Math - Others Questions

A car rental company s standard charge includes an initial fee plus an additional fee for each mile driven The standard charge S in dollars is given by the function S 14 95 0 50M where M is the number of miles driven The company also offers an option to insure the car against damage The insurance charge I in dollars is given by the function I 5 70 0 15 M Let C be the total charge in dollars for a rental that includes insurance Write an equation relating C to M Simplify your answer as much as possible 0 C X

Trey and his wife are each starting a saving plan Trey will initially set aside 250 and then add 155 every month to the savings The amount A in dollars saved this way is given by the function A 155N 250 where N is the number of months he has been saving His wife will not set an initial amount aside but will add 395 to the savings every month The amount B in dollars saved using this plan is given by the function B 395 N Let T be total amount in dollars saved using both plans combined Write an equation relating T to N Simplify your answer as much as possible

Write the equation of a sine or cosine function to describe the graph FIN 70 2 RIN 2 3 2 2 fela 5 T 0

The Sugar Sweet Company delivers sugar to its customers Let C be the total cost to transport the sugar in dollars Let S be the amount of sugar transported in tons The company can transport up to 20 tons of sugar Suppose that C 110S 3500 gives C as a function of S Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values O amount of sugar transported in tons O cost to transport sugar in dollars O amount of sugar transported in tons O cost to transport sugar in dollars Set of Values Choose one Choose one

A small publishing company is planning to publish a new book Let C be the total cost of publishing the book in dollars Let N be the number of copies of the book produced For the first printing the company can produce up to 200 copies of the book Suppose that C 20N 500 gives C as a function of N during the first printing Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set of values Domain Range Description of Values Onumber of copies produced O cost of publishing book in dollars Onumber of copies produced O cost of publishing book in dollars Set of Values Choose one Choose one

The population sizes of many animal species rise and fall over time Suppose that the population size of a certain species can be modeled by the following p t 4002 1224 cos In this equation p t represents the total population size and f is the time in years Suppose we start at 1 0 years During the first 9 years when will the population size be 4700 Do not round any intermediate computations and round your answer s to the nearest hundredth of a year If there is more than one answer enter additional answers with the or button t 7 years or O

Suppose a projectile is fired from a cannon with velocity vo and angle of elevation 0 The horizontal distance R 0 it travels in feet is given by the following R 0 vo sin 20 32 If vo 80 ft s what angle in radians should be used to hit a target on the ground 106 feet in front of the cannon 0 Do not round any intermediate computations and round your answer s to the nearest hundredth of a radian If there is more than one answer enter additional answers with the or button 0 rad or

Suppose that an airplane is asked to stay in a holding pattern near an airport The distance of the plane to the airport is described by the following d t 149 67 sin 7 t 9 In this equation d t is the distance of the plane to the airport in miles and t is the time in minutes after the plane enters the holding pattern During the first 9 minutes after the plane enters the holding pattern when will the plane be 110 miles from the airport Do not round any intermediate computations and round your answer s to the nearest hundredth of a minute If there is more than one answer enter additional answers with the or button t 0 minutes or

For a fixed location the number of sunlight hours in a day fluctuates throughout the year Suppose that the number of daily sunlight hours in a particular location can be modeled by the following L t 12 2 9 cos 2 365 In this equation L t is the number of sunlight hours in a day and I is the number of days after June 21st So 1 0 means June 21st 1 1 means June 22nd 1 2 means June 23rd etc Suppose we start at 1 0 which is June 21s During the first 365 days when will there be 13 hours of sunlight Do not round any intermediate computations and round your answer s to the nearest day If there is more than one answer enter additional answers with the or button t days after June 21 st of D

The length of a rectangle is 1 yd more than twice the width and the area of the rectangle is 66 yd Find the dimension the rectangle Length 0 yd 010 5

A model rocket is launched with an initial upward velocity of 188 ft s The rocket s height h in feet after t seconds is given by the following h 1881 16 2 Find all values of t for which the rocket s height is 92 feet Round your answer s to the nearest hundredth If there is more than one answer use the or button ground 1 0 seconds or X

The table of ordered pairs x y gives an exponential function Write an equation for the function 0 X 1 0 1 2 y 14 7 7274 8 08

Let 0 be an angle such that sec 0 4 and tan0 0 Find the exact values of cote and csc 0 cot0 csc0 X

The table of ordered pairs x y gives an exponential function Write an equation for the function 0 X 1 0 1 y 5 10 20 2 40 8 08

At the beginning of a study a certain culture of bacteria has a population of 40 The population grows according to a continuous exponential growth model Aft 12 days there are 124 bacteria a Lett be the time in days since the beginning of the study and let y be the number of bacteria at time t Write a formula relating y to t Use exact expressions to fill in the missing parts of the formula Do not use approximations y 0 b How many bacteria are there 13 days after the beginning of the study Do not round any intermediate computations and round your answer to the nearest whole number bacteria X In S

A laptop computer is purchased for 1600 Each year its value is 75 of its value the year before After how many years will the laptop computer be worth 300 or less Use the calculator provided if necessary Write the smallest possible whole number answer yea years X

Nicole is going to fill a beaker with two solutions The table shows the amount in ounces she could fill with solution A along with the amount in ounces she would then fill with solution B Using x for the solution A amount and y for the solution B amount do the following Plot the ordered pairs described by the table Write an equation relating x and y Solution A amount x Solution B amount y in ounces in ounces 1 15 8 10 8 6

Incremental Analysis of Special Sales Order Decision Ludolph Industries has an annual plant capacity of 74 000 units current production is 59 000 units per year At the current production volume the variable cost per unit is 31 00 and the fixed cost per unit is 4 40 The normal selling price of Ludolph s product is 46 00 per unit Ludolph has been asked by Bramwall Company to fill a special order for 11 000 units of the product at a special sales price of 23 00 per unit Bramwall is located in a foreign country where Ludolph does not currently operate Bramwall will market the units in its country under its own brand name so the special order is not expected to have any effect on Ludolph s regular sales Read the requirements Revenue from special order Less expenses associated with the order Less Variable manufacturing cost Contribution margin Less Additional fixed expenses associated with the order Increase decrease in operating income from the special order Incremental Analysis of Special Sales Order Decision Total Order 11 000 units 253 000 Revenue from special order Less expenses associated with the order Less Variable manufacturing cost Contribution margin Less Additional fixed expenses associated with the order Increase decrease in operating income from the special order 0 Total Order 11 000 units possible CO Ludolph should accept the special sales order because it will increase operating income Requirement 2 How would your analysis change if the special order sales price were to be 38 00 per unit and Ludolph would have to pay an attorney a fee of 17 000 to make sure it is complying with export laws and regulations relating to the special order Enter a 0 for any zero balances Use parentheses or a minus sign to indicate a decrease in contribution margin and or operating income from the special order test

The function T x 17 4 In shows the relationship bety and the amount of time the money is invested For this function x represents the starting amount of the investment and T represents the amount of time in years The function measures the amount of time needed for the starting amount to grow to 8000 Luis is interested in a 13 year investment and wants to know what his starting investment should be A Draw a graph that shows the function as it intersects the time value 13 years and state the window you used Graph Window used Format is Xmin Xmax X Xin Ymax B According to your graph what is the starting value of the investment needed x for the 13 year investment Round your answer to the nearest 0 01 algebraic couation that would determine the initial investment x needed for the 13 year

The table shows the time in minutes that it took Kareem to read different numbers of pages of his book Using x for the number of pages and y for the time do the following Plot the ordered pairs described by the table Write an equation relating x and y Number of pages x 2 Time y in minutes 3 6 12

The temperature of a cup of hot coffee in degrees Fahrenheit can be modeled by the function T x 75 82 0 97 where x is the number of minutes after the cup of coffee has been poured into the cup Determine how many minutes it will take until the coffee reaches a temperature of 117 F The amount of time is A Less than 17 minutes B Between 17 and 20 minutes C Between 20 and 23 minutes D Between 23 and 26 minutes E More than 26 minutes

4 5pts How many full sib progeny are needed to achieve an accuracy of 0 9 if the h for a trait is 0 34 What does this mean in terms of management

The yearly tuition cost at a specific university in California has been increasing exponential rate In 1990 the yearly tuition cost was 5700 In 2007 17 years later the yearly tuition cost was 12 400 The yearly tuition cost can be modeled by the formula P Ce where t measures the number of years since 1990 A Use the data points to determine the value of k in the formula P Ce Use 6 decimal places for the value of k Do not round any decimals in the middle of your solution B Write the formula using your value of k This means your formula P Ce should have the constants C and k plugged in C Use your formula from part B to determine the year when the tuition cost will first reach 30 000 Malta gure you state the year not just the number of years it will

Solve for x using the natural logarithm A x ln 7 In 7 1 4 B x In 6 4 C x D x ln x ln 7 1 E x ln e4x 1

Solve for x A x 2 5 only x only B x C x 3 6 only D x 6 only E x 3 only log 5 x log 2 x 3

Consider the beam assembly shown below Two horizonal beam member A B and B D are connected by a double shear pin at B Note that points A and D are a simple roller and pinned supports respectively A 1 8m long beam E F is parallel to A D and fixed onto a wall at F A 2m long axial member C E is perpendicular to A D and joined to other beam members by single shear pins at C and E The two members between A D are loaded by a uniformly distributed load 5 kN m Assume that all pins are frictionless Take E 200 GPa for all beam members a a cross section i A 2 m 5 kN m B E C 1 m 1 m Figure 3 Beam assembly A a F D a Draw the shear and ending moment diagrams between A and D b Draw the shear and bending moment diagrams between E and F a If shear stresses in the pins cannot exceed Tyield 40 MPa find the minimum diameters of pins at B and C Use F S 2 5 c Find the maximum bending stress in the member E F and draw the corresponding strain and stress distributions at the cross section where the maximum bending stress occurs i If the member E F has a 10cm tall and 5cm wide rectangular cross section as shown in inset i ii If the member E F has a 5cm radius circular cross section as shown in inset ii

Find the equation of the quadratic function f whose graph is shown below 3 4 2 7 8 10

Use properties of logarithms to completely expand the logarithmic expression Wherever possible evaluate logarithmic expressions 8 R T

Answer the following compound interest questions Show your work algebraically and use correct rounding and units for your answers A The amount of money in a savings account is modeled by A 7000e0 063r where t is measured in years since money was first placed in the account Determine how many years it would take until the account has a value of 37 000 Round your answer to the nearest 0 01 years

Determine the domain and range for the function g x log 3 8x A Domain 0 00 Range 0 00 13 00 B Domain C Domain D Domain m 100 3 8 8 318 E Domain 00 Range 0 00 Range Range 0 00 Range 0 00

4 Solve for x A x B x In 7 0 3 E x In 6 0 3 C x ln 4 0 3 D x ln 7 0 3 In 4 0 3 10 1 e 0 3 2

The one to one function h is defined below h x 7x 9x 2 Find h x where his the inverse of h Also state the domain and range of h in interval notat h n x Domain of h

Suppose Maria invests 25 000 in an account bearing 5 7 interest compounded monthly How long will it take for the deposit to triple in value Do not round your decimals in the middle of the solution Round your answer to the nearest 0 01 year

Determine the inverse of y f x 2 ln x 6 A f y 2 e 6 B f y e 6 C f y 2 e 6 D f y e 6 E f y 6 ln y 2

Consider a 400mm long beam with a pinned left and simple roller right supports at each end respectively The beam is subjected to three concentrated forces P P and 3P as shown in the figure below The beam cross section with detailed dimensions is shown in the figure right Take E 200 GPa Length unit mm X 100 P 100 A 3P 50 50 4 100 12 Figure 2 Beam with concentrated loads and cross section 16 Neutral axis a Find the location of the neutral axis on the beam cross section and the moment of inertia about the neutral axis b If Ex 50 x 10 5 at A determine how much P is given that the applied forces are P P and 3P The point A see the red dot right is 3 mm from the top edge of the cross section and the section containing the point A is shown in the figure i e at 150 mm from the roller support c Draw the shear and bending moment diagrams for the beam using the value of P you found in part b Use the graphical method to get full credit Label your diagrams with appropriate values and justify them showing your calculations d Find the maximum tensile and compressive stresses max in the beam and indicate their locations e If the cross section is flipped 180 from the inversed T to T shape how much would the maximum compressive and maximum tensile stresses be

A blog surveyed 96 college students regarding which popular search engines they use regularly in their research and obtained the following information 10 use Site A Site B and Site C 21 use Site B and Site C 28 use Site A and Site C 35 use Site A but do not use Site B 80 use Site A or Site C 11 use only Site C 2 use none of these three sites How many of those surveyed use Site A How many do not use Site C Select the appropriate problem solving method A Guessing is okay OB Use the counterexample principle OC Look for patterns D Draw pictures How many students use Site A

Find the number of elements in sets A B and C using the given information Anc 0 n An B 6 n C B 4 n B C 10 n B U C 19 n A U B 18 Choose the appropriate problem solving method below A Draw pictures B Look for patterns OC Try a simpler version of the problem OD Try guessing Select the correct choice below and fill in the answer box es within your choice O A n A n B n C Simplify your answers OB There is an inconsistency caused by the given value of and the answers cannot be found

K In the set of the ten top grossing movies of all time shown in the table available below define the sets as shown below M the set of movies that earned more than 1 5 billion L the set of movies that earned less than 2 billion B the set of movies that were made before 2015 Describe the set L M U B in words and then find the set Click on the icon to view the table of the ten top grossing movies of all time CITE Describe the set L M U B in words Choose the correct answer below A The set of movies that earned less than 2 billion that did not earn less than 1 5 billion or were made before 2015 B The set of movies that earned more than 2 billion or earned less than 1 5 billion or were made before 2015 C The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were not made before 2015 OD The set of movies that earned less than 2 billion that did not earn more than 1 5 billion or were made before 2015 Identify the elements of the set L M U B Type the letter s of the movie s that is are in the specified set For example an answer could be B a b d g h j L M U B Use a comma to separate answers as needed Table of the Ten Top Grossing Movies Movie Movie a Movie b Movie c Movie d Movie e Movie f Movie g Year 1996 1994 2015 1992 2015 2015 2010 Gross billions 2 9 2 3 1 8 1 5 1 5 1 4 1 3

Find if possible the number of elements in sets A B and C using the given information If there is an inconsistency state where it occurs AnB 0 n An C 6 n B nC 5 n C A 6 n A C 4 n U 16 Select the correct choice below and fill in the answer box es within your choice O A n A n B n C Simplify your answers OB There is an inconsistency caused by the given value of and the answers cannot be found

K A group of young adults who were asked which issues would be important during the next decade gave the following answers 12 believed that nuclear war terrorism and environmental concerns would be important 44 believed that nuclear war would be important 15 believed that nuclear war and terrorism would be important 22 believed that nuclear war or terrorism but not the environment would be important 28 believed that nuclear war and the environment would be important 17 believed that terrorism but not nuclear war would be important 9 believed that only the environment would be a serious issue 4 believed that none of these issues would be important Complete parts a through c Points 0 of 1 a How many people were surveyed people Simplify your answer

Under 41 Y oung 41 to 55 M iddle aged Over 55 S enior Total K An exercise video company surveyed its customers to determine whether they prefer to purchase videos using an access code to download them from a website purchase them on DVDs or access them via a podcast The results are shown in the table Use the table to find the cardinal number of the set A YUS Access Code A Podcast P 12 32 13 57 22 46 31 99 The cardinal number of the set A Y US is DVD D 8 6 7 21 Simplify your answer Total 42 84 Points 0 of 1 51 177 Save

For the given confidence level and values of x and 7 find the following x 44 n 96 confidence level 99 Part 1 of 3 a Find the point estimate Round the answers to at least four decimal places if necessary The point estimate for the given data is 4583 Alternate Answer 0 4583 Part 1 3 Part 2 of 3 b Find the standard error Round the answers to at least four decimal places if necessary

K O Points 0 of 1 There are 86 people protesting the destruction of the rain forests There are 37 males 22 of whom are students and 20 female nonstudents How many female students are protesting There are female students protesting Simplify your answer Save

K In the set of the ten top grossing movies of all time define the sets shown below the set of movies that earned more than 900 million the set of movies that won a movie award B the set of movies that were made before 1970 Describe the set En B in words and then find the set E A Define the set En B in words Choose the correct answer below A The set of movies that earned more than 900 million and were made before 1970 O B The set of movies that earned more than 900 million and were made after 1970 OC The set of movies that earned less than 900 million or were made after 1970 D The set of movies that earned more than 900 million or were made before 1970 Identify the elements of the set En B Type the letter s of the movie s that are in the specified set For example an answer could be En B a b m EnB Use a comma to separate answers as needed Data table 11111 Movie Movie a Movie b Movie c Movie d Movie e Movie f Year 1958 1942 1965 1979 1983 1934 Inflation Adjusted Gross millions 1 326 1 219 985 950 909 883 990 Won Movie Awar Yes Yes Yes Yes Yes No Yes

Describe the set by referring to the numbered regions WOX NY What is are the number s for the region s describing the set W nx nY Type a whole number Use a comma to separate answers as needed

F Describe the set by referring to the numbered regions E What are the numbers for the regions describing the set E Type a whole number Use a comma to separate answers as needed

The formula for the volume V of a cylinder with radius and height h is as follows V nr h Suppose the height of the cylinder is 7 units shorter than the radius Rewrite V in terms of only It is not necessary to simplify

The numbers in the regions of the given Venn diagram indicate the number of elements in each region Use the diagram to solve for the indicated set n A B 5 A6 10 n A B Simplify your answer

Gun ownership A friend read online that 30 or less Americans have a gun in their household I claim that the percent of Americans that have a gun in their household is actually greater than 30 To test this claim I survey 200 random Americans and find that 74 of them have a gun in their household At the 05 alpha level what should I conclude about my claim a Select the correct null and alternative hypotheses O Ho p 0 3 Ha p 0 3 O Ho p 0 37 Ha p 0 37 O Ho P 0 3 Ha p 0 3 Ho p 0 37 Ha p 0 37 OH P 0 37 Ha p 0 37 O Ho p 0 3 H p 0 3 b Find the p value round to four decimal places c Write the final conclusion using everyday language using a 5 level of significance O There is not sufficient evidence to reject my claim O There is sufficient evidence to reject my claim There is not sufficient evidence to support my claim There is sufficient evidence to runner

In the universal set U a b c h define subsets of cars with the characteristics shown to the right Describe the following set in words and then find the set WOG Click on the icon to view the table of new car features Define the set Wn G in words Choose the correct answer below 00000 A The set of cars that have 3 or more years warranty or do not have a good safety rating B The set of cars that have 3 or more years warranty and do not have a good safety rating C The set of cars that have 3 or more years warranty and have a good safety rating OD The set of cars that have 3 or more years warranty or have a good safety rating Identify the elements of the set Wn G Select all that apply A e C h E f G a I I Wn G is the empty set B C D d F g H b P price is above 20 000 C is compact G has a good safety rating A has antitheft package W warranty is at least three years