Functions Questions and Answers

A random variate has the following triangular density f x 1 16 min x 8 x 0 x 8 Develop algorithms to generate this variate using Inverse transformation 1 Write the density function f x in two parts 2 Find f 4 f 8 3 Find the expectation of x 4 Draw f x 5 Find CDF F x 6 Draw F x 7 Find F 4 F 8 and F 10 8 Find the inverse of F x 9 Find the random variate 10 Find the value of the random variate for U 0 0 5 8 and 1

According to a census bureau from 2000 to 2016 the population of a certain region grew from 276 million to 309 million What was the percent of increase The percent of increase is Round to one decimal place as needed

Last year Charlie had 30 000 to Invest He Invested some of it in an account that paid 8 simple Interest per year and he Invested the rest in an account that paid 5 simple Interest per year After one year he received a total of 1710 in Interest How much did he invest in each account

1 Using the common denominator what is an equivalent fraction for 5

t 2 8n t 6 8n The signal x t 4 A 6 has 811 O 1 Has real Fourier series coefficients with the even indexed terms equal zero O 2 Has complex Fourier series coefficients with the odd indexed terms equal zero O 3 None of the answers O 4 Has complex Fourier series coefficients with no symmetry O 5 Has imaginary Fourier series coefficients with the even indexed terms equal zero

The trigonometric Fourier series represents a single sided spectral representation O True O False

Use the revenue and cost functions below to answer parts A B and C R x 75x 3x 1 x 20 C x 125 14x 1 x 20 C 0 75 OD 0 175 B Complete the table x Millions 1 4 8 12 16 20 Profit Profit P x Millions 67

Hamada invests 20 000 at 8 annual interest leaving the money invested without withdrawing any of the interest for 8 years At the end of th years Hamada withdraws the accumulated amount of money the amount of interest assuming the investment earns simple interest is O a 37 018 60 O b 12 800 O c 32 800 O d 7 200

Question 5 1 pts Which of these is the correct way to allocate a dynamic memory location for an integer O int x new int O int x new int O int x int new

Question 4 1 pts The operator used to access a member function of an object using a pointer to the object is none of the above is correct

Factor completely 1 9 1 20 X

Use the graph of y f x to answer the following 7 in to 4 3 2 m A 2 3

3 Part 2 of 8 b Determine f 3 f 3 3 Part 3 of 8 X X c Find all x for which f x 1 If there is more than one value separate them with commas or write your answer in interval notation if necessary Select None if Value s of x for which f x 1 0 0 0 0 0 0 0 0 0 0

Use the graph of y f x to answer the following Part 1 of 8 3 a Determine f 3 f 3 2 X

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

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

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

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

The Customer Service Center in a large New York department store has determined that the amount of time spent with a custome about a complaint is normally distributed with a mean of 8 3 minutes and a standard deviation of 2 3 minutes What is the probability that for a randomly chosen customer with a complaint the amount of time spent resolving the complaint will be as follows Round your answers to four decimal places USE SALT a less than 10 minutes 0 7700 b longer than 5 minutes c between 8 and 15 minutes 0 5501

Determine whether p and p are logically equivalent or not by completing the given truth table 4 p p T Click to select F Click to select

y 29 5 X

Calculate 0 03cm 3 73mm 0 027m 340 m Give the result in mm do not round up your answer Write exact answer Your Answer I

It s true sand dunes in Colorado rival sand dunes of the Great Sahara Desert The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara extending over 700 feet in height However like all sand dunes they tend to move around in the wind This can cause a bit of trouble for temporary structures located near the escaping dunes Roads parking lots campgrounds small buildings trees and other vegetation are destroyed when a sand dune moves in and takes over Such dunes are called escape dunes in the sense that they move out of the main body of sand dunes and by the force of nature prevailing winds take over whatever space they choose to occupy In most cases dune movement does not occur quickly An escape dune can take years to relocate itself Just how fast does an escape dune move Let x be a random variable representing movement in feet per year of such sand dunes measured from the crest of the dune Let us assume that x has a normal distribution with 18 feet per year and a 3 2 feet per year USE SALT Under the influence of prevailing wind patterns what is the probability of each of the following Round your answers to four decimal places a an escape dune will move a total distance of more than 90 feet in 4 years X b an escape dune will move a total distance of less than 80 feet in 4 years c an escape dune will move a total distance of between 80 and 90 feet in 4 years

In the following problem check that it is appropriate to use the normal approximation to the binomial Then use the normal distribution to estimate the requested probabilities Suppose it is estimated that 3 3 of the general population will live past their 90th birthday In a graduating class of 785 hig school seniors find the following probabilities Round your answers to four decimal places LUSE SALT a 15 or more will live beyond their 90th birthday 0 9887 b 30 or more will live beyond their 90th birthday X c between 25 and 35 will live beyond their 90th birthday d more than 40 will live beyond their 90th birthday 0 0018

Given triangle JKL which of the following is a proper representation of the sine law a sin K I k sin L b kx sin K I x sin L Oc sinsink J K K Od sink sin L Question 16 1 point Saved Corinne invested 3200 in a three year regular interest CSB that earns 7 annually How much will her investment be worth at the end of the term a 6720 b 6192 c 3872

Webster s Widgets collects random samples of 100 widgets from their widget factory several times per shift and records the mean weight of the sample in grams The means of 400 samples are summarized in the following frequency table Range 6 87 2 Yes No 7 2 7 6 7 6 8 0 8 0 8 4 8 4 8 8 8 8 9 2 9 2 9 6 Frequency 21 73 103 108 76 15 4 The five number summary of the 400 sample means was found to be min 6 816 Q 7 617 median 8 0075 Q3 8 385 max 9 569 The three smallest values were 6 816 6 825 and 6 833 The three largest values were 9 370 9 514 and 9 569 The mean of the 400 sample means was 7 9877 with a standard deviation of 0 5360 a Sketch a histogram based on the frequency table Does it appear to be roughly symmetric and mound shaped b Compute the interquartile range Determine if there are any outliers in the data Recall that an outlier is a value above Q3 by more than 1 5 times the interquartile range or below Q by more than 1 5 times the interquartile range The rule described above identifies one outlier s c Compute the Pearson index Round your answer to four decimal places Does this indicate that the data is skewed

If f x x 4x and h 0 find the following and simplify a f x h b f x h f x h

Find the z value such that 39 of the standard normal curve lies between z and z Round your answer to two decimal places USE SALT

Compose f g x You must show your work for full crec f x 2x x 1 g x x 1 Find f g x

f x 10 5 10 5 5 10 g x 5 10

D Consider a sample with data values of 26 24 21 18 30 35 29 and 24 Compute the range interquartile range variance and standard deviation Round to 2 decimals if necessary Range Interquartile range Variance Standard deviation 0000

Use the following information Sales of organic food have increased rapidly in recent years The demand for organic food seems to be unquenchable says Laura Batcha of the Organic Trade Association Suppose the rate of increase in organic food sales from 2006 to 2016 in a certain country can be modeled by 6 43 1 26x 6 x 16 0 otherwise f x where x represents the number of years since 2000 and f x represents the rate of change in organic food sales in billions of dollars What were the total sales in billions of dollars of organic food in this country from 2007 to 2011 billion

Consider the following A 2016 report from the National Academies of Sciences Engineering and Medicine found that genetically engineered crops such as corn are safe to eat and do not harm the environment Suppose the rate of increase in the number of varieties of a herbicide tolerant genetically engineered crop from 2000 to 2016 can be modeled by the rate function f x 1 58 0 04x 0 0 x 16 otherwise where x represents the number of years since 2000 and f x represents the rate of increase in the number of varieties of the genetically engineered crop per year Use the model to determine the following Calculate the area under f x on the interval 10 x 16 Round your answer to the nearest whole number 13 Interpret the result The area under f x on the interval 10 x 16 describes the total increase in the rate of change in the number of varieties of the genetically engineered crop from 2010 to 2016 The area under f x on the interval 10 x 16 describes the rate of change in the number of varieties of the genetically engineered crop available in 2010 The area under f x on the interval 10 x 16 describes the number of varieties of the genetically engineered crop available in 2010 The area under f x on the interval 10 x 16 describes the total increase in the number of varieties of the genetically

4 Graph y 14 2xl and y 4 Then solve using the graphs a 14 2x1 0 b 14 2x1 4 10 19 17 6 9 y axis E JA

7 Write a formula for the piecewise defined function below f x 5 4 3 4 3 2 1 2 1 O H 1 2 1 2 3 4 X

3 Graphs of functions y f x are shown Sketch the graph of y If x I by hand on the same axes Domain of Ifl Range of I fl 2 2 X

5 Solve using the picture on the right a f x g x b f x g x f x x 7 5 15 14 13 12 11 10 9 8 7 6 5 10 3 g x 4

1 The figure shows a transformation of the graph of y x Write the equation of the graph Then find the domain and range of the function on the left 0 5 104 Equation D R

Fun Park charges an entry fee of 2 for any family with less than 5 members The park charges 3 less than the number of family members for the entry of any family with 5 or more members Write a piecewise equation for this situation 5 f x 3 7 5 f x 2 f x f x m x 3 x 5 5 52 0 x 4 22 0 x 2 x 5 x 3 0 x 5 x 3 x 5

Determine the area of the shaded region in square units 3 5 3 2 5 2 1 5 1 0 5 2 square units 4 68 10 12 14 16 X

13 Give instructions for preparing 500 mL of a 0 5 M solution of Mg OH FW 58

Suppose that the average score on the Scholastic Aptitude Test now known simply as the SAT in a particular year can be determined by solving the equation 649 2 m 1 96 380 Solve for m m Interpret the result This is the Select score on the SAT for this particular year Need He Submit Ans 0 Points NOTES Solve the ed Select exact

Use this table to compute the percent error when writing 15 in decimal form Round your answer to two decimal places 32

Use this table to convert 0 781 decimal inch to fraction inches

Find the area of the shaded region in square units 11 10 9 006 8 7 6 5 4 3 2 1 1 square units f x 10 2x 2 3 4 5 6

3 Given the graph below a Does this equation represent growth or decay Exer b What is the domain c What is the equation of the asymptote 4 0 x d State the intervals of increase or decrease increases Decan X

Solve for x Leave the answer as a reduced fraction and enter negative signs if any in the numerator 625 5 7 2 3125 X

Use the following information for the Exercises below Algo The following information applies to the questions displayed below On December 1 Jasmin Ernst organized Ernst Consulting On December 3 the owner contributed 85 460 in assets in exchange for its common stock to launch the business On December 31 the company s records show the following ite and amounts Cash Accounts receivable Office supplies Office equipment Land Accounts payable Common stock Exercise 1 20 Algo Preparing a balance sheet LO P2 Assets 6 650 Cash dividends 18 650 Consulting revenue Rent expense 4 640 19 560 Salaries expense 46 000 Telephone expense 9 890 Miscellaneous expenses 85 460 Use the above information to prepare a December 31 balance sheet for Ernst Consulting Cash Accounts receivable Office supplies Office equipment Land ERNST CONSULTING Balance Sheet 6 650 Common stock 18 650 4 640 19 560 46 000 Accounts payable Equity Liabilities X S X XX 85 460 85 460 X X 3 490 18 650 4 920 8 500 X 9 890 X 890 700

Business at your design engineering firm has been brisk To keep up with the increasing workload you are considering the purchase of a new state of the art CAD CAM system costing 360 000 which would provide 6 000 hours of productive time per year Your firm puts a lot of effort into drawing new product designs At present this is all done by design engineers on an old CAD CAM system installed five years ago If you purchase the system 30 of the productive time will be devoted to drawing CAD and the remainder to CAM While drawing the system is expected to out produce the old CAD CAM system by a factor of 3 1 You estimate that the additional annual out of pocket cost of maintaining the new CAD CAM system will be 200 000 including any tax effects The expected useful life of the system is eight years after which the equipment will have no residual value As an alternative you could hire more design engineers Each normally works 1 800 hours per year and 60 of this time is productive The total cost for a design engineer is 65 per hour There are five design engineers Identify the net cash flows benefits and costs associated with the drawing activities if the CAD CAM system is purchased instead of hiring more design engineers In year 0 the net cash flow associated with the drawing activities if the CAD CAM system is purchased instead of hiring more design engineers will be Round to the nearest dollar