Functions Questions and Answers

In an aquarium there are 10 large fish and 5 small fish Half of the large fish are red One fish is selected at random Find the probability that it is a large red fish Write your answer as a fraction 00

The hourly wages of a sample of 34 employees of a textile company are summarized in the table below Number of employees 3 E 17 14 Hourly wage in dollars 6 00 7 75 9 75 Find the mean hourly wage of these 34 employees Round your answer to at least two decimal places

A real number between 0 and 10 will be picked according to the probability distribution shown in the figure Regions under the curve are labeled with A B C and D The area of each region is shown in the table A 0 1 2 B 1 3 4 C 5 6 7 D 8 Use the figure and the table to answer the parts below 9 10 11 a Find the probability that a real number between 0 and 4 is picked 1 b Find the probability that a real number between 2 and 7 is picked 0 Region A B D X Area 0 10 0 30 0 45 0 15 S

Problem ID PRABM6PR Complete the table with the area of each square in square units and its exact side length in units a A figure area side length 8 A B C D D E Create and fill in the table using the table button

Problem ID For the polynomial function f x x 2x 5x 6 we have f 0 6 f 2 4 f 2 0 f 3 0 f 1 8 f 1 0 Rewrite f x as a product of linear factors f x 2019 Illustrative Mathematics All Rights Reserved Type your answer below mathematical expression

e doesn Problem ID PRABR7TF Which one doesn t belong Explain your reasoning A 2 9 B 932 C 2 2 2 2 16 D a 2 a

Given f x 4x 3 and g x x 3 determine f g x and state what you can conclude about f x and g x Oa f g x O X therefore f x and g x are inverses of each other b f g x x therefore f x and g x are not inverses of each other Oc f g x x 2x 2 therefore f x and g x are not inverses of each other Od f g x x x 2 therefore it cannot be determined whether f x and g x are inverses of each other

Which equation describes the line with slope that passes through the given point on the graph y x y 3x 2 y x y x 1 Y 5 5 I

Express the given percent as a decimal 8 Round to five decimal places as needed

tch the correct term to its description below given a function in the form y a sin k x d c this V represents a horizontal compression with respect to y sin x the name of one complete repetition of the pattern for a periodic function having the curved form of a sine or cosine wave given a function in the form y a sin k x d c this 1 represents a translation down with respect to y sin x the domain of a sinusoidal function given a function in the form y a sin x d c this represents a translation to 2 d 0 3 4 c 0 5 XER cycle k 1

A periodic function f x has a maximum value of 34 and an amplitude of 10 What is the minimum value of the function a 34 Ob 24 O c 4 d 14

Translate the English sentence into an equation using the variables indicated The length of the rectangle is 10 meters shorter than five times the width Use L for the length and W for the width of the rectangle The equation is

Assume that the spinner cannot land on a line Determine the odds against the spinner landing on the color red The odds are cwer R

Watch the video and then solve the Click here to watch the video Solve the triangle A 50 b 5 c 7 a Do not round until the final answer Then round to the nearest tenth as needed B Do not round until the final answer Then round to the nearest degree as needed o C Do not round until the final answer Then round to the nearest degree as needed A b 5 50 C c 7 a B

Solve the following by using the square root property of equality 1 1 18 www y 6 2 Simplify your answer Type exact answers using radicals as needed Use a comma to separate answer needed

A circle with center 7 3 and radius of 5 is graphed below with a square inscribed in the circle 10 JA G Part A Dillon and Chelsey are discussing how to write the equation of a tangent line to circle J through point G Both agree that they start the problem by drawing the radius JG and find the slope of that segment They also know that a tangent line is perpendicular to the radius Dillon says to write the equation of the tangent line you need the opposite reciprocal slope of the slope of the radius and Chelsey says you need to use the same slope as the radius Who is correct and why Write the equation of the tangent line Part B Find the perimeter of FGHI Part C Find the area of FGHI Part D Prove FGHI is a square

utorial Assignment and Test Page Fall 2022 hboard My courses SC MATH1506 A B C D E F G H I Mathematics I for the Biological and Health Sciences Tutorial Assignment and Test Page Fall 2022 C estion 12 ot yet swered arked out of 00 Flag question Mathematics I for the Biological A fungal colony grows on a flat surface starting with a single spore The shape of the colony edge is circular with the initial site of the spore at the centre of the circle Suppose the radius of the colony increases at a constant rate 15 3 units per unit time At what rate does the area covered by the colony change when the radius is 30 9 units O a 91788 4969 O b 48 0664 O c 1485 2508 O d 2970 5015 O e 1470 8308 Fir

Jse a calculator to approximate the expression If the expression is not a real number and an approxima possible so state A 2 258 Select the correct choice below and if necessary fill in the answer box to complete your choice OA 2 258 OB The solution is not a real number Round to three decimal places

A tennis pro s workout schedule is to have both morning and afternoon practice for 3 days rest for 1 day have only morning practice for 2 days rest for 2 days and then start the cycle again If the tennis pro is on her rest for one day part of the schedule determine what she will be doing a 22 days from today b 50 days from today c 142 days from today and d Will the tennis pro have a day off 82 days from today a What day of the workout schedule will the tennis pro be on 22 days from now OA Second rest day of the cycle OB First training day of the cycle C Second training day of the cycle OD Third rest day of the cycle b What day of the workout schedule will the tennis pro be on 50 days from now OA Second training day of the cycle OB Fourth training day of the cycle OC Fifth training day of the cycle OD Third training day of the cycle

orial Assignment and Test Page Fall 2022 Doard My courses SC MATH1506 A B C D E F G H I Mathematics I for the Biological and Health Sciences Tutorial Assignment and Test Page Destion 19 ot yet nswered Marked out of 1 00 Flag question A ball is dropped from a height of 196 5 meters Its height above ground in meters t seconds later is given by s t 18 2 2 196 5 What is the instantaneous velocity of the ball when it strikes the ground a 59 80 Ob 7152 60 c None of these choices are correct Od 59 80 Oe 119 60 Of 119 60

of stion Consider the following table and assume that f x and g x are differentiable functions with values as given X 1 2 3 4 f x 5 9 9 2 1 9 6 g x 8 6 5 3 4 2 9 f x 1 6 5 7 0 8 9 1 g x 2 3 6 7 7 7 4 6 Calculate h 4 if a 25 77 Ob 49 16 c 67 55 Od 19 77 Oe This derivative does not exist f 21 77 h x 2x f x g x

f cion Consider the following table and assume that f x and g x are differentiable functions with values as given X 1 2 3 4 f x 0 9 2 2 8 24 g x 4 4 2 5 6 2 2 5 f x 7 1 5 1 4 3 5 g x 3 4 2 7 6 3 4 4 Calculate h 1 if O a 1 77 O b 1 46 O c 6 40 Od The derivative does not exist e 0 16 f 1 61 h x g x

Tori rode her bike for 7 hours at 12 mph to get her van She drove back at 42 mph How long did the entire trip take hours

14 aved ut of uestion In thermodynamics the Van der Waal s equation relates the mean pressure p of a substance to its molar volume v at some temperature T as follows p 7 v v1 4 RT Chemists are interested in the curves called isotherms described by this equation when the temperature is held fixed and R is a constant What is the value of dp dv when p 9 5 and v 8 6 O a 3433 377885 O b 1 316025 O c 1 358804 O d 0 945161 O e 1 322943

Biological and ard My courses SC MATH1506 A B C D E F G H I Mathematics I for the Biological and Health Sciences Tutorial Assignment and Test Page Fall 2022 Online Ass 10 aved ut of estion What is the tangent line to when x 4 9 O a y 294560 5100x 1333246 6558 O b This tangent line does not exist O c y 0 8107x 110112 9525 O d y 2 6754x 13 1094 O e y 2 6754x 110112 9525 Of y 2 6754x 110099 8431 Clear my choice y x 3 z

18 ved ut of estion If what is B C D E F G H I Mathematics I for the Biological and Health Sciences Tutorial Assignment and Test Page Fall 2022 Online Assignments Assignmen O a The 118th derivative is sin x O b This derivative does not exist O c The 118th derivative is cos x Od The 118th derivative is sin x O e The 118th derivative is cos x O f The 118th derivative is sin x cos x Clear my choice f x sin x f 118 r

Consider the following table x f x g x f x g x 02 5 0 2 2 3 0 11 24 4 1 1 33 3 2 3 What is h 3 if O a 5 O b 0 O C This derivative does not exist O d 10 O e 10 Cloar muchoice h x f g x f x

The population of Adamsville grew from 7 000 to 11 000 in 7 years Assuming uninhibited exponential growth what is the expected population in an additional 5 years

cal Engineers A and B studied the effect of temperature and stirring rate on the yield of a certain product Both engineers ran the process 16 times and calculated the correlation coefficients among the three parameters temperature stirring rate and product yield Correlation coefficient Temperature and Temperature and Stirring rate and between Product yield Product yield Stirring rate 0 9064 Engineer A Engineer B 0 0000 0 7323 0 0009 0 7513 0 7707 A For the experiment of Engineer A do these data provide good evidence that increasing the temperature will increase the product yield Explain why or why not B For the experiment of Engineer A do these data provide good evidence that increasing the stirring rate will increase the product yield Explain why or why not C For the experiment of Engineer B do these data provide good evidence that the product yield is unaffected by temperature Explain why or why not D For the experiment of Engineer B do these data provide good evidence that increasing the stirring rate will increase the product yield Explain why or why not E Who Engineer A or Engineer B designed the experiment better Why

a Find an angle b Find an angle between 0 and 2 tha e exact values for your answers a 0 b radians

es empt in Progress ALU one of the largest groce Information in millions was

ork Question Part ght of 1400 pounds is suspended from two cables as is the tension in the two cables

Write the following complex number in rectangular form 6 cos 60 i sin 60 The rectangular form of 6 cos 60 i sin 60 is

7 Order the set of rational numbers from least to greatest 4 625 5 2 4 4 O 4 5 2 4 4 0 O 5 2 4 4 4 4 625 4 5 2 4 4 625 4 O O 8 11 8 4 625 11 4 625 4 4 5 2

how that the given functions are orthogonal on the indicated interval f x x f x x6 5 5 1 x x dx 1 x16 8 X 8 11 3 90625 dx dx give integrand in terms of x

1 lim sin 0 n What is the rate of convergence of this sequence

A ferris wheel is 45 meters in diameter and boa The six o clock position on the ferris wheel is le revolution in 4 minutes The function h f t g the wheel begins to turn What is the Amplitude What is the Midline y What is the Period Write an equation for h f t f t How high are you off of the ground after 2 min met me n

f t t t 21 t 1 can be used to model the measles pathogenesis curve in the figures below The peak infection time for this function was found to be tp 14 Use seven subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms of measles x infected cells mL days NO Number of infected cells per ml of blood plasma N 1500 1000 500

5 POINTS 20 USE THE NORMAL CURVE TABLE TO DETERMINE THE PER A BETWEEN z 1 34 AND z 2 24 B GREATER THAN z 1 90 C TO THE RIGHT OF 1 78 00 CURSTONERE HOW M

3 POINTS 22 EVALUATE THE F A 85 82 B nCo

2 POINTS 10 FIND THE INDICATED PROBA A IF P A OR B 0 6 P B

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The figure illustrates a normal distribution for the prices paid for a particular model of a new car The mean is 12 000 and the standard deviation is 500 Number of Car Buyers Use the 68 95 99 7 Rule to find the percentage of buyers who paid between 10 500 and 12 000 99 7 95 68 10 500 11 000 11 500 12 000 12 500 13 000 13 500 Price of a Model of a New Car What percentage of buyers paid between 10 500 and 12 000 Ne

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u x 32 Answer if x 2 Step 1 of 3 Identify the general shape and direction of the graph of this function on the interval o 2 f Keyboard

nework Find the standard deviation for t 12 13 14 15 16 The standard deviation is

Classify if possible each critical point of the given second order differential equation as a stable node a stable spiral point an unstable spiral point an unstable node or a saddle point Assume y 8 Order your answers from smallest to largest 8 then from smallest to largest y 8 cos 8 3 2 sin 8 181 8 y 0 y 0 y X Conclusion not possible to classify saddle point not possible to classify

Without solving explicitly classify the critical points of the given first order autonomous differential equation as either asymptotically stable or unstable All constants are assumed to be positive Enter the critical points for each stability category as a comma separated list If there are no critical points in a certain category enter NONE p 0 a bc dp dt P a bp 1 CP asymptotically stable P unstable P

7 Does the graph represent a function Explain your answer Explanation y H

y 4 Find the output y when the input x is 4 y 8 Vrite the function s formula 6 6 8 9 A I 5 Nala is escaping from the dragon s lair She is running toward the entrance of the at a speed of 9 2 meters per second The entrance is 180 meters away The distance d between Nala and the entrance of the lair is a function of t the time seconds since Nala began running