Math - Others Questions

Question Owners of a bike rental company that charges customers between 5 and 25 per day have determined that the number of bikes rented per da can be modeled by the linear function n p 450 18p where p is the daily rental charg How much should the company charge each custom per day to maximize revenue Do not include units c dollar sign in your answer

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle Find the area of the largest possible Norman window with a perimeter of 20 feet Round your answer to one place after the decimal

A falling head permeability test gives these values L 29 73cm A area of the specimen 157 4cm a area of the vertical tube 4 61cm beginning head h 45 cm ending head h 12 cm Collected period is 5 mins Calculate the hydraulic conductivity in cm s

The graph of 0 5x 2y 3 is shown on the grid 3 2 S 54 142 14 1 3 AT 2 1 14 Z Which ordered pair is in the solution set of 0 5x 2y 3 A 2 0 5 B 2 1 C 2 1 D 2 0 5 4

1 Which ordered pair is in the solution set of y 2x 4 A 6 1 B 1 6 C 6 1 D 1 6 47 wana M in 10 68 1234 S 7 X

Len Use a transformation of the graph of y to graph the function h z 6 x 1 3 29 9 9 X 122 9 X

oblem 3 Consider the following 5 statements 2 of the statements are false in general Determine which 2 statements are false by testing out each statement on an appropriate matrix like we did with the properties of determinants in Section 3 3 of the tutorial file Note You should not use a magic or pascal matrix for i or ii below because they have special properties not shared by other matrices Try using rand instead 1 i If A is nxn then A and A have the same eigenvalues ii If A is n xn then A and A have the same eigenvectors iii If A is n n then det Ak det A k iv If I is the nx n identity matrix and J is an nxn matrix consisting entirely of ones then the matrix I is invertible and 1 1 J J n 1 n 1 v If I is the nxn identity matrix and J is an n x n matrix consisting entirely of ones then the matrix A I is idempotent i e A A J n 1 Don t forget that you are selecting which statements are false you are not selecting which statements are true A i and iv B iv and v C iii and v D ii and iv E iii and iv F i and v G ii and v H i and ii

dath 1111 Te wh Question 19 1 point Analyze the graph of the function R x 1 What is the domain of R x A x x 0 8 x x 5 5 C x x 0 25 D x x 5 E All real numbers For part 1 the answer is Type a letter 2 What is the equation of vertical asymptote s of R x A x 0 B x 5 5 C x 0 25 D x 5 E There is no vertical asymptote x x 10 x 25x A 3 What is the equation of the horizonta or oblique asymptote of R x A y 0 B y 1 C y 10 D y x E There is no horizontal or oblique asymptote

Use the intermediate value theorem to determine wh has a zero in the given interval f x 7x 6x 7x 8 2 1 a f 2 4 Listen A Simplify your answer b f 1 A plify your answer ding to the int

According to a particular test a normal score is 600 It can be with a score that satisfies the inequality 600 2 54 has an unusual score Determine the scores that would be considered unusual Only test scores less than 564 44 would be considered unusual Test scores between 564 44 and 635 56 would be considered unusual Test scores less than 564 44 or greater than 635 56 would be considered nusual Jy test scores greater than 635 56 would be considered unusual ge Next Fl

4 Listen List the potential rational zeros of the polynomial function f x 2x3 3x 4x 8 0 1 11 12 4 8 O 1 2 4 O 1 2 4 8 10

4 Listen Find all zeros of the function and write the polynomial as a product of f x x 3x 6x 12x 8 Of x x 1 x 2 x 2i x 2i f x x 1 x 2 x 2 x 2i f x x i 2 x 2 x 2 x 2 f x x 1 x 2 x 2 x 2

Question 5 1 point Listen For the polynomial list each real zero and its multiplicity Determine whether th graph crosses or touches the x axis at each x intercept f x x 3 4 x 815 O multiplicity 4 crosses x axis 8 multiplicity 5 touches x axis O multiplicity 4 crosses x axis 8 multiplicity 5 touches x axis multiplicity 4 touches x axis 8 multiplicity 5 crosses x axis multiplicity 4 touches x axis 8 multiplicity 5 crosses x axis

4 Licen Construct a polynomial function that might have the give 27 2 1 1 11 2 2 Wo Which of the following is a polynomial function that might have the given graph Of x x 2 x 1 x 1 2 x 2 1 1

Construct a polynomial function F zeros 1 1 and 4 degree 3 y intercept 12 Choose the correct answer below Of x 2 x 1 x 1 x 4 Of x 3 x 1 x 1 x 4 f x 3 x 1 x 1 x 4 2 2 x 1 x 1 x 4

di Listen The graph of the function hole and a horizontal asymptote The vertical asymptote equation is H T A Type an integer or a simplified fraction The X coordinate of the hole is A pe an integer or a simplified fraction orizontal asymptote nauti 32 15 25 2 has one vertical asymptote on

10 uestion 13 1 point Lite Lise the graph to find the horizontal asymptote if any and vertical asymptotes if any of the function 10 10 D 1 The A y 3 y 3 B no horizontal asymptotes C y 0 D y 3 y 3 y 0 2 The vertical asymptote s is are A no vertical asymptotes B x 3 x 3 x 0 C X 0 D x 3 x 3

Solve the abs 1 42 11 2 The smaller solution is fraction symbol A Type an integer or a simplified fraction Use the slash key as a The larger solution is on symbol A Type an integer or a simplified fraction Use the slash key as a

Form a polynomial whose zeros and degree are given Use a leading Zeros 3 2 3 degree 3 Of x x3 2x2 9x 18 f x x 2x 9x 18 f x x3 2x 9x 18 f x x3 2x2 9x 18

1 Which rational function has the given graph 3r 4 A 4 X

Use the given zero to find the remaining zeros of the f x x3 5x 17x 13 zero 2 3i O 2 31 1 3 21 1 2 31 1 3 21 1

4 Listen Give the equation of the oblique asymptote if any of the function x2 2x 8 x 4 f x x2 Oy x 6 no oblique asymptote y x 10 x y 2

41 Listen Use the Remainder Theorem to find the remainder when f x Is f x 3x6 5x3 8 x 1 OR 8 R 10 R 6 R 16

4 Listen Form a polynomial f x with real coefficients having the gl Degree 3 zeros 1 i and 5 Of x x x 8x 10 f x x3 5x 8x 12 f x x3 3x 8x 10 x x 3y 108 8

Listen Solve the inequality Express your answer using 5x 2 3 01 13 O 1 or 00 1 or a 1

If 3 x 6 7 5x are consecutive terms of a geometric progression G P with constan ratior 0 find the i value of x ii constant ratio

2 Compute gross profit on the sale of Job 201 Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare a job cost sheet for Job 201 and for Job 202 for the month Materials Labor Overhead Job Number Job Number 201 202

QUESTION 11 4 pts Find the following limits If the limit does not exist explain why You may NOT use guessing by plugging in values a lim 1 0 2e 2x 2 sin x

Graph the y 4 3 x 2

State the domain range for each of the following relations and if it is a function or not a 2 1 1 0 0 1 1 0 2 1 b 2 1 1 0 0 1 1 0 2 1 c 5 2 00 3 MM d e 5

g 0 6x 5x 6 h 6a 25 25a i 100 16x 60

d 0 5a 18a 9 e 6x 54 0 f 0 8n 20z

a 2 1 1 0 0 1 1 0 2 1 c f X Y 00 2 WONS following relations and if it is a function or not b 2 1 1 0 0 1 1 0 2 1 d g MA e h

ns Use long division or synthetic division to factor each polynomial completely with the given factor Then give the zeros of the function 1 f x x 5x 12x 36 x 2 2 f x x 7x 25x 175 x 7 3 f x 6x 25x 29x 20 2x 1 4 f x 3x 7x 25x 63x 18 x 2 Directions Divide using long division or synthetic division 5 x x 9x 44 x 4 6 4x 3x 20x 20 4x 3

Directions Find the zeros of the functions below by factoring 1 f x x 5x 6x 3 f x x 17x 16 5 f x 6x 7x 5x 7 f x 4x 5x 1 9 f x 4x 16x 25x 100 2 f x 2x 22x 56x 4 f x 2x 5x 7x 6 f x 3x 13x 4x 8 f x 4x 80x 204x 10 f x 3x x 12x 4

2 2

In this project you will create your own lottery game with a theme 1 Create at least 5 dollar amount prizes for your lottery game List them from the smallest prize to the largest prize 2 Create the probabilities for each prize in your lottery game using PERCENTS i e 30 0 5 etc Any percent is ok if they add up to 100 You may also want the probability to go down as the prize goes up but it does not have to be 3 Find the expected value for your lo4ery game 4 Using the expected value determine how much you are going to charge for a Ticket to play your game so that you can expect to make money over Eme 5 Choose a theme for your game it can be anything from pirates to sports to superheroes anything goes if it is appropriate 6 Finally create the back of your Lottery Ticket on a separate sheet of paper that shows the prizes and probabilities for your lottery Make sure to also have the cost of your Ticket visible as well Finally decorate the back of the Ticket to fit your theme 7 The Project will be submitted on paper In addition you can also post pictures of your project in Google classroom

Question A boat starts off 172 miles directly west from the city of Johnstown It travels due south at a speed of 30 miles per hour After travelling 126 miles how fast is the distance between the boat and Johnstown changing Do not include units in yo answer and round to the nearest hundredth

Directions Complete the follow providin formula booklet Round to 3 s f if not otherwise specified Six restaurant locations labelled A B C D E and F are shown together with their Voronoi diagram All distances are measured in kilometres 8 7 6 4 C

Two schools are represented by points A 2 20 and B 14 24 on the graph below A road represented by the line R with equation 2 y 4 passes near the schools An architect is asked to determine the location of a new bus stop on the road such that it is the same distance from the two schools y 28 24 20 16 12 8 4 A 2 20 B 14 24 R

3 km Island Provide your answer below 7 km Tent Shoreline A visitor is staying in a tent that is 7 kilometers east of the closest point on a shoreline to an island The island is 3 kilometers due south of the shoreline The visitor plans to travel from the tent to the island by running and swimming If the visitor runs at a rate of 6 kmph and swims at a rate of 5 kmph how far should the visitor run to minimize the time it takes to reach the island Round to two decimal places

Inn Provide your answer below 8 mi Shoreline 10 mi A visitor is staying in an inn that is 10 miles west of the closest point on a shoreline to a coral reef The coral reef is 8 miles due north of the shoreline The visitor plans to travel from the inn to the coral reef by running and swimming If the visitor runs at a rate of 5 mph and swims at a rate of 2 mph how far should the visitor run to minimize the time it takes to reach the coral reef Round to two decimal places

Question A bike rental company charges its customers p dollars per day to rent a bike where 5 p 30 The number of bikes rented per day can be modeled by the linear function n p 600 20p How much should the company charge each customer per day to maximize revenue Do not include units or a dollar sign in your answer Provide your answer below

Assume that a sample is used to estimate a population mean Find the 95 confidence interval for a sample of size 28 with a mean of 76 7 and a standard deviation of 12 2 Enter your answer as a tri linear inequality accurate to 3 decimal places ft

Use the formula above to determine the accumulated amount for each of the following different scenarios Round solutions to the nearest cent Assume there are 365 days in a year If 43 000 is invested for 27 years and earns 12 5 interest compounded annually the accumulated amount is If 43 000 is invested for 27 years and earns 12 5 interest compounded semi annually the accumulated amount is A If 43 000 is invested for 27 years and earns 12 5 interest compounded quarterly the accumulated amount is If 43 000 is invested for 27 years and earns 12 5 interest compounded monthly the accumulated amount is A If 43 000 is invested for 27 years and earns 12 5 interest compounded daily the accumulated amount is

Question Tent Provide your answer below 11 km 3 km Coral reef Shoreline A visitor is staying in a tent that is 11 kilometers west of the closest point on a shoreline to a coral reef Th coral reef is 3 kilometers due south of the shoreline The visitor plans to travel from the tent to the coral reef by running and swimming If the visitor runs at a rate of 7 kmph and swims at a rate of 2 kmph how f should the visitor run to minimize the time it takes to reach the coral reef Round to two decimal places

7 What is the constant of proportionality in the equation y 5x

etween a hot and cold reservoirs at T 1800 K and T 600 K respectively Use the Clausius nequality to evaluate and classify each case as reversible possible or impossible Your onclusion has to be based on the result of the evaluation of the inequality Also for each case ndicate if there is a violation of the first and or second law of thermodynamics Case kJ s Q kJ s Wnet kW Conclusion 100 350 200 250 a b 500 500

A refrigerator operates at steady state with a coefficient of performance of 4 5 and a power input of 0 8 kW Energy is rejected from the refrigerator to the surroundings at 20 C by heat transfer from metal coils attached to the back Determine a the rate energy is rejected in kW b the lowest theoretical temperature inside the refrigerator in K

Find a unit vector u in the direction opposite of 3 9 9 u 3 9 9