Math - Others Questions

Consider the following sets a Compute the set S A 9 4 8 S 5z 8 ze A T x 5x A b Compute the set T Hint Be sure to read this set correctly see the Edfinity demo

Select all of the following that describe the set 1 2 3 OA ala Z OB bER 6 Z OC ffe R and f Z recall that If denotes the absolute value of f OD d de Z OE CER c EZ

Sam is an agricultural inspector who earns 3 528 per month He pays 308 per month for health insurance and 56 23 per month for vision insurance for himself and his wife His federal tax rate is 15 How much money will Sam save by having insurance premiums withheld before taxes are calculated

2 Use the table to write an equation that defines the volume V in quarts of the air in the diver s lungs at a given pressure P in atmospheres 3 Using the equation you wrote and P 1 write an equation that defines volume V at a given depth d for finding the value y at a depth We V r d Given equation is P 1 P 1 Here V Volume d depth T radiw 33 d 33 P 1 put in equation V Tr 33 P 1 then the equation of Volume is V 3 TTY P 1 4 Use technology to graph your equation Sketch the graph here Volume qt 14 12 10 80 5 4 2 O y 0 33 66 99 Depth ft 132 165 5 Identify any asymptotes How do they apply to the real world situation Here are some Common types of asymptotes and their real Word applications Horizontal asynodotes in finance a stocks Price may approach the market Stability 2 Vertical asymtote In chemistry reactant Concentrations do to reaction Kinetics x 198 a Certain value but neve reach it do may approach zuo but never reach it

For any function y f x the average rate of change of y with Ay Ar respect to x is Estimate the instantaneous rate of change when t 35

Example 2 An antiseptic spray is applied to a culture of bacteria The percent of bacteria b that are alive after t minutes is shown on the graph A secant has been drawn through the points for t 5 min and t 35 min A tangent has been drawn at the point where t 20 min a Calculate the slope of the secant Describe what the slope represents Explain the sign of the slope b Estimate the instantaneous rate of change of b with respect to t at t 20 min 100 Percent of bacteria 50 Percent of Bacteria against Time 0 5 80 20 43 35 26 20 Time minutes 40

3 What is the Domain of each of the following y 4 x 4 7 x y Y 1

3 3 2 3

Find the equation of a line determined by the given information 3 a slope of 3 b passes through 2 4 and 6 8 c slope of 3 passing through 1 3 a y intercept of 4

A function fis defined for all x and its values are given by 3 x if x 0 3 x if x20 Compute each of the following f 33 f 0 f 78 f x

1 Using limits find the slope of the tangent to the curve f x x 3 at the point where x 7

3 a What does the limit lim o f h 4 f 4 h 8 indicate about the function f x x

Is the following statement true Explain why or why not Provide an example to support your claim The limit of a function limx a f x may not exist even if f a exists

Using limits find the slope of the tangent to the curve f x x 3 at the point where x 7

Sketch the graphs here 2 Part D Use the graph to find the x value where the two designs have the same surface area to volume ratio For which values of x would the engineer choose the dorian Explain

Omar is a loan officer at a local bank He carries health insurance for himself his wife and their three children The monthly premium for health insurance that is deducted from his paycheck is 575 20 Omar s salary places him in the 15 federal income tax rate Calculate the amount of tax savings Omar will have if his health insurance premiums are withheld from his paycheck before his taxes are calculated

There are typically 31 gallons of beer in a standard barrel What is Shannon s market share in gallons if it brews and sells 3 430 barrels in 2014 Express your answer in percent to two decimal places Assume the total market size in barrels sold is 194 472 Do not include the symbol For example if you compute a market share of 5 785 percent you should enter 5 79

What is the type of economy in which the government controls the supply of goods but not the demand called O Command economy O Demand economy O Market capitalism

Assume that Shannon s brews and sells 3 720 barrels of beer in 2014 What will be Shannon s relative unit market share compared to its largest competitor in the DFW area Assume the total market size in barrels sold is 194 472 Express your answer in percent to two decimal places Do not include the symbol For example if you compute a market share of 5 785 percent you should enter 5 79

Assume that Shannon s brews and sells 3 470 barrels of beer in FY 2014 What will be Shannon s absolute unit market share in barrels sold during that period Round your answer to two decimal places but do not include the percent sign Assume the total market size in barrels sold is 194 472 For example if your answer is 6 7577 round to 6 76 again do not include the percent sign

3 What transformations of the parent graph of f x x produce the graph of k x 4x 12 12

1 The air in a diver s lungs takes up a volume of 4 qt at a depth pressure is 3 atm As the diver changes depth the pressure changes and so the volume of this air changes Find the pressure at each depth and use the fact that volume and pressure are inversely related to complete the table Depth ft 0 33 66 99 132 165 Pressure atm 3 Volume qt

6 The volume of air in a diver s lungs increases as the diver resurfaces This expansion can cause damage to the membranes of the lungs A diver fills her lungs with 4 qt of air at a depth of 66 ft How many quarts of air will she need to exhale during her ascent to still have 4 qt of air in her lungs when she reaches the surface Explain

3 Using the equation you wrote and P volume V at a given depth d d 1 write an equation that defines 33

5 Identify any asymptotes How do they apply to the real world situation

7 At greater depths the increased pressure causes a diver to use the air in the tank more quickly Assume that the amount of time a tank of air will last is inversely proportional to the pressure at the depth of the dive Suppose a tank has enough air to last 60 min at the surface How long will it last at a depth of 99 ft

3 1 The volume V of a sphere is given by V Tr where r is the sphere s radius Part A Solve the equation V 4 3 3 r for r Part B If a spherical ball has a volume of about 33 51 cm what is the ball s radius Round if needed Part C If a spherical ball has a volume of 500 cm what is the ball s radius Round if

6 Solve the radical equation 2x 36 2x 6

4 Leo solved the equation b a 1 for a but made an error Leo s work is 2 shown below Explain Leo s error and find the correct solution i ii iii iv 4b 1 a b a 1 2b a 1 4b a 1 3

Write 2 4 3a 3 8b in reduced radical form

The length of one side s of a shipping box is s x 2x where x is the volume of the box in cubic inches A manufacturer needs the volume of the box to be between 108 in 3 and 256 in What are the minimum and maximum possible lengths of s

1 Graph f x x 2 What are the domain and range of the function

5 The half life of caffeine is 5 h If you drink an energy drink with 80 mg of caffeine 5 the formula y 80 0 5 tells the amount of caffeine left in your system in mg after t hours How much caffeine will be left in your system after 8 hours Round as needed

3 3 Solve the equation 4x 32

5 What is the reduced radical form of 250 54 72

4 8 12 2 Simplify the expression 81m n

3 Write 7 3 2 in reduced radical form

Each of the following families of the differential equations depends on a parameter a Sketch the corresponding bifurcation diagrams as well as the phase lines on both sides of bifurcation values Identify the types of bifurcations that occur a x 1 ax x 3 b x x ax c x x x a X

Solve the following problems to calculate the cost of a printing job 1 A printer estimates that running a small press costs 25 00 per hour The total cost of a job that took 1 1 2 hours or press time is 650 00 How much of the cost of this job is unrelated to press time 2 A printer estimates that each page of a booklet costs 22 50 to produce How much will a 64 page booklet cost to produce 3 A printer uses two sided plates which cost 1 30 each Seventy cents is added to the price of each plate to cover the cost of chemicals to process the plate A job consisting of 32 flats is produced What is the total cost for the plates for this job 4 A skid of paper weighs 2 000 lbs and the paper costs 40 per lb How much is the skid worth 5 A service technician comes to fix one of our machines and they charge 75 per hour If they need five hours to fix the machine how much will it cost us

Q3 Consider the matrix A 0 1 0 0 0 1 a Find the eigenvalues A s doubly degenerate and the eigenvectors la i 1 2 3 c the operator A b Show that each of the sets la la la3 forms an orthonormal and complete basis c Consider the matrix U which is formed from the normalized eigenvectors of A Verify that U is unitary U U 1 d Show that U satisfies the relation U AU 12 0 0 0 22 0 1 2 22 23 are the eigenvalues of A

The results of the shirt sales research are as follows Demand Function P 600Q 180 000 Supply Function P 400Q 90 000 a If the government imposes a tax of Rp 10 000 per piece calculate the equilibrium price and quantity after the tax b Calculate the tax borne by consumers c Calculate the tax borne by producers d Calculate the tax revenue received by the government from these shirts

1 For each of the following statements i plug in at least four values of r on both sides of the point at which the limit is taken to obtain evidence not a proof that the statement is true ii Explain why the evidence in a is not a proof of the statement iii Prove that the statement is true by definition a lim 0 b lim 1 7 1 c lim 2 2 x 2 d limo 00 e lim In z 0 6 lim

2 Alison wants to use an affine cipher to encrypt messages containing capital let ters lower case letters and five symbols for punctuation period comma colon question mark and space a Verify that e x 28r 35 is a valid affine cipher for this extended alphabet b Calculate the decryption function for Alison s cipher c How many such ciphers are possible

U Show Transcribed Text J

2 A portion of the graph of f x sin x is shown a What is the domain of the function b What is the range of the function 2 y 24 1 5 1 0 5 1 9 0 5 1 5 2 2

Generate another 10 integer values from 0 to 50 and divide these by 5 these will be your y coordinates Use your values from the FIRST generation of UNORDERED integers as your x coordinates Create a scatter diagram and describe any linear correlation Compute x y s s for each set of coordinates above Graph x y on its scatter x y diagram Divide diagram into quarters and label the quarters as high or low x and y values Label each quarter with the sign of x x y y Create a spreadsheet that calculates Ex Ex Ey Ey for each scatter x y diagram Use these values to calculate x y s s r for each of the scatter diagrams and state the formulas for each variable calculated on the scatter diagram

In a High School a survey was taken of 130 students to find out which sports they liked The survey showed all the students who liked wrestling also liked football Of those who like wrestling 12 also liked baseball There were 43 students who liked basketball of those 29 liked football None of the students who liked basketball liked wrestling or baseball There were 87 students who liked football and 28 of them only liked football There were 49 students who liked baseball and 29 of them only liked baseball Use the information from the survey above to match the letters in the venn diagram with the sports A B Sports by Baseball d Wrestling av Basketball Football C Diagram Letter a A b B c C d D D

REDO 11 92 315 mg 12 8 787 792 ag 13 0 0020918 Tm 14 895 992 CL 15 0 0003285 GL 16 0 487 L 17 2 235 g 18 0 00049 km 19 0 035 dL 20 0 00012633 Kg g mL fg pg hL daL km m hL ag

A 44 Using the Venn diagram above find the following n U 4 n A 1 n AUB A B A nB 61 An B 44 61 85 X 18 X X 61 B 85

Suppose that out of 262 professional 119 of them owned a convertible 105 of them owned a giant screen TV 123 owned a sporting goods store 26 owned a convertible and a store 35 owned a TV and a store 64 owned a convertible and a TV 7 owned all three items Hint To answer the following questions draw and label a Venn diagram that numerically represents th information above 1 How many athletes did not own any of the three items 33 2 How many owned a convertible and a TV but not a store 57 3 How many athletes owned a convertible or a TV 160 4 How many athletes owned exactly one type of item in the survey 98 5 How many athletes owned at least one type of item in the survey 229 6 How many owned a TV or a store but not a convertible 74 X X