

en A 1 0 2 00 4 0 1 3 1 solve the system A x b where b 2 4

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

Evaluate f s 5 3x x dx a 39 b 5 c 16 25 d 65

Use properties of limits and algebraic methods to find the limit if it exists x 16 lim 4 x 4 Oa 8 Ob 8 c 6 Od 1 6 6

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

Use the graph to match the limit with the correct answer 0 6 lim f x x 2 lim f x x 2 lim f x x 2 ef 2 2 2 y f x 6 A 0 B DNE C 1

Integrate Oa 1 x 2x 5 3 C x 2x 5 2 x 2x 5 1 C Ob x 2x 5 x 1 dx C d x 2x 5 2 Od

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

Integrate 13 6x 21x dx a 6 126x5 b 13x 3x 3x7 OC 6 126x5 C d 13x 3x 3x C

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

Find the derivative y x 4 x 4 ln x4 5 ay x 4 x 2 In x 5 Ob y 4x 5 2x In x 5 x 4 x 4 y 4x 5 2x 3 In x4 5 x 4 x2 4 y 4x 5 2x 3 4x3 x4 5 Od x 4 5 4x3 x 5

Evaluate S 1 a 108 Ob 6 5 3x x dx c 90 Od 112

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

oblem 2 The graph of z f x y is shown below In each part determine whether the given partial derivatives are positive negative or zero Note that the function is symmetric about 0 in both the x and y directions 15 10 5 0 5 10 4 2 0 a f 2 2 and fxx 2 2 b fy 2 2 and fyy 2 2 c fx 2 0 and fxx 2 0 d fy 2 0 and fyy 2 0 2 A positive negative B negative zero C zero zero D zero positive E positive positive F positive zero G negative negative H negative positive D zero negative

16 What percent of the total population is found between the mean and the standardized z score 1 25 Use the standard normal distribution table and enter your answer to two decimal places

10 Find the sum of the first 30 terms of the arithmetic sequence whose first term is 15 and whose common difference is 4

4 Determine if U 0 1 0 and V 1 2 0 are parallel othogonal or neither

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places Z 0 90

3 Given U 3 2 5 find a a unit vector in the direction of U

Find the distance between U 0 1 2 and V 1 4 1

1 Find the dot product U V for U 4 1 V 6 3 8

2 Find the cross product UXV for U 1 3 4 V 2 7 5

Suppose the probability of an event is 0 60 What are the odds in favor of this event